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We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure states constituting a decomposition of the considered mixture. The method repro...
The scattering of a wave obeying Helmholtz equation by an elliptic obstacle can be described exactly using series of Mathieu functions. This situation is relevant in optics, quantum mechanics and fluid dynamics.
Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality?
Quantum mechanics has maintained over the years the reputation of being "the most obscure theory. " It works perfectly well, but nobody seems to know why.
We propose an entanglement generation scheme that requires neither the coherent evolution of a quantum system nor the detection of single photons. Instead, the desired state is heralded by a {\em macroscopic} quantum jump.
Quantum observables of generic many-body systems exhibit a universal pattern of growth in the Krylov space of operators. This pattern becomes particularly manifest in the Lanczos basis, where the evolution superoperator assumes the tridiagonal form.
Essential to the description of a quantum system are its local degrees of freedom, which enable the interpretation of subsystems and dynamics in the Hilbert space. While a choice of local tensor factorization of the Hilbert space is often implicit in the writing of a Hamiltonian or Lagrangian, the identification of lo...
Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task of boson-sampling.
We develop a general optimization strategy for performing a chosen unitary or non-unitary task on an open quantum system. The goal is to design a controlled time-dependent system Hamiltonian by variationally minimizing or maximizing a chosen function of the system state, which quantifies the task success (score), such...
We study resonant dipole-dipole coupling and the associated van der Waals energy shifts in Rydberg excited atomic rubidium and potassium and investigate Förster resonances between interspecies pair states. A comprehensive survey over experimentally accessible pair state combinations reveals multiple candidates with sm...
Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for achieving quantum advantage in combinatorial optimization. However, its variational framework presents a long-standing challenge in selecting circuit parameters.
Reinforcement learning has witnessed recent applications to a variety of tasks in quantum programming. The underlying assumption is that those tasks could be modeled as Markov Decision Processes (MDPs).
Quantum resources and protocols are known to outperform their classical counterparts in variety of communication and information processing tasks. Random Access Codes (RACs) are one such cryptographically significant family of bipartite communication tasks, wherein, the sender encodes a data set (typically a string of...
In this paper, a novel quantum dialogue (QD) protocol is proposed based on single photons in both polarization and spatial-mode degrees of freedom. In the proposed QD protocol, the initial states of single photons in both polarization and spatial-mode degrees of freedom used for encoding are privately shared between t...
The paper "Physics without determinism: Alternative interpretations of classical physics" [Phys. Rev. A, 100:062107, Dec 2019] defines finite information quantities (FIQ). A FIQ expresses the available information about the value of a physical quantity.
We present a theoretical description of a system of many spins strongly coupled to a bosonic chain. We rely on the use of a spin-wave theory describing the Gaussian fluctuations around the mean-field solution, and focus on spin-boson chains arising as a generalization of the Dicke Hamiltonian.
One of the most effective ways to advance the performance of quantum computers and quantum sensors is to increase the number of qubits or quantum resources in the system. A major technical challenge that must be solved to realize this goal for trapped-ion systems is scaling the delivery of optical signals to many indi...
Non locality appearing in QFT during the free evolution of localized field states and in the Feynman propagator function is analyzed. It is shown to be connected to the initial non local properties present at the level of quantum states and then it does not imply a violation of Einstein's causality.
The Closest String Problem is an NP-complete problem which appears more commonly in bioinformatics and coding theory. Less surprisingly, classical approaches have been pursued with two prominent algorithms being the genetic algorithm and simulated annealing.
We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence.
A recent rebuttal to criticism of Bell's analysis is shown to be defective by fault of failure to consider all hypothetical conditions input into the derivation of Bell Inequalitites.
Using a position operator obtained for spin 1 particles by the present author and Wigner, we obtain a quantum relativistic result for the hidden momentum force experienced by particles with structure. In particular, our result applies to the hidden magnetic forces manifest in some problems of electromagnetism.
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean logic of complementary features may also apply to classical systems, if their sta...
We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower ...
We show that the saturation of a multiphoton transition is accompanied by a gradual collapse of quantum multimodality in the strong-coupling limit of the weakly driven Jaynes-Cummings (JC) model. By means of a perturbative method, we illustrate the prominent role of quantum fluctuations by focusing on the two and thre...
We demonstrate experimentally that a polarized nuclear spin modifies the dynamic behavior of a neighboring electronic spin. Specifically, an out-of-phase component appears in the electronic spin-echo signal.
We show that universal quantum computation can be made fault-tolerant in a scenario where the error-correction is implemented without mid-circuit measurements. To this end, we introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $\mathit{CCZ}$ gate, enabling a universal set of ...
Property-based testing has been previously proposed for quantum programs in Q# with QSharpCheck; however, this implementation was limited in functionality, lacked extensibility, and was evaluated on a narrow range of programs using a single property. To address these limitations, we propose QuCheck, an enhanced proper...
Using techniques from semidefinite programming, we study the problem of finding a closest quantum channel to the projection onto a matricial subsystem. We derive two invariants of matricial subsystems which are related to the quantum Lovász theta function of Duan, Severini, and Winter.
We construct an operator for the Aharonov-Anandan phase for time independent Hamiltonians. This operator is shown to generate the motion of cyclic quantum systems through an equation of evolution involving only geometric quantities, i.e. the distance between quantum states, the geometric phase and the total length of ...
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an alternating sequence of classically tunable unitaries.
Quantum teleportation is the name of a problem: how can the real-valued parameters encoding the state at Alice's location make their way to Bob's location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a conjuring trick.
We introduce a new decomposition of the multiqubit states of the form $\rho^{\otimes N}$ and employ it to construct the optimal single qubit purification procedure. The same decomposition allows us to study optimal quantum cloning and state estimation of mixed states.
We study the dynamics of entanglement asymmetry in periodically driven quantum systems. Using a periodically driven XY chain as a model for a driven integrable quantum system, we provide semi-analytic results for the behavior of the dynamics of the entanglement asymmetry, $\Delta S$, as a function of the drive frequen...
We systematically investigate local phonon hopping in the radial direction of a linear trapped-ion string. We measure the decay of hopping as a function of key trap parameters and analyze the results in terms of the decay time and the number of oscillations.
We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks.
Entanglement in continuous-variable non-Gaussian states provides irreplaceable advantages in many quantum information tasks. However, the sheer amount of information in such states grows exponentially and makes a full characterization impossible.
We study state engineering through bilinear interactions between two remote qubits and two-mode Gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane.
It is of fundamental interest in controlling the light-matter interaction for a long time in the field of quantum information processing. However, usual excitation with the propagating photon can hardly excite a localized state of light while keeping the atom under a subradiant decay in an atom-waveguide system.
We derive analytic expressions of the recursive solutions to the Schrödinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately determining the transmission probabilities as well as the wave function in both classic...
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and environmentally-induced dissipative effects, and the concept known as geometric phases.
Quantum error-correcting codes are a vital technology for demonstrating reliable quantum computation. They require data qubits for encoding quantum information and ancillary qubits for taking error syndromes necessary for error correction.
We investigate the space complexity of two graph streaming problems: Max-Cut and its quantum analogue, Quantum Max-Cut. Previous work by Kapralov and Krachun [STOC `19] resolved the classical complexity of the \emph{classical} problem, showing that any $(2 - \varepsilon)$-approximation requires $\Omega(n)$ space (a $2...
Model optomechanical systems with photon-vibration interactions linear, quadratic, and cubic in mechanical displacements are studied under conditions for adiabatic elimination of the photon field. The opportunity of transformation of effective potential describing the dynamics of the mechanical resonator from single-w...
We study the thermal entanglement in a two-spin-qutrit system with anisotropy in the exchange coupling between two spins. We use the realignment criterion to distinguish the entangled states, and the negativity for measuring the entanglement in this system.
The problem of compiling general quantum algorithms for implementation on near-term quantum processors has been introduced to the AI community. Previous work demonstrated that temporal planning is an attractive approach for part of this compilationtask, specifically, the routing of circuits that implement the Quantum ...
We present an operational framework for Einstein-Podolsky-Rosen steering as a physical resource. To begin with, we characterize the set of steering non-increasing operations (SNIOs) --i.e., those that do not create steering-- on arbitrary-dimensional bipartite systems composed of a quantum subsystem and a black-box de...
Prepare-and-measure scenarios, in their many forms, can be seen as the basic building blocks of communication tasks. As such, they can be used to analyze a diversity of classical and quantum protocols -- of which dense coding and random access codes are key examples -- in a unified manner.
We perform hole burning with a low drift stabilized laser within the zero phonon line of the 4f-5d transition in Ce$^{3+}$:Y$_2$SiO$_5$ at 2K. The narrowest spectral holes appear for small applied magnetic fields and are $6\pm4$ MHz wide (FWHM).
The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions.
This paper reports on experiments realized on several IBM 5Q chips which show evidence for the advantage of using error detection and fault-tolerant design of quantum circuits. We show an average improvement of the task of sampling from states that can be fault-tolerantly prepared in the $[[4,2,2]]$ code, when using a...
Measurement-based quantum computation (MQC) is a leading paradigm for building a quantum computer. Cluster states being used in this context act as one-way quantum computers.
We consider the problem of testing multiple quantum hypotheses $\{\rho_1^{\otimes n},\ldots,\rho_r^{\otimes n}\}$, where an arbitrary prior distribution is given and each of the $r$ hypotheses is $n$ copies of a quantum state. It is known that the average error probability $P_e$ decays exponentially to zero, that is, ...
We examine the classical contents of quantum games. It is shown that a quantum strategy can be interpreted as a classical strategies with effective density-dependent game matrices composed of transposed matrix elements.
We propose a Rydberg molecule dressing scheme to create strong and long-ranged interactions at selective distances. This is achieved through laser coupling ground-state atoms off-resonantly to an attractive molecular curve of two interacting Rydberg atoms.
In order to popularize the so called Schwinger's method we reconsider the Feynman propagator of two non-relativistic systems: a charged particle in a uniform magnetic field and a charged harmonic oscillator in a uniform magnetic field. Instead of solving the Heisenberg equations for the position and the canonical ...
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue degeneracy can be represented in the oscillator-like form in terms of pseudoferm...
The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matters due to their exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matters in one and two spatial dimension...
Photon loss is the dominant source of noise in optical quantum systems. The Gottesman-Kitaev-Preskill (GKP) bosonic code provides significant protection; however, even low levels of loss can generate uncorrectable errors that another concatenated code must handle.
We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semi-classical approximation.
We study the interaction of dielectric rods and disks with the laser field of a high finesse cavity. The quantum master equation for the coupled particle-cavity dynamics, including Rayleigh scattering, is derived for particle sizes comparable to the laser wavelength.
Modern NISQ devices are subject to a variety of biases and sources of noise that degrade the solution quality of computations carried out on these devices. A natural question that arises in the NISQ era, is how fairly do these devices sample ground state solutions.
Integrated entangled photon-pair sources are key elements for enabling large-scale quantum photonic solutions, and addresses the challenges of both scaling-up and stability. Here we report the first demonstration of an energy-time entangled photon-pair source based on spontaneous parametric down-conversion in silicon-...
We show a deterministic secure direct communication protocol using single qubit in mixed state. The security of this protocol is based on the security proof of BB84 protocol.
The extraordinary sensitivity of the output field of an optical cavity to small quantum-scale displacements has led to breakthroughs such as the first detection of gravitational waves \cite{LIGO,LIGODC} and of the motions of quantum ground-state cooled mechanical oscillators \cite{Teufel2011,Chan2011}. While heterodyn...
The information on a quantum process acquired through measurements plays a crucial role in the determination of its non-equilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate for a continuously monitored mesoscopic quantum system.
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution, although fault-tolerant quantum computers will likely not be available in the near ...
We present a simple quantum theory for the pulsed light generated by a synchronously pumped optical parametric oscillator (SPOPO) in the degenerate case where the signal and idler trains of pulses coincide, below threshold and neglecting all dispersion effects. Our main goal is to precise in the obtained quantum effec...
The quantum Zeno effect (QZE) predicts a slow-down of the time development of a system under rapidly repeated ideal measurements, and experimentally this was tested for an ensemble of atoms using short laser pulses for non-selective state measurements. Here we consider such pulses for selective measurements on a singl...
Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov's probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice-Bob EPR paradigm, non-contextuality means that the identity of Alice's spin (i.e., the probability space on which it is defined...
In this work we consider basic principles and problems of the standard quantum mechanical formalism. Especially we consider final measurement or detection procedure (collapse) as a quantum-classical continuous phase transition with spontaneous (non-dynamical) unitary symmetry (superposition) breaking (effective hiding...
Given the increasing use of shotcuts to adiabaticity (STA) to optimize power and efficiency of quantum heat engines, it becomes a relevant question if there are any theoretical limits to their application. We argue that quantum fluctuations in the control device which implements the shortcut deflect the system from th...
The Parrondo game, devised by Parrondo, means that winning strategy is constructed a combination of losing strategy. This situation is called the Parrondo paradox.
We report an experimental study of group-velocity dispersion effect on an entangled two-photon wavepacket, generated via spontaneous parametric down-conversion and propagating through a dispersive medium. Even in the case of using CW laser beam for pump, the biphoton wavepacket and the second-order correlation functio...
A system gradually driven through a symmetry-breaking phase transition is subject to the Kibble-Zurek mechanism (KZM). As a consequence of the critical slowing down, its state cannot follow local equilibrium, and its evolution becomes non-adiabatic near the critical point.
We revisit the Dicke superradiance problem, where an ensemble of N identical two-level systems undergoes collective spontaneous decay. While an exact analytical solution has been known since 1977, its algebraic complexity has hindered practical use.
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability distribution arises from the Born rule and which has a clear physical interpretation.
In \cite{simon2023algorithms} we introduced four algorithms for the training of neural support vector machines (NSVMs) and demonstrated their feasibility. In this note we introduce neural quantum support vector machines, that is, NSVMs with a quantum kernel, and extend our results to this setting.
We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters along with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means.
Steane code is one of the most widely studied quantum error-correction codes, which is a natural choice for fault-tolerant quantum computation (FTQC). However, the original Steane code is not fault-tolerant because the CNOT gates in an encoded block may cause error propagation.
The exact evaluation of the molecular ground state in quantum chemistry requires an exponentially increasing computational cost. Quantum computation is a promising way to overcome the exponential problem using polynomial-time quantum algorithms.
In two-dimensions, the laws of physics even permit the existence of anyons which exhibit fractional statistics ranging continuously from bosonic to fermionic behaviour. They have been responsible for the fractional quantum Hall effect and proposed as candidates for naturally fault-tolerant quantum computation.
We introduce an adaptable and modular hybrid architecture designed for fault-tolerant quantum computing. It combines quantum emitters and linear-optical entangling gates to leverage the strength of both matter-based and photonic-based approaches.
We propose an idea of eigenstate clustering in non-Hermitian systems. We show that non-orthogonal eigenstates can be clustered around exceptional points and illustrate our idea on some models.
Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this Letter, we explore this uncertainty relation in relativistic regime.
We study the suppression of qubit dephasing through Uhrig dynamical decoupling (UDD) in nontrivial environments modeled within the spin-boson formalism. In particular, we address the case of
Quantum computing has become increasingly practical in solving real-world problems due to advances in hardware and algorithms. In this paper, we aim to design and estimate quantum machine learning and hybrid quantum-classical models in a few practical materials science tasks, i.e., predicting stacking fault energies a...
Quantum state preparation and measurement of photonic and phononic Schrödinger cat states have gathered significant interest due to their implications for alternative encoding schemes in quantum computation. These scheme employ coherent state superpositions, leveraging the expanded Hilbert space provided by cavity or ...
Classification of medical images plays a vital role in medical image analysis; however, it remains challenging due to the limited availability of labeled data, class imbalances, and the complexity of medical patterns. To overcome these challenges, we propose a novel Hybrid Quantum-Classical Neural Network (HQCNN) for ...
The aim of the paper is to propose a bounded-error quantum polynomial time (BQP) algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems.
Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are modeled as a binary measurement outcome flipped with some probability.
We investigate the electronic structure of methanimine (CH2NH) and water (H2O) molecules in an effort to locate conical intersections (CIs) using variational quantum algorithms. Our approach implements and compares a range of hybrid quantum-classical methods, including the Variational Quantum Eigensolver (VQE), Variat...
We have composed the ideas of quantum renormalization group and quantum information by exploring the low energy states dynamic of entanglement resources of a system close to its quantum critical point. We demonstrate the low energy states dynamical quantities of the one dimensional magnetic systems could show the quan...
One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem symmetries and typical optimal parameters as initial points if they concentrate.
In the context of energy storage at the nanoscale, exploring the notion of \textit{quantum advantage} implies walking on the thin line at the boundary between quantum mechanics and thermodynamics, which underpins our conventional understanding of battery devices. With no classical analogue, the Sachdev-Ye-Kitaev (SYK)...
This paper explains how a popular, commercially-available software package for solving partial-differential-equations (PDEs), as based on the finite-element method (FEM), can be configured to calculate, efficiently, the frequencies and fields of the whispering-gallery (WG) modes of axisymmetric dielectric resonators. ...
A short quantum Markov chain is a tripartite state $\rho_{ABC}$ such that system $A$ can be recovered perfectly by acting on system $C$ of the reduced state $\rho_{BC}$. Such states have conditional mutual information $I(A;B\|C)$ equal to zero and are the only states with this property.
We investigate an operational description of identical noninteracting particles in multiports. In particular we look for physically motivated restrictions that explain their bunching probabilities.
We propose the scheme realizing the two-level control over the unitary operators $U_k$ creating the required quantum state of the system $S$. These operators are controlled by the superposition state of the auxiliary subsystem $R$ which is governed by two control centers.
Recently, the creation of photonic Landau levels in a twisted cavity has been demonstrated in Nature \textbf{534}, 671 (2016). Here we propose a scheme to adiabatically transfer flux quanta in multiples of $3\hbar$ simultaneously to all cavity photons by coupling the photons through flux-threaded cones present in such...

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