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In this work, we investigate the bound state problem in one dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that, the flat band has significant effects on the bound states.
Using the stabilizer formalism we construct the minimal code into a D-dimensional Hilbert space (qudit) to protect a qubit against phase damping. The effectiveness of this code is then studied by means of input-output fidelity.
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using these methods, and to compare/relate them with other measures based on the ...
We show how a test of macroscopic realism based on Leggett-Garg inequalities (LGIs) can be performed in a macroscopic system. Using a continuous-variable approach, we consider quantum non-demolition (QND) measurements applied to atomic ensembles undergoing magnetically-driven coherent oscillation.
It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets of a (locally compact and Hausdorff) sample space that satisfies the formal req...
Claude Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a mess...
When estimating the phase of a single mode, the quantum Fisher information for a pure probe state is proportional to the photon number variance of the probe state. In this work, we point out particular states that offer photon number distributions exhibiting a large variance, which would help to improve the local esti...
A large class of non-Markovian quantum processes in open systems can be formulated through time-local master equations which are not in Lindblad form. It is shown that such processes can be embedded in a Markovian dynamics which involves a time dependent Lindblad generator on an extended state space.
The Stern-Gerlach (SG) effect, discovered almost a century ago, has become a paradigm of quantum mechanics. Surprisingly there is little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process.
We propose an experimental scheme to implement a second-order nonlocal superposition operation and its variants by way of Hong-Ou-Mandel interference. The second-order coherent operations enable us to generate a NOON state with high particle number in a heralded fashion and also can be used to enhance the entanglement...
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are independent of the eigenvalues and based on the algebraic-geometric invariants introduced in [1-2]. Our results indicate that the problem of efficient simulation of Hamiltonians for arbitrary and multi...
Nondegenerate triple-photon parametric downconversion (NTPD) is a potential source for unconditional tripartite non-Gaussian entangled states of continuous variables. Recent experiment has demonstrated strong third-order correlations among bright photon triplets via microwave NTPD in a superconducting cavity [Phys. Re...
Due to the coupling of a quantum system to its environment energy can be transfered between the two subsystems in both directions. In the present study we consider this process in a general framework for interactions with different properties and show how these properties govern the exchange.
In the future-included real action theory whose path runs over not only past but also future, we demonstrate a theorem, which states that the normalized matrix element of a Hermitian operator $\hat{\cal O}$ defined in terms of the future state at the final time $T_B$ and the fixed past state at the initial time $T_A$ b...
The generalized Dirac oscillator as one of the exact solvable model in quantum mechanics was introduced in 2+1-dimensional world in this paper. What is more, the general expressions of the exact solutions for these models with the inverse cubic, quartic, quintic and sixtic power potentials in radial Dirac equation wer...
Although two-qubit entangling gates are necessary for universal quantum computing, they are notoriously difficult to implement with high fidelity. Recently, tunable couplers have become a key component for realizing high-fidelity two-qubit gates in superconducting quantum computers.
We propose an IR for quantum computing that directly exposes quantum and classical data dependencies for the purpose of optimization. The Quantum Intermediate Representation for Optimization (QIRO) consists of two dialects, one input dialect and one that is specifically tailored to enable quantum-classical co-optimiza...
We determine the exact AND-gate cost of checking if $a\leq x < b$, where $a$ and $b$ are constant integers. Perhaps surprisingly, we find that the cost of interval checking never exceeds that of a single comparison and, in some cases, it is even lower.
Weak single-photon nonlinearities have many potential applications in quantum computing and quantum information. Here we demonstrate a relatively simple system for producing low-power cross-phase modulation using metastable xenon inside a high finesse cavity.
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental.
We study by comparison the structure of singlet type states in Q-bit space in the light of quantum and classical paradigms. It is shown that only the classical paradigm implies a variation in the visibility of correlation coefficients, that has been observed in fact in experiments.
Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in paral...
We present a time-multiplexed interferometer based on Faraday mirrors, and apply it to quantum key distribution. The interfering pulses follow exactly the same spatial path, ensuring very high stability and self balancing.
We study the fidelity of single qubit quantum gates performed with two-frequency laser fields that have a Gaussian or super Gaussian spatial mode. Numerical simulations are used to account for imperfections arising from atomic motion in an optical trap, spatially varying Stark shifts of the trapping and control beams,...
Formalizations of quantum information theory in category theory and type theory, for the design of verifiable quantum programming languages, need to express its two fundamental characteristics: (1) parameterized linearity and (2) metricity. The first is naturally addressed by dependent-linearly typed languages such as...
We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operato...
We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system. We exhibit an approximate reversal operation, adapted to the initial density operator and the ``noise'' dynamics to be reversed.
Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems.
In a sequence of single spins interacting longitudinally with a mechanical oscillator, and using the micromaser model with random injection, we show that after an appropriate post-selection of each spin, a phonon laser analog with Poisson statistics is created with nearly perfect coherence, evidenced by the second orde...
We successfully demonstrate low-frequency noise suppression in the resonant frequency fluctuations of a cavity-embedded Cooper pair transistor (cCPT) driven at single-photon occupancy. In particular, we report a reduction in the resonant frequency fluctuations caused by the internal charge noise over a bandwidth of $\...
Quantum-inspired optimization (QIO) algorithms are computational techniques that emulate certain quantum mechanical effects on a classical hardware to tackle a class of optimization tasks. QIO methods have so far been employed to solve various binary optimization problems and a significant (polynomial) computational s...
Experiments in the field of quantum optics often require very low concentrations of dust particles in the laboratory, but the complexity of working routines precludes operation within a proper clean room. Research teams have established a multitude of different approaches, precaution measures, and habits to keep the d...
Quantum Sensing is a rapidly expanding research field that finds one of its applications in Fundamental Physics, as the search for Dark Matter. Devices based on superconducting qubits have already been successfully applied in detecting few-GHz single photons via Quantum Non-Demolition measurement (QND).
We study time-dependent discrete-time quantum walks on the one-dimensional lattice. We compute the limit distribution of a two-period quantum walk defined by two orthogonal matrices.
An analytical expression for the relativistic corrections to the energy spectra of particles completely confined in an one-dimensional limited length in real space is given, based upon the wave property of particles, the relativistic energy-momentum relation and two mathematical equations.
We derive an expression for the nearest-neighbor spacing distribution $P(s)$ of the energy levels of quantum systems with intermediate dynamics between regularity and chaos and missing levels due to random experimental errors. The expression is based on the Brody distribution, the most widely used for fitting mixed sp...
Rare-earth ion doped crystals have proven to be solid platforms for implementing quantum memories. Their potential use for integrated photonics with large multiplexing capability and unprecedented coherence times is at the core of their attractiveness.
Using the Nikiforov Uvarov method, an application of the relativistic Duffin Kemmer Petiau equation in the presence of a deformed Hulthen potential is presented for spin zero particles. We derived the first order coupled differential radial equations which enable the energy eigenvalues as well as the full wavefunction...
A new class of time-energy uncertainty relations is directly derived from the Schrödinger equations for time-dependent Hamiltonians. Only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full time-dependent wave functions, which would demand a full solution for a time-dependen...
Integrated quantum light source is increasingly desirable in large-scale quantum information processing. ~Despite recent remarkable advances, new material platform is constantly being explored for the fully on-chip integration of quantum light generation, active and passive manipulation, and detection.
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around i...
Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algorithm for a subset of classically simulable quantum circuit models. The gradient-free algorithm, presented as a sequence of exactly solvable...
Measurement-based quantum computing (MBQC), a.k.a. one-way quantum computing (1WQC), is a universal quantum computing model, which is particularly well-suited for photonic platforms. In this model, computation is driven by measurements on an entangled state, which serves as an intermediate representation (IR) between ...
The dynamic structure factor (DSF) is a central quantity for interpreting a vast array of inelastic scattering experiments in chemistry and materials science, but its accurate simulation is a considerable challenge for classical computational methods. In this work, we present a quantum algorithm and an end-to-end simu...
A heavy focus for optical quantum computing is the introduction of error-correction, and the minimisation of resource requirements. We detail a complete encoding and manipulation scheme designed for linear optics quantum computing, incorporating scalable operations and loss-tolerant architecture.
Realization of devices based on quantum laws might lead to building processors that outperform their classical analogues and establishing unconditionally secure communication protocols. Solids do usually present a serious challenge to quantum coherence.
Chiral molecules may exist in superpositions of left- and right-handed states. We show how the amplitudes of such superpositions may be teleported to the polarization degrees of freedom of a photon and thus measured.
In the lead up to fault tolerance, the utility of quantum computing will be determined by how adequately the effects of noise can be circumvented in quantum algorithms. Hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) have been designed for the short-term regime.
Quantum key distribution is among the foremost applications of quantum mechanics, both in terms of fundamental physics and as a technology on the brink of commercial deployment. Starting from principal schemes and initial proofs of unconditional security for perfect systems, much effort has gone into providing secure ...
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between their corresponding strings.
We consider a generalized double Jaynes-Cummings model consisting of two isolated two-level atoms, each contained in a lossless cavity, with the cavities interacting with each other through a controlled photon hopping mechanism. The temporal dynamics of entanglement between the two atoms, as the atom-cavity system evo...
We here present the rate analysis and a proof of principle realization of a device-independent quantum key distribution (QKD) protocol requiring the lowest detection efficiency necessary to achieve a secure key compared to device-independent protocols known so far. The protocol is based on non-maximally entangled stat...
Quantum metrology overcomes standard precision limits by exploiting collective quantum superpositions of physical systems used for sensing, with the prominent example of non-classical multiphoton states improving interferometric techniques. Practical quantum-enhanced interferometry is, however, vulnerable to imperfect...
In the present paper we examine in a systematic way the most relevant orderings of pure kinetic Hamiltonians for five different position-dependent mass (PDM) profiles: soliton-like, reciprocal quadratic and biquadratic, exponential and parabolic. As a result of the non-commutativity between momentum and position opera...
We show that the claims expressed in the Comment <a href="https://arxiv.org/abs/0810.3244v1" data-arxiv-id="0810.3244v1" class="link-https">arXiv:0810.3244v1</a> by R.S. Decca et al against our paper, D.A.R. Dalvit and S.K. Lamoreaux, Phys. Rev. Lett.
We demonstrate the quantum Talbot effect using pairs of single photons produced by parametric down conversion. In contrast to the previous works, we use a programmable spatial light modulator to behave as a diffraction grating.
We present the RF Quantum Upconverter (RQU) and describe its application to quantum metrology of electromagnetic modes between dc and the Very High Frequency band (VHF) ($\lesssim$300MHz). The RQU uses a Josephson interferometer made up of superconducting loops and Josephson junctions to implement a parametric interac...
We introduce the quantum-house effect, a non-local phenomenon which apparently does not require quantum discord to be present. It suffices for the effect if neither subsystem of a bipartite system is in a pure state.
We propose a novel optomechanical gyroscope architecture based on a spinning cavity optomechanical resonator (COM) evanescently coupled to a tapered optical fiber without relying on costly quantum light sources. Our study reveals a striking dependence of the gyroscope's sensitivity on the propagation direction of ...
We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a ``relativistic'' formulation leads to a complete analysis of the question of separability.
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a quasiprobability representation for quantum computation which is covariant with respec...
We introduce deterministic state-transformation protocols between many-body quantum states which can be implemented by low-depth Quantum Circuits (QC) followed by Local Operations and Classical Communication (LOCC). We show that this gives rise to a classification of phases in which topologically-ordered states or oth...
Semidefinite programs (SDPs) are convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization and operational research. Noisy intermediate-scale quantum (NISQ) algorithms aim to make an efficient use of the current generation of quantum hardware.
It has previously been shown that the gated detectors of two commercially available quantum key distribution (QKD) systems are blindable and controllable by an eavesdropper using continuous-wave illumination and short bright trigger pulses, manipulating voltages in the circuit [L. Lydersen et al., Nat. Photonics DOI:<a...
Surface codes are the most promising candidates for fault-tolerant quantum computation. Single qudit errors are typically modelled as Pauli operators, to which general errors are converted via randomizing methods.
This paper presents key enhancements to our previous work~\cite{naghmouchi2024mixed} on a hybrid Benders decomposition (HBD) framework for solving mixed integer linear programs (MILPs). In our approach, the master problem is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) model and solved on a neu...
One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for the sample complexity of the identification and decision versions of the hidden s...
We examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a two-level approximation for a system, intermolecular interactions are introduced by a mean-fie...
Numerical simulation is an important method for verifying the quantum circuits used to simulate low-energy nuclear states. However, real-world applications of quantum computing for nuclear theory often generate deep quantum circuits that place demanding memory and processing requirements on conventional simulation met...
State, trace, and moment polynomials are polynomial expressions in several operator or random variables and positive functionals on their products (states, traces or expectations). While these concepts, and in particular their positivity and optimization, arose from problems in quantum information theory, yet they nat...
We analytically solve the position-dependent mass (PDM) 1D Schrödinger equation for a new class of hyperbolic potentials $V_q^p(x) = -V_0\frac{\sinh^px}{\cosh^qx}, \, p= -2, 0, \dots q$ [see C. A. Downing, J. Math. Phys. 54 072101 (2013)] among which several hyperbolic single- and double-wells. For a solitonic mass di...
Quantum optimal control has enjoyed wide success for a variety of theoretical and experimental objectives. These favorable results have been attributed to advantageous properties of the corresponding control landscapes, which are free from local optima if three conditions are met: (1) the quantum system is controllabl...
We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth, while circuits composed of both cannot.
In this work, we study the problem of testing properties of the spectrum of a mixed quantum state. Here one is given $n$ copies of a mixed state $\rho\in\mathbb{C}^{d\times d}$ and the goal is to distinguish whether $\rho$'s spectrum satisfies some property $\mathcal{P}$ or is at least $\epsilon$-far in $\ell_1$-d...
An extractor is a function E that is used to extract randomness. Given an imperfect random source X and a uniform seed Y, the output E(X,Y) is close to uniform.
The back-action exerted by the moving electron on the magnetic flux in the A-B effect is analyzed. It is emphasized that a reasonable interpretation on the A-B effect should be consistent with the uncertain principle.
The superposition principle is fundamental to quantum theory. Yet a recent no-go theorem has proved that quantum theory forbids superposition of unknown quantum states, even with nonzero probability.
We propose a new single photon source based on the principle of active multiplexing of heralded single photons which, unlike previously reported architecture, requires a limited amount of physical resources. We discuss both its feasibility and the purity and indistinguishability of single photons as function of the ke...
A quantum state is called concordant if it has zero quantum discord with respect to any part. By extension, a concordant computation is one such that the state of the computer, at each time step, is concordant.
In 1926, Erwin Schrodinger wrote a series of papers that invented wave mechanics and set the foundation for much of the single-particle quantum mechanics that we teach today. In his first paper, he solved the Schrodinger equation using the Laplace method, which is a technique that is quite powerful, but rarely taught....
The Quantum Approximate Optimization Algorithm (QAOA) uses a quantum computer to implement a variational method with $2p$ layers of alternating unitary operators, optimized by a classical computer to minimize a cost function. While rigorous performance guarantees exist for the QAOA at small depths $p$, the behavior at...
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit and gate teleportation, minimizing the required Einstein-Podolsky-Rosen (EPR) p...
We study experimentally the lifetime of a special class of entangled states in an atomic clock, squeezed spin states. In the presence of anisotropic noise, their lifetime is strongly dependent on squeezing orientation.
Determining whether a subspace spanned by certain quantum states is entangled and its entanglement dimensionality remains a fundamental challenge in quantum information science. This paper introduces a geometric measure of $r$-bounded rank, $E_r(\mathcal{S})$, for a given subspace $\mathcal{S}$.
In spite of all of its successes, quantum mechanics leaves us with a central problem: How does Nature create a "foot-bridge" from fragile quanta to the objective world of everyday experience? Here we identify within quantum mechanics a fundamental process leading to the perceived objectivity and called state i...
The dynamics and thermal equilibrium of spin waves (magnons) in a quantum ferromagnet as well as the macroscopic magnetisation are investigated. Thermal noise due to an interaction with lattice phonons and the effects of spatial correlations in the noise are considered.
Population evolution in a magnetic impurity doped semiconductor quantum dot has been studied by applying a sequence of pulses of chosen pulse area. By optical excitation mechanism, the population in (J_z=+3/2), heavy hole state of valence band is carried over to (J_z=-3/2), valance band state, via the (J=+1/2) conduct...
Link prediction methods use patterns in known network data to infer which connections may be missing. Previous work has shown that continuous-time quantum walks can be used to represent path-based link prediction, which we further study here to develop a more optimized quantum algorithm.
Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial.
Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose we have additional k qubits available.
A significant aspect of the study of quantum strategies is the exploration of the game-theoretic solution concept of the Nash equilibrium in relation to the quantization of a game. Pareto optimality is a refinement on the set of Nash equilibria.
We investigate the qubit in the hierarchical environment where the first level is just one lossy cavity while the second level is the N-coupled lossy cavities. In the weak coupling regime between the qubit and the first level environment, the dynamics crossovers from the original Markovian to the new non-Markovian and...
Geometrically frustrated spin-chain compounds such as Ca3Co2O6 exhibit extremely slow relaxation under a changing magnetic field. Consequently, both low-temperature laboratory experiments and Monte Carlo simulations have shown peculiar out-of-equilibrium magnetization curves, which arise from trapping in metastable co...
Local pure states are an important resource for quantum computing. The problem of distilling local pure states from mixed ones can be cast in an information theoretic paradigm.
Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in excellent agreement with the ones obtained before.
Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players.
Quantum metrology promises unprecedented measurement precision but suffers in practice from the limited availability of resources such as the number of probes, their coherence time, or non-classical quantum states. The adaptive Bayesian approach to parameter estimation allows for an efficient use of resources thanks t...
A simple algebraic procedure is described for deriving Maxwell-Bloch-type equations from single-atom cavity quantum electrodynamics (cavity QED) master equations via orthogonal projection onto a manifold of semiclassical states. In particular the usual Maxwell-Bloch Equations are obtained--up to a state-dependent corr...
Memory effects play a fundamental role in the dynamics of open quantum systems. There exist two different views on memory for quantum noises.
Maxwell's equations in the vacuum can be formally cast in the form of Schrödinger's equation. Unfortunately, the vector to which this equation directly applies is not a wavefunction: its amplitude squared is not a probability density but the expected energy density of the field.

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