Daily Papers

We study the electromagnetic field equations on an arbitrary quantum curved background in the semiclassical approximation of Loop Quantum Gravity. The effective interaction hamiltonian for the Maxwell and gravitational fields is obtained and the corresponding field equations, which can be expressed as a modified wave equation for the Maxwell potential, are derived. We use these results to analyze electromagnetic wave propagation on a quantum Robertson-Walker space time and show that Lorentz Invariance is not preserved. The formalism developed can be applied to the case where back reaction effects on the metric due to the electromagnetic field are taken into account, leading to non covariant field equations.

The infinite tower of positive-helicity soft gravitons in any minimally coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was recently shown to generate a w_{1+infty} asymptotic symmetry algebra. It is natural to ask whether this classical algebra acquires quantum corrections at loop level. We explore this in quantum self-dual gravity, whose amplitudes acquire known one-loop exact all-plus helicity quantum corrections. We show using collinear splitting formulae that, remarkably, the w_{1+infty} algebra persists in quantum self-dual gravity without corrections.

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

In a novel application of the tools of topological data analysis (TDA) to nonperturbative quantum gravity, we introduce a new class of observables that allows us to assess whether quantum spacetime really resembles a ``quantum foam" near the Planck scale. The key idea is to investigate the Betti numbers of coarse-grained path integral histories, regularized in terms of dynamical triangulations, as a function of the coarse-graining scale. In two dimensions our analysis exhibits the well-known fractal structure of Euclidean quantum gravity.

The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be found by considering the classical counterparts of a quantum theory. For example, conservation laws in a quantum theory often stem from conservation laws of the corresponding classical theory. In order to construct such laws, this thesis is concerned with the interplay between symmetries and conservation laws of classical field theories and their application to asymptotically flat spacetimes. This work begins with an explanation of symmetries in field theories with a focus on variational symmetries and their associated conservation laws. Boundary conditions for general relativity are then formulated on three-dimensional asymptotically flat spacetimes at null infinity using the method of conformal completion. Conserved quantities related to asymptotic symmetry transformations are derived and their properties are studied. This is done in a manifestly coordinate independent manner. In a separate step a coordinate system is introduced, such that the results can be compared to existing literature. Next, asymptotically flat spacetimes which contain both future as well as past null infinity are considered. Asymptotic symmetries occurring at these disjoint regions of three-dimensional asymptotically flat spacetimes are linked and the corresponding conserved quantities are matched. Finally, it is shown how asymptotic symmetries lead to the notion of distinct Minkowski spaces that can be differentiated by conserved quantities.

Modifying the fundamental commutation relation of quantum mechanics to reflect the influence of gravity is an important approach to reconcile the contradiction between quantum field theory and general relativity. In the past two decades, researchers have conducted extensive research on geometric phase problems in non-commutative spaces, but few have mentioned the correction of geometric phase problems using the Generalized Uncertainty Principle (GUP). This paper is the first to study the phase correction of Aharonov-Bohm (AB) effect by GUP.

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

Is there more to Dirac's gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac's space-time algebra to Clifford algebra Cl(0,6). The resultant rich geometric structure can be leveraged to establish a combined framework of the standard model and gravity, wherein a gravi-weak interaction between the extended vierbein field and the extended weak gauge field is allowed. In conjunction with the composite Higgs model, we examine the vierbein field as a Cooper-pair-like fermion-antifermion condensation. Quantum gravity is realized indirectly via the quantized standard model spinor fields which underlie the composite space-time metric. We propose that the fundamental energy scales of the universe including the Planck scale are emergent and resulted from quantum condensations, thus possibly addressing the cosmological constant problem through an unconventional multi-scale renormalization procedure for multiplications of divergent Feynman integrals. The Clifford algebra approach also permits a weaker form of charge conjugation without particle-antiparticle interchange, leading to a Majorana-type mass that conserves lepton number. Additionally, with reshuffling the traditional quark-lepton pairing pattern of three generations of fermions, we explore a three-Higgs-doublet model with Higgs VEVs 246 GeV, 42 GeV and 2.5 GeV which could explain the mass hierarchies of fermions.

We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho{rmr}ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.

The Sachdev-Ye-Kitaev (SYK) model, known for its strong quantum correlations and chaotic behavior, serves as a key platform for quantum gravity studies. However, variationally preparing thermal states on near-term quantum processors for large systems (N>12, where N is the number of Majorana fermions) presents a significant challenge due to the rapid growth in the complexity of parameterized quantum circuits. This paper addresses this challenge by integrating reinforcement learning (RL) with convolutional neural networks, employing an iterative approach to optimize the quantum circuit and its parameters. The refinement process is guided by a composite reward signal derived from entropy and the expectation values of the SYK Hamiltonian. This approach reduces the number of CNOT gates by two orders of magnitude for systems Ngeq12 compared to traditional methods like first-order Trotterization. We demonstrate the effectiveness of the RL framework in both noiseless and noisy quantum hardware environments, maintaining high accuracy in thermal state preparation. This work advances a scalable, RL-based framework with applications for quantum gravity studies and out-of-time-ordered thermal correlators computation in quantum many-body systems on near-term quantum hardware. The code is available at https://github.com/Aqasch/solving_SYK_model_with_RL.

We study the dynamics of gravitons in a squeezed vacuum state in a thermal radiation background. Unlike traditional treatments that rely on the Boltzmann equation, we employ the Heisenberg equation and average it over general quantum states. In contrast to the usual Boltzmann-based descriptions, our approach captures the subtleties arising from quantum coherence in different number eigenstates, which is essential for soft graviton modes in the squeezed vacuum state. Our new method successfully reproduces the previous one-loop results within the in-in formalism when the expansion parameter is small and deviates significantly as the parameter increases, indicating that our results extend beyond the one-loop in-in formalism. We examine the implications of graviton emission effects stimulated by quantum coherence in both flat and expanding backgrounds. In the flat background, it is found that backreaction of radiation on the spacetime dynamics is crucial for significant stimulated emission. In the expanding background, to avoid the subtleties associated with superhorizon modes, we investigate the effect of emission within the horizon immediately after reheating and find a significant effect. We examined the IR graviton evolution from a symmetry perspective and propose a regularization prescription to eliminate the secular growth problem.

The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space the conformal dimension Delta (Q) of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q. This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups. Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in different dimensions. We analyze the convexity properties of the leading and next-to-leading order terms stemming from the semiclassical computation, de facto, extending previous tests beyond the leading perturbative contributions and to arbitrary charges. In particular, the leading contribution is sufficient to test convexity in the semiclassical computations. We also consider intriguing cases in which the models feature a transition from real to complex conformal dimensions either as a function of the charge or number of matter fields. As a relevant example of the first kind, we investigate the O(N) model in 4+epsilon dimensions. As an example of the second type we consider the U(N)times U(M) model in 4-epsilon dimensions. Both models display a rich dynamics where, by changing the number of matter fields and/or charge, one can achieve dramatically different physical regimes. We discover that whenever a complex conformal dimension appears, the real part satisfies the convexity property.

Adopting general frameworks for quantum-classical dynamics, we analyze the interaction between quantum matter and a classical gravitational field. We point out that, assuming conservation of momentum or energy, and assuming that the dynamics obeys Hamiltonian formalism or a particular decomposition property set out in the paper, the classical gravitational field cannot change the momentum or energy of the quantum system, whereas the quantum gravitational field can do so. Drawing upon the fundamental relationship between conservation laws and the quantum properties of objects, our analysis offers new perspectives for the study of quantum gravity and provides a novel interpretation of existing experimental observations, such as free fall.

Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short distances; interaction of photons with the graviton background leading to the important cosmological consequences; the time delay of photons due to interactions with gravitons; deceleration of massive bodies in the graviton background which may be connected with the Pioneer anomaly and with the problem of dark matter.

We propose a general correspondence between gravity and spin models, inspired by the well-known IR equivalence between lattice gauge theories and the spin models. This suggests a connection between continuous type Hawking-phase transitions in gravity and the continuous order-disorder transitions in ferromagnets. The black-hole phase corresponds to the ordered and the graviton gas corresponds to the disordered phases respectively. A simple set-up based on Einstein-dilaton gravity indicates that the vicinity of the phase transition is governed by a linear-dilaton CFT. Employing this CFT we calculate scaling of observables near T_c, and obtain mean-field scaling in a semi-classical approximation. In case of the XY model the Goldstone mode is identified with the zero mode of the NS-NS two-form. We show that the second speed of sound vanishes at the transition also with the mean field exponent.

Quantum microwave transmission is key to realizing modular superconducting quantum computers and distributed quantum networks. A large number of incoherent photons are thermally generated within the microwave frequency spectrum. The closeness of the transmitted quantum state to the source-generated quantum state at the input of the transmission link (measured by the transmission fidelity) degrades due to the presence of the incoherent photons. Hence, high-fidelity quantum microwave transmission has long been considered to be infeasible without refrigeration [3,4]. In this study, we propose a novel method for high-fidelity quantum microwave transmission using a room-temperature lossy waveguide. The proposed scheme consists of connecting two cryogenic nodes (i.e., a transmitter and a receiver) by the room-temperature lossy microwave waveguide. First, cryogenic preamplification is implemented prior to transmission. Second, at the receiver side, a cryogenic loop antenna is placed inside the output port of the waveguide and coupled to an LC harmonic oscillator located outside the waveguide. The loop antenna converts quantum microwave fields (which contain both signal and noise photons) to a quantum voltage across the coupled LC harmonic oscillator. The loop antenna detector at the receiver is designed to extensively suppress the induced photons across the LC oscillator. The signal transmittance is maintained intact by providing significant preamplification gain. Our calculations show that high-fidelity quantum transmission (i.e., more than 95%) is realized based on the proposed scheme for transmission distances reaching 100 m.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

Through use of the Pauli-Villars regulator procedure we construct a second- plus fourth-order-derivative theory of gravity that serves as an ultraviolet completion of standard second-order-derivative quantum Einstein gravity that is ghost-free, unitary and power counting renormalizable.

Calculating the action and the interaction Hamiltonian at higher orders in cosmological perturbation theory is a cumbersome task. We employ the formalism of EFT of inflation in models of single field ultra slow-roll inflation and obtain a non-perturbative result for the Hamiltonian in terms of the Goldstone field pi. To complete the dictionary, a non-linear relation between the curvature perturbations and pi is presented. Equipped with these non-linear results, we calculate the higher order loop corrections in USR models which are employed for PBHs formation. It is shown that the loop corrections on long CMB scales increase rapidly with the number of loop L and the setup will go out of perturbative control at the four-loop level.

Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and high-energy physics, along with potential applications in quantum information and science technologies. In light of the impressive ongoing efforts to achieve such realizations, a fundamental question regarding quantum link model regularizations of lattice gauge theories is how faithfully they capture the quantum field theory limit of gauge theories. Recent work [Zache, Van Damme, Halimeh, Hauke, and Banerjee, at https://journals.aps.org/prd/abstract/10.1103/PhysRevD.106.L091502 has shown through analytic derivations, exact diagonalization, and infinite matrix product state calculations that the low-energy physics of 1+1D U(1) quantum link models approaches the quantum field theory limit already at small link spin length S. Here, we show that the approach to this limit also lends itself to the far-from-equilibrium quench dynamics of lattice gauge theories, as demonstrated by our numerical simulations of the Loschmidt return rate and the chiral condensate in infinite matrix product states, which work directly in the thermodynamic limit. Similar to our findings in equilibrium that show a distinct behavior between half-integer and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between half-integer and integer spin quantum link models in the regime of strong electric-field coupling. Our results further affirm that state-of-the-art finite-size ultracold-atom and NISQ-device implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the far-from-equilibrium regime.

This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language model with a systematic Tree Search (TS) framework and automated numerical feedback, that successfully derived novel, exact analytical solutions for the power spectrum of gravitational radiation emitted by cosmic strings. Specifically, the agent evaluated the core integral I(N,α) for arbitrary loop geometries, directly improving upon recent AI-assisted attempts BCE+25 that only yielded partial asymptotic solutions. To substantiate our methodological claims regarding AI-accelerated discovery and to ensure transparency, we detail system prompts, search constraints, and intermittent feedback loops that guided the model. The agent identified a suite of 6 different analytical methods, the most elegant of which expands the kernel in Gegenbauer polynomials C_l^{(3/2)} to naturally absorb the integrand's singularities. The methods lead to an asymptotic result for I(N,α) at large N that both agrees with numerical results and also connects to the continuous Feynman parameterization of Quantum Field Theory. We detail both the algorithmic methodology that enabled this discovery and the resulting mathematical derivations.

Like general relativity, metric-affine gravity should be a viable effective quantum theory, otherwise it is a mathematical curiosity without physical application. Assuming a perturbative quantum field theory, the universal, flat limit of metric-affine gravity offers a good foundation for model-building only when symmetry constraints are themselves sufficient to get rid of ghosts and tachyons in the spectrum of propagating particle states, without requiring any further tuning of the couplings. Using this symmetry-first criterion, we find that for parity-preserving models with a totally symmetric distortion, only massless spin-one and spin-three modes are possible besides the graviton. Moreover, no viable models result from gauge symmetries generated by a scalar field.

In this Essay, we will look at the relation between the No Transmission principle and the Strong cosmic censorship (SCC), which we will highlight in the background of quantum gravity. We show that taking quantum gravity into account, one can provide a complete picture of the instability of the inner horizon and the principle that two independent CFTs, under the gauge-gravity duality, imply that the dual bulks must also be independent in that there must not exist a way to transmit a signal between the two spacetimes. We show that this can simply be interpreted as SCC, and that the inner horizon must be unstable (at either linear or nonlinear orders) to be in accordance with holographic quantum gravity.

The quantum geometric tensor (QGT) is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena. The traditional QGT, defined only for pure states, has limited applicability in realistic scenarios where mixed states are common. To address this limitation, we generalize the definition of the QGT to mixed states using the purification bundle and the covariant derivative. Notably, our proposed definition reduces to the traditional QGT when mixed states approach pure states. In our framework, the real and imaginary parts of this generalized QGT correspond to the Bures metric and the mean gauge curvature, respectively, endowing it with a broad range of potential applications. Additionally, using our proposed mixed-state QGT (MSQGT), we derive the geodesic equation applicable to mixed states. This work establishes a unified framework for the geometric analysis of both pure and mixed states, thereby deepening our understanding of the geometric properties of quantum states.

We derive bounds on the lifetime of an evaporating black hole. The bound follows from energy conservation and purification, within the framework of `asymptotically semiclassical spacetimes'. We use the recently derived expression for the Bondi flux of Hawking radiation, together with the expression for the entanglement entropy of Hawking radiation at null infinity, to investigate the purification phase after the last semiclassical ray. We discuss the energy-cost of entanglement purification and we find a lower bound on the purification time of the black hole, which scales as M_0^4/hbar^{3/2}, where M_0 is the initial black hole mass. Additionally, motivated by quantum gravity considerations, we include the additional assumption that a Planck mass black hole is metastable. With this assumption, we find that the the purification time is extended to be exponential in the square of the initial black hole mass, i.e. in its initial area. We find that the redshift exponent is negative in this purification phase, which indicates the existence of a white-hole remnant which releases information slowly. We comment on phenomenological implications for primordial black hole remnants.

We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or L_{infty} algebra. We extend this dictionary to theories defined on manifolds with a boundary, including the conformal boundary of AdS, taking into account the cyclic structure needed to define an action with the correct boundary terms. Projecting fields to their boundary values then defines a homotopy retract, which in turn implies that the cyclic L_{infty} algebra of the bulk theory is equivalent, up to homotopy, to a cyclic L_{infty} algebra on the boundary. The resulting action is the `on-shell action' conventionally computed via Witten diagrams that, according to AdS/CFT, yields the generating functional for the correlation functions of the dual CFT. These results are established with the help of new techniques regarding the homotopy transfer of cyclic L_{infty} algebras.

Between 1972 and 1975, Jacob Bekenstein proposed that black holes possess entropy proportional to their horizon area, and Stephen Hawking derived this relationship from semiclassical quantum field theory in curved spacetime, predicting thermal radiation from black holes. These developments established black hole thermodynamics as a formal framework connecting general relativity, quantum mechanics, and statistical physics. However, this synthesis rests on approximations whose validity remains unproven in regimes where quantum gravitational effects become important. This article provides a detailed overview of the historical development from 1972 to 1975 and surveys modern proposals, such as the holographic principle and gravitational path integrals. We highlight persistent theoretical challenges, including the information paradox, the trans-Planckian problem, backreaction effects, and the absence of experimental verification. The work concludes by identifying which aspects of black hole thermodynamics are well-established and which remain speculative or fundamentally incomplete.

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr\"{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variational principle, our approach utilizes the implicit mid-point method and generates the solution for all spatial and temporal values simultaneously after optimization. We demonstrate the method in the Schr\"{o}dinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.

The paper studies the quantum action for the five-dimensional real φ^3-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed.

We demonstrate that the unitarity of quantum field theory, through the positivity of spectral functions, underlies thermodynamic irreversibility for a subsystem separated by a horizon, in direct analogy with the irreversibility of renormalization-group flows. To this end, we explicitly find the shear and bulk viscosities -- the entanglement viscosities -- for thermal radiation in Rindler space using the universal spectral representation. A direct consequence of the obtained general formulas is the relationship between the acceleration-induced shear viscosity in flat space and the conformal quantum anomaly in curved space, pointing to a possible novel probe of the conformal anomaly in systems with extreme acceleration. Moreover, for conformal field theories, we explicitly show that globally entanglement viscosity saturates the Kovtun-Son-Starinets bound.

We show in this paper that a strong and easy connection exists between quantum error correction and Lattice Gauge Theories (LGT) by using the Gauge symmetry to construct an efficient error-correcting code for Abelian LGTs. We identify the logical operations on this gauge covariant code and show that the corresponding Hamiltonian can be expressed in terms of these logical operations while preserving the locality of the interactions. Furthermore, we demonstrate that these substitutions actually give a new way of writing the LGT as an equivalent hardcore boson model. Finally we demonstrate a method to perform fault-tolerant time evolution of the Hamiltonian within the gauge covariant code using both product formulas and qubitization approaches. This opens up the possibility of inexpensive end to end dynamical simulations that save physical qubits by blurring the lines between simulation algorithms and quantum error correcting codes.

We report the experimental observation of holographically motivated quantum teleportation on a quantum processor, driven by the highly entangled, chaotic dynamics of a many-body system. Specifically, we implement the traversable-wormhole (TW) protocol utilizing a chaotic binary sparse N = 8 Sachdev--Ye--Kitaev (SYK) model. This optimized approach dramatically reduces circuit depth for noisy intermediate-scale quantum (NISQ) hardware while rigorously preserving the spectral chaos required for gravitational duality. Diagnosing the teleportation signal via mutual information, we find that while inherent noise in NISQ hardware precludes perfect quantitative agreement with exact numerical simulations, our experimental results clearly demonstrate the essential qualitative signature: a sign-dependent asymmetry. This work establishes a practical, scalable framework for holographic quantum simulations, offering a novel empirical testbed for exploring holographic quantum gravity.

Despite the growing application of Large Language Models (LLMs) to theoretical physics, there is little academic exploration into how domain-specific physics reasoning ability develops while training these models. To investigate this, we perform the first academic fine-tuning study of small (7B-parameter) reasoning models dedicated specifically to theoretical physics. Because open-source verifiable training data required to train such capabilities is scarce, we developed a robust data generation pipeline that can both create synthetic problems and make existing human-authored problems suitable for model training. Selecting Quantum Field Theory (QFT) as our primary domain, we generated over 2,500 synthetic problems alongside a curated collection of human-adapted problems sourced from arXiv and standard pedagogical resources. We conduct both Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT) experiments, benchmarking performance gains as well as generalization to other physics domains. We perform an extensive analysis of model chains-of-though before and after fine-tuning, to understand how reasoning errors evolve during RL and SFT. Finally, we publicly release our data pipeline, verifiable QFT training data, and sim200M tokens of QFT reasoning traces.

We introduce and analyze a novel quantum machine learning model motivated by convolutional neural networks. Our quantum convolutional neural network (QCNN) makes use of only O(log(N)) variational parameters for input sizes of N qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices. The QCNN architecture combines the multi-scale entanglement renormalization ansatz and quantum error correction. We explicitly illustrate its potential with two examples. First, QCNN is used to accurately recognize quantum states associated with 1D symmetry-protected topological phases. We numerically demonstrate that a QCNN trained on a small set of exactly solvable points can reproduce the phase diagram over the entire parameter regime and also provide an exact, analytical QCNN solution. As a second application, we utilize QCNNs to devise a quantum error correction scheme optimized for a given error model. We provide a generic framework to simultaneously optimize both encoding and decoding procedures and find that the resultant scheme significantly outperforms known quantum codes of comparable complexity. Finally, potential experimental realization and generalizations of QCNNs are discussed.

Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its role in the dynamics of systems and hinders any formulation to merge quantum mechanics with general relativity, specifically when considering quantum gravity. To overcome those limitations, several authors tried to construct an operator which is conjugate to the Hamiltonian of quantum systems implementing some essential features of the relativistic time. These formulations use the concept of internal or intrinsic time instead of the universal coordinate time used in textbooks. Furthermore, recently it is remarked that the consideration of time with relativistic features could enhance the analysis techniques in quantum information processing and have an impact on its status in causal orders and causal structures of quantum information. The role of clocks, their accuracy and stability has become an important issue in quantum information processing. This article present a substantiative review of recent works which reflect the possibility of utilizing quantum time, measured by quantum clock devised according to Page-Wootters scheme, to stand as a resource for quantum information processing.

Feynman famously asserted that interference is the only real mystery in quantum mechanics (QM). It is concluded that the reason for this mystery, and thereby the related mysteries of complementarity, non-commutativity of observables, the uncertainty principle and violation of Bell's equality, is that the axioms of QM depend vitally on the continuum nature of Hilbert Space, deemed unphysical. We develop a theory of quantum physics - Rational Quantum Mechanics (RaQM) - in which Hilbert Space is gravitationally discretised. The key to solving the mysteries of QM in RaQM is a number-theoretic property of the cosine function, concealed in QM when angles range over the continuum. This number-theoretic property describes mathematically the utter indivisibility of the quantum world and implies that the laws of physics are profoundly holistic. We contrast holism with nonlocality. In theories which embrace the continuum, the violation of Bell's inequality requires the laws of physics to be either nonlocal or not realistic; both incomprehensible concepts. By contrast, holism, as embodied in Mach's Principle or in the fractal geometry of a chaotic attractor, is neither incomprehensible nor unphysical. As part of this, we solve the deepest mystery of all; why nature makes use of complex numbers.

A fundamental problem in quantum many-body physics is that of finding ground states of local Hamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithms for learning ground states. Specifically, [Huang et al. Science 2022], introduced an approach for learning properties of the ground state of an n-qubit gapped local Hamiltonian H from only n^{O(1)} data points sampled from Hamiltonians in the same phase of matter. This was subsequently improved by [Lewis et al. Nature Communications 2024], to O(log n) samples when the geometry of the n-qubit system is known. In this work, we introduce two approaches that achieve a constant sample complexity, independent of system size n, for learning ground state properties. Our first algorithm consists of a simple modification of the ML model used by Lewis et al. and applies to a property of interest known beforehand. Our second algorithm, which applies even if a description of the property is not known, is a deep neural network model. While empirical results showing the performance of neural networks have been demonstrated, to our knowledge, this is the first rigorous sample complexity bound on a neural network model for predicting ground state properties. We also perform numerical experiments that confirm the improved scaling of our approach compared to earlier results.

Based on negative entropy in entanglement, it is shown that a single-system Copenhagen measurement protocol is equivalent to the two-system von Neumann scheme with the memory filling up the system with negative information similar to the Dirac sea of negative energy. After equating the two quantum measurement protocols, we then apply this equivalence to the black hole radiation. That is, the black hole evaporation corresponds to the quantum measurement process and the two evaporation approaches, the observable-based single-system and the two-system entanglement-based protocols, can be made equivalent using quantum memory. In particular, the measurement choice, \theta, with the memory state inside the horizon in the entanglement-based scheme is shown to correspond to the observable of the measurement choice, \theta, outside the horizon in the single-system protocol, that is, O_{\theta}^{out} = Q_{\theta}^{in}. This indicates that the black hole as quantum memory is filling up with negative information outside the horizon, and its entropy corresponds to the logarithm of a number of equally probable measurement choices. This shows that the black hole radiation is no different than ordinary quantum theory.

We explore the consequences of multi-trace deformations in applications of gauge-gravity duality to condensed matter physics. We find that they introduce a powerful new "knob" that can implement spontaneous symmetry breaking, and can be used to construct a new type of holographic superconductor. This knob can be tuned to drive the critical temperature to zero, leading to a new quantum critical point. We calculate nontrivial critical exponents, and show that fluctuations of the order parameter are `locally' quantum critical in the disordered phase. Most notably the dynamical critical exponent is determined by the dimension of an operator at the critical point. We argue that the results are robust against quantum corrections and discuss various generalizations.

We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap programme. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tri-critical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global so(2,2) part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the non-perturbative structure of arbitrary (unitary or non-unitary) CFTs.

In an earlier paper [arXiv:2511.03669] we extracted the OPE of celestial CFT operator duals of positive helicity graviton and scalar particles from the Mellin transformed relevant MHV amplitudes of conformal gravity, realised as the bosonic subsector of the Berkovits-Witten theory. A soft theorem analysis of bulk MHV amplitudes established that this conformal gravity exhibits a chiral bms_4 symmetry on the celestial sphere with the associated sl(2,R) current algebra, which acquires a non-trivial central extension, unlike the Einstein gravity. Here we construct a 2d chiral CFT free-field realisation of the relevant chiral bms_4 algebra in terms of three free scalars (ϕ_i) and three (β_i,γ_i) ghost pairs, and propose vertex operators for the positive-helicity graviton primary G^{++}_Δ(z,z) as well as the scalar primary Φ_Δ(z,z), and compute their OPEs. These OPEs reproduce exactly those obtained from the bulk conformal gravity MHV amplitudes, providing a concrete celestial dual description of its MHV sector.

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semi-circle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the DC ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero DC conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semi-circle transitions between them. The model can be regarded as a strongly coupled analog of the old `composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model.

This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. The lectures may be viewed online at https://goo.gl/3DJdOr. Please send typos or corrections to strominger@physics.harvard.edu.

We present an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer, namely computing the value of the Jones polynomial at the fifth root of unity within additive error for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we implement and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The practical tools provided in this work allow for precise resource estimation to identify near-term quantum advantage for a meaningful quantum-native problem in knot theory.

We propose a 1+1 dimensional CFT dual structure for quantum gravity and matter on the extended 2+1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS_3. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincare patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.

These lectures give an introduction to the theory of holographic superconductors. These are superconductors that have a dual gravitational description using gauge/gravity duality. After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields. Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors. Some familiarity with gauge/gravity duality is assumed. A list of open problems is included at the end.

We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by sequences of elementary braids of quasiparticles with exotic fractional statistics in certain two-dimensional topological condensed matter systems, described by effective topological quantum field theories. We specifically focus on a non-semisimple version of topological field theory, which provides a foundation for an extended theory of Ising anyons and which has recently been shown by Iulianelli et al., Nature Communications {\bf 16}, 6408 (2025), to permit universal quantum computation. While the proofs of this pioneering result are existential in nature, the mixed integer programming provides an approach to explicitly construct quantum gates in topological systems. We demonstrate this by focusing specifically on the entangling controlled-NOT operation, and its local equivalence class, using braiding operations in the non-semisimple Ising system. This illustrates the utility of the Mixed-Integer Quadratically Constrained Quadratic Programming for topological quantum compilation.

The rapid data surge from the high-luminosity Large Hadron Collider introduces critical computational challenges requiring novel approaches for efficient data processing in particle physics. Quantum machine learning, with its capability to leverage the extensive Hilbert space of quantum hardware, offers a promising solution. However, current quantum graph neural networks (GNNs) lack robustness to noise and are often constrained by fixed symmetry groups, limiting adaptability in complex particle interaction modeling. This paper demonstrates that replacing the Lorentz Group Equivariant Block modules in LorentzNet with a dressed quantum circuit significantly enhances performance despite using nearly 5.5 times fewer parameters. Additionally, quantum circuits effectively replace MLPs by inherently preserving symmetries, with Lorentz symmetry integration ensuring robust handling of relativistic invariance. Our Lorentz-Equivariant Quantum Graph Neural Network (Lorentz-EQGNN) achieved 74.00% test accuracy and an AUC of 87.38% on the Quark-Gluon jet tagging dataset, outperforming the classical and quantum GNNs with a reduced architecture using only 4 qubits. On the Electron-Photon dataset, Lorentz-EQGNN reached 67.00% test accuracy and an AUC of 68.20%, demonstrating competitive results with just 800 training samples. Evaluation of our model on generic MNIST and FashionMNIST datasets confirmed Lorentz-EQGNN's efficiency, achieving 88.10% and 74.80% test accuracy, respectively. Ablation studies validated the impact of quantum components on performance, with notable improvements in background rejection rates over classical counterparts. These results highlight Lorentz-EQGNN's potential for immediate applications in noise-resilient jet tagging, event classification, and broader data-scarce HEP tasks.

Motivated by recent analogies between the large-q cSYK model and charged black holes, we aim to find a concrete gravitation theory with a matching partition function. Our main focus is to match the thermodynamics of the (0+1)-dimensional cSYK model, with that of a (1+1)-dimensional gravitational model. We focus on a model of deformed JT gravity, characterized by some unknown dilaton potential function and unknown dilaton-to-Maxwell field coupling. By finding the general solutions, we are able to find the Lagrangian which produces the same partition function and equation of state as that of the considered SYK model. We go beyond showing that the thermodynamics overlaps, by also showing that the Lyapunov exponents, characterizing the degree of chaos, overlap close to the second order phase transition. In the low temperature rescaled regime, there remains open questions about the Lyapunov exponents, given that our analysis ignores the black hole back action which can be large in this regime.

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in g phi^3 QFT, by using the retarded/advanced (R/A) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We "repair" them, while keeping d<4, to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Sigma_{F}(p_0) does not vanish when |p_0|rightarrowinfty and cannot be split to retarded and advanced parts. In the Glaser--Epstein approach, the causality is repaired in the composite object G_F(p_0)Sigma_{F}(p_0). In the FTP approach, after repairing the vertices, the corresponding composite objects are G_R(p_0)Sigma_{R}(p_0) and Sigma_{A}(p_0)G_A(p_0). In the limit drightarrow 4, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition langle 0|phi|0rangle =0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit trightarrow infty .

We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS_4 with its spatially compact boundary S^2. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with m^2 = -2. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of {\it incomplete} C-theorem and an {\it incomplete} attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant (Lambda) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.

We use the extrapolate dictionary to revisit the spectrum of operators in Celestial CFT. Under the Celestial CFT map, each state in the 4D Hilbert space should map to one in the 2D Hilbert space. This implies that, beyond the familiar single particle states/operators, there should be multiparticle operators appearing in the celestial OPE. We extend the existing flat-space dictionary by constructing composite primaries from both Carrollian and Celestial perspectives. In the process, we demonstrate some subtleties in deriving the Poincaré primary condition from the Carrollian limit, clarify the compatibility of principal series representations with highest weight representations and unitarity in Celestial CFT, and discuss how the celestial OPE block expansion emerges from a 2D CFT standpoint.

The ground state search problem is central to quantum computing, with applications spanning quantum chemistry, condensed matter physics, and optimization. The Variational Quantum Eigensolver (VQE) has shown promise for small systems but faces significant limitations. These include barren plateaus, restricted ansatz expressivity, and reliance on domain-specific structure. We present SpinGQE, an extension of the Generative Quantum Eigensolver (GQE) framework to spin Hamiltonians. Our approach reframes circuit design as a generative modeling task. We employ a transformer-based decoder to learn distributions over quantum circuits that produce low-energy states. Training is guided by a weighted mean-squared error loss between model logits and circuit energies evaluated at each gate subsequence. We validate our method on the four-qubit Heisenberg model, demonstrating successfulconvergencetonear-groundstates. Throughsystematichyperparameterexploration, we identify optimal configurations: smaller model architectures (12 layers, 8 attention heads), longer sequence lengths (12 gates), and carefully chosen operator pools yield the most reliable convergence. Our results show that generative approaches can effectively navigate complex energy landscapes without relying on problem-specific symmetries or structure. This provides a scalable alternative to traditional variational methods for general quantum systems. An open-source implementation is available at https://github.com/Mindbeam-AI/SpinGQE.

We study quantum corrections in the gravitational path integral around nearly 1/16-BPS black holes in asymptotically AdS_5 times S^5 space, dual to heavy states in 4D N=4 super Yang-Mills. The analysis provides a gravitational explanation of why 1/16-BPS black holes exhibit an exact degeneracy at large N and why all such states have the same charges, confirming the belief that the superconformal index precisely counts the entropy of extremal black holes. We show the presence of a gap of order N^{-2} between the 1/16-BPS black holes and the lightest near-BPS black holes within the same charge sector. This is the first example of such a gap for black holes states within the context of AdS_5 holography. We also derive the spectrum of near-BPS states that lie above this gap. Our computation relies on finding the correct version of the N=2 super-Schwarzian theory which captures the breaking of the SU(1, 1|1) symmetry when the black hole has finite temperature and non-zero chemical potential. Finally, we comment on possible stringy and non-perturbative corrections that can affect the black hole spectrum.

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in d+1 dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a Z_2 spin liquid has been hypothesized recently.

Modern science emerged from reasoning over repeatedly-observed planetary motions. We present Gravity-Bench-v1, an environment-based benchmark that challenges AI agents on tasks that parallel this historical development. Gravity-Bench-v1 evaluates agents on the discovery of physics concealed within a dynamic environment, using rigorous gravitational dynamics simulations. Gravity-Bench includes out-of-distribution cases, i.e. with physics that deviates from the real world, to evaluate true scientific generalization capabilities. Agents must plan to collect data within an experimental budget and must perform a dynamic form of data analysis and reasoning to solve tasks efficiently. Our benchmark admits an open-ended space of solutions. PhD-level solutions for each task are provided, to calibrate AI performance against human expertise. Technically at an upper-undergraduate level, our benchmark proves challenging to baseline AI agents. Gravity-Bench-v1 and planned extensions should help map out AI progress towards scientific discovery capabilities.

Recently, Fernandes discovered an analytic solution for rotating black holes in semiclassical gravity induced by the trace anomaly. These solutions exhibit some distinctive characteristics, including a non-spherically symmetric event horizon and violations of the Kerr bound. As a crucial assumption to uphold causality in spacetime, we investigate the validity of the weak cosmic censorship conjecture (WCCC) within this class of solutions with type-A trace anomaly by introducing a test particle on the equatorial plane. Our study reveals three distinct mechanisms that can potentially destroy the event horizon, leading to a violation of the WCCC. Our findings indicate that, with the exception of extremal Kerr, static extremal, and static singular black holes, the WCCC may be violated under the first-order perturbation of the test particle. These results suggest the need for further exploration of modifications to the behavior of the test particle under quantum effects in order to address the violation of the WCCC in this system.

We study a variant of the equidistribution of mass conjecture on the sphere posed by Böcherer, Sarnak, and Schulze-Pillot: quantum unique ergodicity in shrinking sets. Conditionally on the generalized Lindelöf hypothesis, we show that quantum unique ergodicity holds on every shrinking spherical cap whose radius is considerably larger than the Planck scale, and that it holds on almost every shrinking spherical cap whose radius is larger than the Planck scale. Additionally, conditionally on GLH, we provide explicit upper bounds for the 1-Wasserstein distance and the spherical cap discrepancy between the involved measures.

In this paper we deploy for the first time Reinforcement-Learning algorithms in the context of the conformal-bootstrap programme to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft Actor-Critic algorithm and find approximate solutions to the truncated crossing equations of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compactified scalar. Our methods can perform efficient high-dimensional searches that can be used to study arbitrary (unitary or non-unitary) CFTs in any spacetime dimension.

I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented by a one-parameter family of operators, evolving on its own time scale. I formalize stratified state spaces capturing multiple levels of synchronized behavior, define an asynchronous evolution metric that quantifies phase-offset distances between subsystems, and characterize emergent coherent topologies arising when subsystems synchronize. Within this framework, I develop formal operators for the evolution of each subsystem and give precise conditions under which phase-aligned synchronization occurs across the lattice. The main results include: (1) the existence and uniqueness of coherent (synchronized) states under a contractive coupling condition, (2) stability of these coherent states and criteria for their emergence as a collective phase transition in a continuous operator topology, and (3) the influence of symmetries, with group-invariant coupling leading to flow-invariant synchrony subspaces and structured cluster dynamics. Proofs are given for each theorem, demonstrating full mathematical rigor. In a final section, I discuss hypothetical applications of this framework to symbolic lattice systems (e.g. subshifts), to invariant group actions on dynamical lattices, and to operator fields over stratified manifolds in the spirit of noncommutative geometry. Throughout, I write in the first person to emphasize the exploratory nature of this work. The paper avoids any reference to cosmology or observers, focusing instead on clean, formal mathematics suitable for a broad array of dynamical systems.

We elaborate on the role of extremal surfaces probing the internal space in AdS/CFT. Extremal surfaces in AdS quantify the "geometric" entanglement between different regions in physical space for the dual CFT. This, however, is just one of many ways to split a given system into subsectors, and extremal surfaces in the internal space should similarly quantify entanglement between subsectors of the theory. For the case of AdS_5timesS^5, their area was interpreted as entanglement entropy between U(n) and U(m) subsectors of U(n+m) N=4 SYM. Making this proposal precise is subtle for a number of reasons, the most obvious being that from the bulk one usually has access to gauge-invariant quantities only, while a split into subgroups is inherently gauge variant. We study N=4 SYM on the Coulomb branch, where some of the issues can be mitigated and the proposal can be sharpened. Continuing back to the original AdS_5timesS^5 geometry, we obtain a modified proposal, based on the relation of the internal space to the R-symmetry group.

Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. In geometric quantum machine learning, one achieves this by encoding group structure into parameterised quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans\"atze -- circuits possessing spin rotation symmetry. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalised permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and on the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.

We consider holography for d-dimensional scale invariant but non-Lorentz invariant field theories, which do not admit the full Schrodinger symmetry group. We find new realizations of the corresponding (d+1)-dimensional gravity duals, engineered with a variety of matter Lagrangians, and their finite temperature generalizations. The thermodynamic properties of the finite temperature backgrounds are precisely those expected for anisotropic, scale invariant field theories. The brane and string theory realizations of such backgrounds are briefly discussed, along with their holographic interpretation in terms of marginal but non Lorentz invariant deformations of conformal field theories. We initiate discussion of holographic renormalization in these backgrounds, and note that such systematic renormalization is necessary to obtain the correct behavior of correlation functions.

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on Nv , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64*64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers.

We develop a differential-geometric framework for variational quantum circuits in which noisy single- and multi-qubit parameter spaces are modeled by weighted projective lines (WPLs). Starting from the pure-state Bloch sphere CP1, we show that realistic hardware noise induces anisotropic contractions of the Bloch ball that can be represented by a pair of physically interpretable parameters (lambda_perp, lambda_parallel). These parameters determine a unique WPL metric g_WPL(a_over_b, b) whose scalar curvature is R = 2 / b^2, yielding a compact and channel-resolved geometric surrogate for the intrinsic information structure of noisy quantum circuits. We develop a tomography-to-geometry pipeline that extracts (lambda_perp, lambda_parallel) from hardware data and maps them to the WPL parameters (a_over_b, b, R). Experiments on IBM Quantum backends show that the resulting WPL geometries accurately capture anisotropic curvature deformation across calibration periods. Finally, we demonstrate that WPL-informed quantum natural gradients (WPL-QNG) provide stable optimization dynamics for noisy variational quantum eigensolvers and enable curvature-aware mitigation of barren plateaus.

We investigate the anomaly-induced activation of a gauge-invariant scalar degree of freedom in General Relativity, the conformalon mode, directly at the level of \(2\to2\) scattering amplitudes. The analysis couples anomalous three-point functions of conformal sectors, involving gravitons \((TTT)\) and Abelian gauge currents \((TJJ)\), through single-graviton exchange derived from the quadratic expansion of the Einstein--Hilbert action. Unlike related treatments based on the nonlocal anomaly action, these interactions are suppressed by the Planck scale. We show that the conformalon, invariant under linearized diffeomorphisms, admits an interpretation as an effective scalar correction to scattering amplitudes, both in virtual exchange channels and in effective real-emission processes. Around flat space, this behaviour arises from anomaly-induced nonlocal massless insertions on the external graviton and photon legs of the three-point functions, sewn through the scalar component of the graviton propagator in de Donder gauge. The resulting anomaly-mediated \(4\)-point interaction reduces to contact terms, with the Planck mass setting the suppression scale. The construction consistently matches the spin decomposition of flat-space conformal Ward identities in momentum space, which determine the vertices, with the corresponding spin decomposition of the graviton propagator. In the eikonal limit, these interactions generate contact corrections to the leading logarithmic phase in impact-parameter space. We further show that anomaly-mediated \(2\to2\) graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

We study a kinematical consequence of the Hopf-algebraic momentum composition law in κ-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues P_μ are nonlinearly related to the ordered-plane-wave labels p_μ. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity P_+equiv P_0+P_4=κe^{p_0/κ} enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent κ-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by P_μ can be expanded into distinct auxiliary branches. If P_μ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables p_μ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

Quantum Zeno Effect (QZE) has been one of the most interesting phenomena in quantum mechanics ever since its discovery in 1977 by Misra and Sudarshan [J. Math. Phys. 18, 756 (1977)]. There have been many attempts for experimental realization of the same. Here, we present the first ever simulation of QZE on IBM quantum experience platform. We simulate a two-level system for Rabi-driven oscillation and then disturb the time evolution by intermediate repetitive measurements using quantum gates to increase the survival probability of the qubit in the initial state. The circuits are designed along with the added intermediate measurements and executed on IBM quantum simulator, and the outcomes are shown to be consistent with the predictions. The increasing survival probability with the number of intermediate measurements demonstrates QZE. Furthermore, some alternative explanations for the obtained results are provided which leads to some ambiguity in giving the exact reasoning for the observed outcomes.

We investigate the exceptional points (EPs) and their pseudospectra in black hole perturbation theory. By considering a Gaussian bump modification to the Regge-Wheeler potential with variable amplitude, position, and width parameters, (varepsilon,d,σ_0), a continuous line of EPs (exceptional line, EL) in this three-dimensional parameter space is revealed. We find that the vorticity ν=pm1/2 and the Berry phase γ=π for loops encircling the EL, while ν=0 and γ=0 for those do not encircle the EL. Through matrix perturbation theory, we prove that the ε-pseudospectrum contour size scales as ε^{1/q} at an EP, where q is the order of the largest Jordan block of the Hamiltonian-like operator, contrasting with the linear ε scaling at non-EPs. Numerical implements confirm this observation, demonstrating enhanced spectral instability at EPs for non-Hermitian systems including black holes.

The discovery of causal relations from observed data has attracted significant interest from disciplines such as economics, social sciences, and biology. In practical applications, considerable knowledge of the underlying systems is often unavailable, and real data are usually associated with nonlinear causal structures, which makes the direct use of most conventional causality analysis methods difficult. This study proposes a novel quantum Peter-Clark (qPC) algorithm for causal discovery that does not require any assumptions about the underlying model structures. Based on conditional independence tests in a class of reproducing kernel Hilbert spaces characterized by quantum circuits, the proposed algorithm can explore causal relations from the observed data drawn from arbitrary distributions. We conducted systematic experiments on fundamental graphs of causal structures, demonstrating that the qPC algorithm exhibits better performance, particularly with smaller sample sizes compared to its classical counterpart. Furthermore, we proposed a novel optimization approach based on Kernel Target Alignment (KTA) for determining hyperparameters of quantum kernels. This method effectively reduced the risk of false positives in causal discovery, enabling more reliable inference. Our theoretical and experimental results demonstrate that the quantum algorithm can empower classical algorithms for accurate inference in causal discovery, supporting them in regimes where classical algorithms typically fail. In addition, the effectiveness of this method was validated using the datasets on Boston housing prices, heart disease, and biological signaling systems as real-world applications. These findings highlight the potential of quantum-based causal discovery methods in addressing practical challenges, particularly in small-sample scenarios, where traditional approaches have shown significant limitations.

Leggett and Garg derived inequalities that probe the boundaries of classical and quantum physics by putting limits on the properties that classical objects can have. Historically, it has been suggested that Leggett-Garg inequalities are easily violated by quantum systems undergoing sequences of strong measurements, casting doubt on whether quantum mechanics correctly describes macroscopic objects. Here I show that Leggett-Garg inequalities cannot be violated by any projective measurement. The perceived violation of the inequalities found previously can be traced back to an inappropriate assumption of non-invasive measurability. Surprisingly, weak projective measurements cannot violate the Leggett-Garg inequalities either because even though the quantum system itself is not fully projected via weak measurements, the measurement devices are.

This study examines the performance of finite spin quantum batteries (QBs) using Heisenberg spin models with Dzyaloshinsky-Moriya (DM) and Kaplan--Shekhtman--Entin-Wohlman--Aharony (KSEA) interactions. The QBs are modeled as interacting quantum spins in local inhomogeneous magnetic fields, inducing variable Zeeman splitting. We derive analytical expressions for the maximal extractable work, ergotropy and the capacity of QBs, as recently examined by Yang et al. [Phys. Rev. Lett. 131, 030402 (2023)]. These quantities are analytically linked through certain quantum correlations, as posited in the aforementioned study. Different Heisenberg spin chain models exhibit distinct behaviors under varying conditions, emphasizing the importance of model selection for optimizing QB performance. In antiferromagnetic (AFM) systems, maximum ergotropy occurs with a Zeeman splitting field applied to either spin, while ferromagnetic (FM) systems benefit from a uniform Zeeman field. Temperature significantly impacts QB performance, with ergotropy in the AFM case being generally more robust against temperature increases compared to the FM case. Incorporating DM and KSEA couplings can significantly enhance the capacity and ergotropy extraction of QBs. However, there exists a threshold beyond which additional increases in these interactions cause a sharp decline in capacity and ergotropy. This behavior is influenced by temperature and quantum coherence, which signal the occurrence of a sudden phase transition. The resource theory of quantum coherence proposed by Baumgratz et al. [Phys. Rev. Lett. 113, 140401 (2014)] plays a crucial role in enhancing ergotropy and capacity. However, ergotropy is limited by both the system's capacity and the amount of coherence. These findings support the theoretical framework of spin-based QBs and may benefit future research on quantum energy storage devices.

In a graph convolutional network, we assume that the graph G is generated wrt some observation noise. During learning, we make small random perturbations ΔG of the graph and try to improve generalization. Based on quantum information geometry, ΔG can be characterized by the eigendecomposition of the graph Laplacian matrix. We try to minimize the loss wrt the perturbed G+Δ{G} while making Δ{G} to be effective in terms of the Fisher information of the neural network. Our proposed model can consistently improve graph convolutional networks on semi-supervised node classification tasks with reasonable computational overhead. We present three different geometries on the manifold of graphs: the intrinsic geometry measures the information theoretic dynamics of a graph; the extrinsic geometry characterizes how such dynamics can affect externally a graph neural network; the embedding geometry is for measuring node embeddings. These new analytical tools are useful in developing a good understanding of graph neural networks and fostering new techniques.

Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems. The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities. The third lecture presents transport coefficients derived from AdS/CFT that should be applicable in the quantum critical region associated to a quantum phase transition. The fourth lecture builds in the physics of a superconducting or superfluid phase transition to the simple holographic model of the third lecture.

Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood as key operational resources for quantum computation, communication, and simulation. Although traditionally investigated in distinct settings, recent theoretical and experimental advances have revealed deep conceptual, mathematical, and operational connections between them. This review presents a unified perspective on these developments based on sheaf-theoretic and graph-theoretic frameworks, which provide theory-independent characterizations of statistical correlations. These approaches clarify the structural relationship between contextuality and nonlocality, facilitate the formulation of experimentally testable inequalities, and guide implementations in realistic physical platforms, with particular emphasis on photonic systems. By bridging abstract theoretical structures and concrete experimental realizations, this review sheds light on the nonclassical foundations of quantum correlations and their emerging role in quantum technologies.

In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon [arXiv:1711.07945]. Equations are presented using a diagrammatic calculus for tensor categories. To this quantum question and answer setting, we extend the standard definitions, including strategies, correlations, and synchronicity, and we use these definitions to extend results about synchronicity. We extend the graph homomorphism (isomorphism) game to quantum graphs, and show it is synchronous (bisynchronous) and connect its perfect (bi)strategies to quantum graph homomorphisms (isomorphisms). Our extended definitions agree with the existing quantum games literature, except in the case of synchronicity.

The James Webb Space Telescope's (JWST) discovery of an unexpectedly high abundance of UV-bright galaxies at redshifts z > 10 poses a significant challenge to the standard LambdaCDM cosmology. This work tests whether this tension can be resolved solely by modifying the cosmological background, without invoking significant evolution in the astrophysical properties of early galaxies. We investigate an alternative framework featuring the presence of an anti-de Sitter vacuum in the dark energy sector, a model that naturally arises in quantum gravity models like string theory and can enhance early structure formation. Using a self-consistent semi-analytical model that couples galaxy evolution with reionization, we confront this scenario with a wide range of observations. We first show that while a model tailored to fit the high-z UV luminosity functions (UVLFs) shows promise, it is in strong tension with well-established cosmological constraints from the CMB and other low-redshift probes. Conversely, models within this framework that are consistent with these constraints provide only a modest boost to structure formation and fail to reproduce the observed JWST galaxy abundances at z > 10. While these models remain consistent with the cosmic reionization history, our primary result is that this class of cosmological modifications is insufficient on its own to explain the galaxy excess. Our study underscores the critical importance of holistic testing for any beyond-LambdaCDM proposal; apparent success in one observational regime does not guarantee overall viability. By demonstrating the limitations of a purely cosmological solution, our results strengthen the case that evolving astrophysical properties are a necessary ingredient for solving the challenge of early galaxy formation.

A universal class of light-ray operators formed from null integrals of the stress tensor is constructed in generic interacting Lorentzian conformal field theories in four spacetime dimensions. This class of light-ray operators generates the wedge algebra of {rm w}_{1+infty}, which was recently identified among the asymptotic symmetries of asymptotically flat spacetimes. In four-dimensional conformal field theories with an additional spin-one conserved current, a second universal class of light-ray operators is constructed and shown to generate the ''S algebra,'' the gauge-theoretic analog of {rm w}_{1+infty}. Finally, a precise relation is established between the one-point functions of these light-ray operators in scalar states and the universal soft factors in the infinite tower of soft graviton theorems. The results presented in this paper will be accompanied by detailed calculations and proofs in a longer forthcoming work.

We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows that, given access to error-free, efficient quantum realizations of the agent and environment, quantum methods can yield provable improvements over classical Monte-Carlo based methods in terms of sample complexity. Our approach shows in detail how to combine amplitude estimation and Grover search into a policy evaluation and improvement scheme. We first develop quantum policy evaluation (QPE) which is quadratically more efficient compared to an analogous classical Monte Carlo estimation and is based on a quantum mechanical realization of a finite Markov decision process (MDP). Building on QPE, we derive a quantum policy iteration that repeatedly improves an initial policy using Grover search until the optimum is reached. Finally, we present an implementation of our algorithm for a two-armed bandit MDP which we then simulate.

The paper is a continuation of the study started in Yorzh1. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of delta type. Either an infinite series of trace formulae (provided that edge potentials are infinitely smooth) or a finite number of such formulae (in the cases of L_1 and C^M edge potentials) are obtained which link together two different quantum graphs under the assumption that their spectra coincide. Applications are given to the problem of recovering matching conditions for a quantum graph based on its spectrum.

We attempt to reveal the geometry, emerged from the entanglement structure of any general N-party pure quantum many-body state by representing entanglement entropies corresponding to all 2^N bipartitions of the state by means of a generalized adjacency matrix. We show this representation is often exact and may lead to a geometry very different than suggested by the Hamiltonian. Moreover, in all the cases, it yields a natural entanglement contour, similar to previous proposals. The formalism is extended for conformal invariant systems, and a more insightful interpretation of entanglement is presented as a flow among different parts of the system.

We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and configure a variety of different optical experiments, while the runtime environment provides unique capabilities for visualization and analysis. All standard linear optical components are available as well as sources of thermal, coherent, and entangled Gaussian states. A unique aspect of VQOL is the introduction of non-Gaussian measurements using detectors modeled as deterministic devices that "click" when the amplitude of the light falls above a given threshold. We describe the underlying theoretical models and provide several illustrative examples. We find that VQOL provides a a faithful representation of many experimental quantum optics phenomena and may serve as both a useful instructional tool for students as well as a valuable research tool for practitioners.

Soft theorems describe the behavior of scattering amplitudes when one or several external particles are taken to be energetically soft. In tree-level gravity there are universal soft theorems for the three leading orders in the soft expansion, and they can be shown to be equivalent to Ward identities of asymptotic symmetries. While the leading and subleading symmetries are understood as supertranslations and superrotations respectively, the precise symmetry interpretation of the sub-subleading soft theorem is still a matter of investigation. The form of the sub-subleading soft graviton theorem was elucidated by Cachazo and Strominger using a BCFW expansion of graviton amplitudes. In this work we show that consistency with results based on asymptotic charges requires a careful treatment of collinear singularities in the amplitude, giving rise to collinear corrections to the usual Cachazo-Strominger soft theorem.

In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional outcome distribution, and (ii) a multi-basis measurement setting that concatenates measurement probabilities in different bases (Z, X, Y) into a twelve-dimensional output space. By combining a multioutput regression model (e.g., random forests) with distributional conformal prediction, we validate coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data. Our results confirm that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes. Such synergy opens the door to next-generation quantum-classical hybrid frameworks, providing both improved interpretability and rigorous coverage for quantum machine learning tasks. All codes and full reproducible Colab notebooks are made available at https://github.com/detasar/QECMMOU.

This paper introduces the Quantum Generative Diffusion Model (QGDM), a fully quantum-mechanical model for generating quantum state ensembles, inspired by Denoising Diffusion Probabilistic Models. QGDM features a diffusion process that introduces timestep-dependent noise into quantum states, paired with a denoising mechanism trained to reverse this contamination. This model efficiently evolves a completely mixed state into a target quantum state post-training. Our comparative analysis with Quantum Generative Adversarial Networks demonstrates QGDM's superiority, with fidelity metrics exceeding 0.99 in numerical simulations involving up to 4 qubits. Additionally, we present a Resource-Efficient version of QGDM (RE-QGDM), which minimizes the need for auxiliary qubits while maintaining impressive generative capabilities for tasks involving up to 8 qubits. These results showcase the proposed models' potential for tackling challenging quantum generation problems.

Understanding the loss landscape is an important problem in machine learning. One key feature of the loss function, common to many neural network architectures, is the presence of exponentially many low lying local minima. Physical systems with similar energy landscapes may provide useful insights. In this work, we point out that black holes naturally give rise to such landscapes, owing to the existence of black hole entropy. For definiteness, we consider 1/8 BPS black holes in N = 8 string theory. These provide an infinite family of potential landscapes arising in the microscopic descriptions of corresponding black holes. The counting of minima amounts to black hole microstate counting. Moreover, the exact numbers of the minima for these landscapes are a priori known from dualities in string theory. Some of the minima are connected by paths of low loss values, resembling mode connectivity. We estimate the number of runs needed to find all the solutions. Initial explorations suggest that Stochastic Gradient Descent can find a significant fraction of the minima.

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an n-qubit gapped local Hamiltonian after learning from only O(log(n)) data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require O(n^c) data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as O(n log n) in the number of qubits n. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.

Gauging fermion parity and summing over spin structures are subtly distinct operations. We introduce 'bosonisation cohomology' groups H_B^{d+2}(X) to capture this difference, for theories in spacetime dimension d equipped with maps to some X. Non-trivial classes in H_B^{d+2}(X) contain theories for which (-1)^F is anomaly-free, but spin structure summation is anomalous. We formulate a sequence of cobordism groups whose failure to be exact is measured by H_B^{d+2}(X), and from here we compute it for X=pt. The result is non-trivial only in dimensions din 4Z+2, being due to the presence of gravitational anomalies. The first few are H_B^4=Z_2, probed by a theory of 8 Majorana-Weyl fermions in d=2, then H_B^8=Z_8, H_B^{12}=Z_{16}times Z_2. We rigorously derive a general formula extending this to every spacetime dimension. Along the way, we compile many general facts about (fermionic and bosonic) anomaly polynomials, and about spin and pin^- (co)bordism generators, that we hope might serve as a useful reference for physicists working with these objects. We briefly discuss some physics applications, including how the H_B^{12} class is trivialised in supergravity. Despite the name, and notation, we make no claim that H_B^bullet(X) actually defines a cohomology theory (in the Eilenberg-Steenrod sense).

Understanding Quantum Technologies 2025 is the 8th update of a free open science ebook that provides a 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections, quantum computing energetics and a new subsection of the effects of the Lieb-Robinson limit), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors scientific and engineering approaches and roadmaps), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs and manufacturing process, raw materials), unconventional computing (potential alternatives to quantum and classical computing), quantum computing algorithms, software development tools, resource estimate and benchmark tools, use case and case studies analysis methodologies, application use cases per market, quantum communications and cryptography (including QKD, PQC and QPU interconnect technologies), quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an update to the 2024, 2023, 2022, and 2021 editions published respectively in October 2024, 2023, 2022 and 2021. An update log is provided at the end of the book.

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.

We study Einstein-Maxwell-dilaton gravity models in four-dimensional anti-de Sitter (AdS) spacetime which admit the Reissner-Nordstrom (RN) black hole solution. We show that below a critical temperature the AdS-RN solution becomes unstable against scalar perturbations and the gravitational system undergoes a phase transition. We show using numerical calculations that the new phase is a charged dilatonic black hole. Using the AdS/CFT correspondence we discuss the phase transition in the dual field theory both for non-vanishing temperatures and in the extremal limit. The extremal solution has a Lifshitz scaling symmetry. We discuss the optical conductivity in the new dual phase and find interesting behavior at low frequencies where it shows a "Drude peak". The resistivity varies with temperature in a non-monotonic way and displays a minimum at low temperatures which is reminiscent of the celebrated Kondo effect.

Mott insulators with large and active (or multiflavor) local Hilbert spaces widely occur in quantum materials and ultracold atomic systems, and are dubbed "multiflavor Mott insulators". For these multiflavored Mott insulating materials, the spin-only description with the quadratic spin interactions is often insufficient to capture the major physical processes. In the situation with active orbitals, the Kugel-Khomskii superexchange model was then proposed. We briefly review this historical model and discuss the modern developments beyond the original spin-orbital context. These include and are not restricted to the 4d/5d transition metal compounds with the spin-orbit-entangled J=3/2 quadruplets, the rare-earth magnets with two weakly-separated crystal field doublets, breathing magnets and/or the cluster and molecular magnets, et al. We explain the microscopic origin of the emergent Kugel-Khomskii physics in each realization with some emphasis on the J=3/2 quadruplets, and refer the candidate multiflavor Mott insulators as "J=3/2 Mott insulators". For the ultracold atoms, we review the multiflavor Mott insulator realization with the ultracold alkaline and alkaline-earth atoms on the optical lattices. Despite a large local Hilbert space from the atomic hyperfine spin states, the system could naturally realize a large symmetry group such as the Sp(N) and SU(N) symmetries. These ultracold atomic systems lie in the large-N regime of these symmetry groups and are characterized by strong quantum fluctuations. The Kugel-Khomskii physics and the exotic quantum ground states with the "baryon-like" physics can appear in various limits. We conclude with our vision and outlook on this subject.

We explore a minimal scenario where the sole Standard-Model Higgs is responsible for reheating the Universe after inflation, produces a significant background of gravitational waves and maintains the full classical stability of the electroweak vacuum. As the Higgs self-coupling runs toward negative values at high energy scales, a non-minimal interaction with curvature during a stiff background expansion era drives the Higgs fluctuations closer to the instability scale. This curvature-induced tachyonic instability leads to an intense production of Higgs particles, accompanied by a stochastic gravitational-wave background. The characteristic features of such signal can be directly correlated to the inflationary scale, the non-minimal coupling parameter and the top quark Yukawa coupling. We distinguish between three possible scenarios: absolute stability with low top quark masses, potential vacuum instability, and absolute stability with new physics above the instability scale. Our findings suggest that the detection of a peaked background of gravitational waves together with its inflationary tail has the potential to unveil the features of the Higgs effective potential at very high energy scales while providing a minimal explanation for the reheating phase and the emergence of the Standard-Model plasma in the early Universe. Unlike other studies in the literature, the generation of gravitational waves in our scenario does not depend on the quantum instability of the Standard Model vacuum.

The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical foundations of this link and show how it opens up a new avenue for the design of quantum machine learning algorithms. We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. A quantum computer can now analyse the input data in this feature space. Based on this link, we discuss two approaches for building a quantum model for classification. In the first approach, the quantum device estimates inner products of quantum states to compute a classically intractable kernel. This kernel can be fed into any classical kernel method such as a support vector machine. In the second approach, we can use a variational quantum circuit as a linear model that classifies data explicitly in Hilbert space. We illustrate these ideas with a feature map based on squeezing in a continuous-variable system, and visualise the working principle with 2-dimensional mini-benchmark datasets.

We introduce and describe tt GrayHawk, a publicly available Mathematica-based tool designed for the efficient computation of gray-body factors for spherically symmetric and asymptotically flat black holes. This program provides users with a rapid and reliable means to compute gray-body factors for massless fields with spin \(s = 0, 1/2, 1, 2\) in modes specified by the angular quantum number \(l\), given a black hole metric and the associated parameter values. tt GrayHawk is preloaded with seven different black hole metrics, offering immediate applicability to a variety of theoretical models. Additionally, its modular structure allows users to extend its functionality easily by incorporating alternative metrics or configurations. This versatility makes tt GrayHawk a powerful and adaptable resource for researchers studying black hole physics and Hawking radiation. The codes described in this work are publicly available at https://github.com/marcocalza89/GrayHawk.

Quantum Machine Learning (QML) has surfaced as a pioneering framework addressing sequential control tasks and time-series modeling. It has demonstrated empirical quantum advantages notably within domains such as Reinforcement Learning (RL) and time-series prediction. A significant advancement lies in Quantum Recurrent Neural Networks (QRNNs), specifically tailored for memory-intensive tasks encompassing partially observable environments and non-linear time-series prediction. Nevertheless, QRNN-based models encounter challenges, notably prolonged training duration stemming from the necessity to compute quantum gradients using backpropagation-through-time (BPTT). This predicament exacerbates when executing the complete model on quantum devices, primarily due to the substantial demand for circuit evaluation arising from the parameter-shift rule. This paper introduces the Quantum Fast Weight Programmers (QFWP) as a solution to the temporal or sequential learning challenge. The QFWP leverages a classical neural network (referred to as the 'slow programmer') functioning as a quantum programmer to swiftly modify the parameters of a variational quantum circuit (termed the 'fast programmer'). Instead of completely overwriting the fast programmer at each time-step, the slow programmer generates parameter changes or updates for the quantum circuit parameters. This approach enables the fast programmer to incorporate past observations or information. Notably, the proposed QFWP model achieves learning of temporal dependencies without necessitating the use of quantum recurrent neural networks. Numerical simulations conducted in this study showcase the efficacy of the proposed QFWP model in both time-series prediction and RL tasks. The model exhibits performance levels either comparable to or surpassing those achieved by QLSTM-based models.

We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for supporting empirical evidence and formal statements concerning mathematical generality. We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure, most notably grammar. In particular, the fact that it takes a quantum-like model to combine meaning and structure, establishes QNLP as quantum-native, on par with simulation of quantum systems. Moreover, the now leading Noisy Intermediate-Scale Quantum (NISQ) paradigm for encoding classical data on quantum hardware, variational quantum circuits, makes NISQ exceptionally QNLP-friendly: linguistic structure can be encoded as a free lunch, in contrast to the apparently exponentially expensive classical encoding of grammar. Quantum speed-up for QNLP tasks has already been established in previous work with Will Zeng. Here we provide a broader range of tasks which all enjoy the same advantage. Diagrammatic reasoning is at the heart of QNLP. Firstly, the quantum model interprets language as quantum processes via the diagrammatic formalism of categorical quantum mechanics. Secondly, these diagrams are via ZX-calculus translated into quantum circuits. Parameterisations of meanings then become the circuit variables to be learned. Our encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

The dynamic of holography between anti-de Sitter space holography and de Sitter holography is a very fascinating comparison, which provides many key insights into what we expect from holography in general. In this Essay, we highlight this dynamic with three examples: first, when taking Wheeler-DeWitt states to the asymptotic boundary, the dual interpretation is unclear in de Sitter. Second, what we make of bulk reconstruction and subregion duality in AdS/CFT is not trivially reflected in the dS/CFT scenario. Third, a way of formulating emergence and subregion-subalgebra duality in de Sitter space does not yet exist. With these examples, we provide some musings on this canvas of holography in the settings of (A)dS/CFT.

In the context of C^* dynamical systems, we consider a locally compact group G acting by ^*-automorphisms on a C^* algebra U of observables, and assume a state of U that satisfies the clustering property with respect to a net of group elements of G. That is, the two-point connected correlation function vanishes in the limit on the net, when one observable is translated under the group action. Then we show that all higher order connected correlation functions (Ursell functions, or classical cumulants) and all free correlation functions (free cumulants, from free probability) vanish at the same rate in that limit. Additionally, we show that mean clustering, also called ergodicity, extends to higher order correlations. We then apply those results to equilibrium states of quantum spin lattice models. Under certain assumptions on the range of the interaction, high temperature Gibbs states are known to be exponentially clustering w.r.t. space translations. Combined with the Lieb-Robinson bound, one obtains exponential clustering for space-time translations outside the Lieb-Robinson light-cone. Therefore, by our present results, all the higher order connected and free correlation functions will vanish exponentially under space-time translations outside the Lieb-Robinson light cone, in high temperature Gibbs states. Another consequence is that their long-time averaging over a space-time ray vanishes for almost every ray velocity.

We theoretically identify the noise-induced coherent contribution to the ergotropy of a four-level quantum heat engine coupled to a unimodal quantum cavity. We utilize a protocol where the passive state's quasiprobabilities can be analytically identified from the population-coherence coupled reduced density matrix. The reduced density matrix elements are evaluated using a microscopic quantum master equation formalism. Multiple ergotropies within the same coherence interval, each characterized by a positive and pronounced coherent contribution, are observed. These ergotropies are a result of population inversion as well as quasiprobability-population inversion, controllable through the coherence measure parameters. The optimal flux and power of the engine are found to be at moderate values of ergotropy with increasing values of noise-induced coherence. The optimal power at different coherences is found to possess a constant ergotropy.

In arXiv:2008.04330 it was shown that supertranslation and SL(2,mathbb C) current algebra symmetries, corresponding to leading and subleading soft graviton theorems, are enough to determine the tree level MHV graviton scattering amplitudes. In this note we clarify the role of subsubleading soft graviton theorem in this context.

We study the inflationary phenomenology of a rescaled Einstein-Gauss-Bonnet gravity. In this framework, the gravitational constant of the Einstein-Hilbert term is rescaled due to effective terms active in the high curvature era. Basically, the total theory is an F(R,G,phi) theory with the Gauss-Bonnet part contributing only a non-minimal coupling to the scalar field, so it is a theory with string theory origins and with a non-trivial F(R) gravity part. The F(R) gravity part in the high curvature regime contributes only a rescaled Einstein-Hilbert term and thus the resulting theory is effectively a rescaled version of a standard Einstein-Gauss-Bonnet theory. We develop the formalism of rescaled Einstein-Gauss-Bonnet gravity, taking in account the GW170817 constraints on the gravitational wave speed. We show explicitly how the rescaled theory affects directly the primordial scalar and tensor perturbations, and how the slow-roll and observational indices of inflation are affected by the rescaling of the theory. We perform a thorough phenomenological analysis of several models of interest and we show that is it possible to obtain viable inflationary theories compatible with the latest Planck data. Also among the studied models there are cases that yield a relatively large blue tilted tensor spectral index and we demonstrate that these models can lead to detectable primordial gravitational waves in the future gravitational wave experiments. Some of the scenarios examined, for specific values of the reheating temperature may be detectable by SKA, LISA, BBO, DECIGO and the Einstein Telescope.

Due to the self-referencing aspect, consciousness is placed in a unique non-computable position among natural phenomena. Non-computable consciousness was previously analyzed on the basis of self-referential cyclical time. This paper extends the cyclical model of vacuum observation and posits that choice, or the experience of reality, may be expressed as the initial part of the self-referencing loop, while the conscious awareness of the experience is the other part of the loop. In particular, the inseparability of the two sides of the loop is established through the cyclical time process, which bears a resemblance to Heidegger's analysis of existence. The cyclical looping model is also discussed in terms of Wittgenstein's analysis of language as attaching semantic meaning, or continuous or infinite conscious awareness, to physical reality. We also discuss the proposed model of subjectivity and cyclical time - as opposed to objectivity and linear time - which may be considered similar to Hebrew thought.

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes mathcal{O}(d^{,3/2}/epsilon) queries to the time-evolution operator of the system and mathcal{O}(d^{,3/2}) queries to a block-encoding of the perturbation, for d cooling steps and an epsilon-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.

Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, largescale real-world domains due to the limited expressivity of classical kernels. Quantum computing offers the potential to overcome this limitation by embedding data into exponentially large Hilbert spaces, capturing complex correlations that remain inaccessible to classical computing approaches. In this paper, we propose a Distributed Quantum Gaussian Process (DQGP) method in a multiagent setting to enhance modeling capabilities and scalability. To address the challenging non-Euclidean optimization problem, we develop a Distributed consensus Riemannian Alternating Direction Method of Multipliers (DR-ADMM) algorithm that aggregates local agent models into a global model. We evaluate the efficacy of our method through numerical experiments conducted on a quantum simulator in classical hardware. We use real-world, non-stationary elevation datasets of NASA's Shuttle Radar Topography Mission and synthetic datasets generated by Quantum Gaussian Processes. Beyond modeling advantages, our framework highlights potential computational speedups that quantum hardware may provide, particularly in Gaussian processes and distributed optimization.

The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the φ^{4} scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the φ^{4} theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the φ^{4} machine learning algorithms and target probability distributions.

We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert Space followed by an imposition of - what effectively amounts to - a superselection rule. We illustrate this procedure with a qubit and apply it to the Mach-Zehnder interferometer. The procedure is somewhat reminiscent of the constrained quantization of the electromagnetic field, where, in order to manifestly comply with relativity, one enlargers the Hilbert Space by quantizing the longitudinal and scalar modes, only to subsequently introduce a constraint to make sure that they are actually not directly observable.

Reduction in effective spacetime dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wavefunction factors depend nontrivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a "covert" pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios.

Neural quantum states (NQS) have emerged as a powerful tool for approximating quantum wavefunctions using deep learning. While these models achieve remarkable accuracy, understanding how they encode physical information remains an open challenge. In this work, we introduce adiabatic fine-tuning, a scheme that trains NQS across a phase diagram, leading to strongly correlated weight representations across different models. This correlation in weight space enables the detection of phase transitions in quantum systems by analyzing the trained network weights alone. We validate our approach on the transverse field Ising model and the J1-J2 Heisenberg model, demonstrating that phase transitions manifest as distinct structures in weight space. Our results establish a connection between physical phase transitions and the geometry of neural network parameters, opening new directions for the interpretability of machine learning models in physics.

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. In this paper we initiate an exploration of "positive geometries" and "canonical forms" as objects of study in their own right in a more general mathematical setting. We give a precise definition of positive geometries and canonical forms, introduce general methods for finding forms for more complicated positive geometries from simpler ones, and present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties. We also illustrate a number of strategies for computing canonical forms which yield interesting representations for the forms associated with wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

It has been shown that a gravitational dual to a superconductor can be obtained by coupling anti-de Sitter gravity to a Maxwell field and charged scalar. We review our earlier analysis of this theory and extend it in two directions. First, we consider all values for the charge of the scalar field. Away from the large charge limit, backreaction on the spacetime metric is important. While the qualitative behaviour of the dual superconductor is found to be similar for all charges, in the limit of arbitrarily small charge a new type of black hole instability is found. We go on to add a perpendicular magnetic field B and obtain the London equation and magnetic penetration depth. We show that these holographic superconductors are Type II, i.e., starting in a normal phase at large B and low temperatures, they develop superconducting droplets as B is reduced.

I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schr\"odinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.

Recent results in relativistic quantum information and quantum thermodynamics have independently shown that in the quantum regime, a system may fail to thermalise when subject to quantum-controlled application of the same, single thermalisation channel. For example, an accelerating system with fixed proper acceleration is known to thermalise to an acceleration-dependent temperature, known as the Unruh temperature. However, the same system in a superposition of spatially translated trajectories that share the same proper acceleration fails to thermalise. Here, we provide an explanation of these results using the framework of quantum field theory in relativistic noninertial reference frames. We show how a probe that accelerates in a superposition of spatial translations interacts with incommensurate sets of field modes. In special cases where the modes are orthogonal (for example, when the Rindler wedges are translated in a direction orthogonal to the plane of motion), thermalisation does indeed result, corroborating the here provided explanation. We then discuss how this description relates to an information-theoretic approach aimed at studying quantum aspects of temperature through quantum-controlled thermalisations. The present work draws a connection between research in quantum information, relativistic physics, and quantum thermodynamics, in particular showing that relativistic quantum effects can provide a natural realisation of quantum thermodynamical scenarios.

We consider the Dto 3 limit of Gauss-Bonnet gravity. We find two distinct but similar versions of the theory and obtain black hole solutions for each. For one theory the solution is an interesting generalization of the BTZ black hole that does not have constant curvature but whose thermodynamics is identical. The other theory admits a solution that is asymptotically AdS but does not approach the BTZ black hole in the limit of small Gauss-Bonnet coupling. We also discuss the distinction between our solutions and those obtained by taking a Dto 3 limit of solutions to D-dimensional Einstein Gauss-Bonnet gravity. We find that these latter metrics are not solutions of the theories we consider except for particular constraints on the parameters.

Non-linear interactions during inflation generate non-Gaussianities in the distribution of primordial curvature. In many theories, the physics is scale-invariant, such that the induced three-point function depends solely on a dimensionless shape function S(x,y)sim k^6B_ζ(kx,ky,k). To confront such models with observations, one typically builds specialized estimators for each shape, then applies them to cosmic microwave background datasets at significant computational expense. In this Letter, we take a different approach, directly reconstructing S(x,y) from observations using an efficient logarithmically-binned estimator in primordial-space (motivated by the modal program). Applying this to temperature and polarization maps from Planck, we obtain high-resolution shape measurements across the full (x,y)-plane, including squeezed limits. Our approach is close-to-optimal, highly interpretable, and preserves the information content on (optimally-analyzed) standard templates within approx 10%; moreover, we can use it to assess the scale-dependence of our constraints, finding that Planck is sensitive to approx 6 e-folds of non-Gaussian evolution with a peak sensitivity around 0.1h,Mpc^{-1}. Since we work directly in shape-space, data and theory can be compared in milliseconds. As an example, we perform a search for massive particle exchange using a suite of over 20,000 theoretical templates computed with exact bootstrap methods (for the first time) across a wide range of masses, spins, and sound-speeds; the spin-two analysis yields a maximum significance of 2.6σ. Our approach can be used to probe a wide range of scale-invariant models in orders-of-magnitude less time than with direct estimators, allowing the inflationary paradigm to be explored in new ways.

We discuss the notion of coherent states from three different perspectives: the seminal approach of Schroedinger, the experimental take of quantum optics, and the theoretical developments in quantum gravity. This comparative study tries to emphasise the connections between the approaches, and to offer a coherent short story of the field, so to speak. It may be useful for pedagogical purposes, as well as for specialists of quantum optics and quantum gravity willing to embed their perspective within a wider landscape.

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang's breakthrough quantum-inspired algorithm for recommendation systems [STOC'19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén, Su, Low, and Wiebe [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all recent results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ell^2-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the design of quantum models for machine learning tasks.

In this paper we discuss a higher spin extension of the holographic symmetry algebra for graviton and gluon. Our primary observation is that in the presence of higher spin particles the soft symmetry algebra has a subalgebra isomorphic to w_{infty} which is generated by the conformally soft higher spin particles. This w_{infty} subalgebra does not commute with the w_{1+infty} subalegbra generated by the conformally soft gravitons. The same thing holds for the colored higher spin particles. One gets a subalgebra isomorphic to the S-algebra which is generated by the conformally soft colored higher spin particles. We further verify the soft algebra for colored higher spin particles using the (tree-level) 4-point MHV amplitude of the higher spin Yang-Mills theory constructed in arXiv:2210.07130. At the end we also discuss the higher spin extension of the deformed holographic symmetry algebra for non-zero cosmological constant as constructed in arXiv:2312.00876.