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In quantum foundations, there is growing interest in the program of reconstructing the quantum formalism from clear physical principles. These reconstructions are formulated in an operational framework, deriving the formalism from information-theoretic principles. It has been recognized that this project is in tension with standard Psi-ontic interpretations. This paper presupposes that the quantum reconstruction program (QRP) (i) is a worthwhile project and (ii) puts pressure on Psi-ontic interpretations. Where does this leave us? Prima facie, it seems that Psi-epistemic interpretations perfectly fit the spirit of information-based reconstructions. However, Psi-epistemic interpretations, understood as saying that the wave functions represents one's knowledge about a physical system, recently have been challenged on technical and conceptual grounds. More importantly, for some researchers working on reconstructions, the lesson of successful reconstructions is that the wave function does not represent objective facts about the world. Since knowledge is a factive concept, this speaks against epistemic interpretations. In this paper, I discuss whether Psi-doxastic interpretations constitute a reasonable alternative. My thesis is that if we want to engage QRP with Psi-doxastic interpretations, then we should aim at a reconstruction that is spelled out in non-factive experiential terms.

The paper presents an extension of the metaphysics of self-subsisting structures set out in a companion paper to the realm of non-relativistic quantum physics. The discussion is centered around a Pure Shape Dynamics model representing a relational implementation of a de Broglie-Bohm $N$-body system. An interpretation of this model in terms of self-subsisting structures is proposed and assessed against the background of the debate on the metaphysics of quantum physics, with a particular emphasis on the nature of the wave function. The analysis shows that elaborating an appropriate Leibnizian/Machian metaphysics of the quantum world requires a substantial revision of the notion of world-building relation., Comment: 32 pages, forthcoming in Foundations of Physics

This paper advocates for an innovative approach designed for estimating optoelectronic properties of quantum structures utilizing Tight-Binding (TB) theory. Predicated on the comparative analysis between estimated and actual properties, the study strives to validate the efficacy of this proposed technique; focusing notably on the computation of bandgap energy. It is observed that preceding methodologies offered a restricted accuracy when predicting complex structures like super-lattices and quantum wells. To address this gap, we propose a methodology involving three distinct phases using orbital interaction parameters (OIPs) and the TB theory. The research employed Aluminium Arsenide (AlAs) and Gallium Arsenide (GaAs) as the primary bulk materials. Our novel approach introduces a computation framework that first focuses on bulk computation, subsequently expanding to super-lattice structures. The findings of this research demonstrate promising results regarding the accuracy of predicated optoelectronic properties, particularly the cut-off wavelength. This study paves the way for future research, potentially enhancing the precision of the proposed methodology and its application scope within the field of quantum optoelectronics., Comment: This paper is published in the journal of Micro and Nanostructures

Quantum Computing (QC) offers significant potential to enhance scientific discovery in fields such as quantum chemistry, optimization, and artificial intelligence. Yet QC faces challenges due to the noisy intermediate-scale quantum era's inherent external noise issues. This paper discusses the integration of QC as a computational accelerator within classical scientific high-performance computing (HPC) systems. By leveraging a broad spectrum of simulators and hardware technologies, we propose a hardware-agnostic framework for augmenting classical HPC with QC capabilities. Drawing on the HPC expertise of the Oak Ridge National Laboratory (ORNL) and the HPC lifecycle management of the Department of Energy (DOE), our approach focuses on the strategic incorporation of QC capabilities and acceleration into existing scientific HPC workflows. This includes detailed analyses, benchmarks, and code optimization driven by the needs of the DOE and ORNL missions. Our comprehensive framework integrates hardware, software, workflows, and user interfaces to foster a synergistic environment for quantum and classical computing research. This paper outlines plans to unlock new computational possibilities, driving forward scientific inquiry and innovation in a wide array of research domains.

Quantum computing is an exciting field with high disruptive potential, but very difficult to access. For this reason, many approaches to teaching quantum computing are being developed worldwide. This always raises questions about the didactic concept, the content actually taught, and how to measure the success of the teaching concept. In 2022 and 2023, the authors taught a total of nine two-week MOOCs (massive open online courses) with different possible learning paths on the Hasso Plattner Institute's OpenHPI platform. The purpose of the platform is to make computer science education available to everyone free of charge. The nine quantum courses form a self-contained curriculum. A total of more than 17{,}000 course attendances have been taken by about 7400 natural persons, and the number is still rising. This paper presents the course concept and evaluates the anonymized data on the background of the participants, their behaviour in the courses, and their learning success. This paper is the first to analyze such a large dataset of MOOC-based quantum computing education. The summarized results are a heterogeneous personal background of the participants biased towards IT professionals, a majority following the didactic recommendations, and a high success rate, which is strongly correlatated with following the didactic recommendations. The amount of data from such a large group of quantum computing learners provides many avenues for further research in the field of quantum computing education. The analyses show that the MOOCs are a low-threshold concept for getting into quantum computing. It was very well received by the participants. The concept can serve as an entry point and guide for the design of quantum computing courses.

As a consequence of the place ascribed to measurements in the postulates of quantum mechanics, if two differently prepared systems are described with the same density operator \r{ho}, they are said to be in the same quantum state. For more than fifty years, there has been a lack of consensus about this postulate. In a 2011 paper, considering variances of spin components, Fratini and Hayrapetyan tried to show that this postulate is unjustified. The aim of the present paper is to discuss major points in this 2011 article, and in their reply to a 2012 paper by Bodor and Diosi claiming that their analysis was irrelevant. Facing some ambiguities or inconsistencies in the 2011 paper and in the reply, we first try to guess their aim, then establish results useful in this context, and finally discuss the use or misuse of several concepts implied in this debate.

Measurements monitoring the inductive coupling between oscillating radio-frequency magnetic fields and objects of interest create versatile platforms for non-destructive testing. The benefits of ultra low frequency measurements, i.e., below 3 kHz, are sometimes outweighed by the fundamental and technical difficulties related to operating pick-up coils or other field sensors in this frequency range. Inductive measurements with the detection based on a two-photon interaction in rf atomic magnetometers address some of these issues, as the sensor gains an uplift in its operational frequency. The developments reported here integrate the fundamental and applied aspects of the two-photon process in magnetic induction measurements. In this paper, all spectral components of the two-photon process are identified, which result from the non-linear interactions between the rf fields and atoms. A method for the retrieval of the two-photon phase information, which is critical for inductive measurements, is also demonstrated. Furthermore, a self-compensation configuration is introduced, whereby high contrast measurements of defects can be obtained due to the sensor's insensitivity to the primary field, including using simplified instrumentation for this configuration by producing two rf fields with a single rf coil., Comment: 10 pages, 9 figures

In this paper we demonstrate that any Markovian master equation defining a completely positive evolution for a quantum-classical hybrid state can always be written in terms of four basic coupling mechanisms. Each of them is characterized by a different "backaction" on each subsystem. On this basis, for each case, we find the conditions under which a diffusive limit is approached, that is, the time evolution can be approximated in terms of the first and second derivatives of the hybrid state with respect to a classical coordinate. In this limit, the restricted class of evolutions that guaranty the positivity of the hybrid state at all times (quantum Fokker-Planck master equations) emerges when the coupling mechanisms lead to infinitesimal (non-finite) changes in both the quantum and classical subsystems. A broader class of diffusive evolutions is obtained when positivity is only granted after a transient time or alternatively is granted after imposing an initial finite width on the state of the classical subsystem. A set of representative examples support these results., Comment: 17 pages, 6 figures

Blockchains have gained substantial attention from academia and industry for their ability to facilitate decentralized trust and communications. However, the rapid progress of quantum computing poses a significant threat to the security of existing blockchain technologies. Notably, the emergence of Shor's and Grover's algorithms raises concerns regarding the compromise of the cryptographic systems underlying blockchains. Consequently, it is essential to develop methods that reinforce blockchain technology against quantum attacks. In response to this challenge, two distinct approaches have been proposed. The first approach involves post-quantum blockchains, which aim to utilize classical cryptographic algorithms resilient to quantum attacks. The second approach explores quantum blockchains, which leverage the power of quantum computers and networks to rebuild the foundations of blockchains. This paper aims to provide a comprehensive overview and comparison of post-quantum and quantum blockchains while exploring open questions and remaining challenges in these domains. It offers an in-depth introduction, examines differences in blockchain structure, security, privacy, and other key factors, and concludes by discussing current research trends.

In this paper, the higher energy levels of the transmon qubit are taken into consideration to investigate the continuous variable entanglement generation between the transmon qubit and the single-mode cavity. Based on the framework of cavity quantum electrodynamics, we show the entanglement generation depends on the the driving field intensity, coupling strength, cavity field frequency, and qubit frequency. The numerical results show that strong entanglement can be generated by properly tuning these parameters. It is our hope that the results presented in this paper may lead to a better understanding of quantum entanglement generation in cavity QED system and provide new perspectives for further research in quantum information processing.

n this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In any empirical science, the first two features are obviously connected but, as is well known, among the different formulations and interpretations of non-relativistic quantum mechanics, only collapse models, as the paper well illustrates with a richness of details, have experimental consequences. Finally, we show that a clarification of the ontological intimations of collapse models is needed for at least three reasons: (1) to respond to the indispensable task of answering the question `what are collapse models (and in general any physical theory) about?'; (2) to achieve a deeper understanding of their different formulations; (3) to enlarge the panorama of possible readings of a theory, which historically has often played a fundamental heuristic role., Comment: 21 pages, LaTeX

Recently it is shown that the non-relativistic quantum formulations can be derived from a least observability principle [36]. In this paper, we apply the principle to massive scalar fields, and derive the Schr\"{o}dinger equation of the wave functional for the scalar fields. The principle extends the least action principle in classical field theory by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a field needs to exhibit in order to be observable. Second, there are constant random field fluctuations. A novel method is introduced to define the information metrics to measure additional observable information due to the field fluctuations, \added{which is then converted to the additional action through the first assumption.} Applying the variation principle to minimize the total actions allows us to elegantly derive the transition probability of field fluctuations, the uncertainty relation, and the Schr\"{o}dinger equation of the wave functional. Furthermore, by defining the information metrics for field fluctuations using general definitions of relative entropy, we obtain a generalized Schr\"{o}dinger equation of the wave functional that depends on the order of relative entropy. Our results demonstrate that the extended least action principle can be applied to derive both non-relativistic quantum mechanics and relativistic quantum scalar field theory. We expect it can be further used to obtain quantum theory for non-scalar fields., Comment: 15 pages. Add journal reference. This is a companion paper to arXiv:2302.14619. It extends the applicability of the least observability principle introduced in arXiv:2302.14619 to quantum scalar field theory

In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent., Comment: 59 pages, 11 figures, submission to the second journal special issue dedicated to the memory of G\"oran Lindblad, sequel to arXiv:2307.14932

Recent studies have increasingly focused on the effect of relativistic motion on quantum coherence. Prior research predominantly examined the influence of relative motion on basis-dependent quantum coherence, underscoring its susceptibility to decoherence under accelerated conditions. Yet, the effect of relativistic motion on basis-independent quantum coherence, which is critical for understanding the intrinsic quantum features of a system, remains an interesting open question. This paper addresses this question by examining how total, collective, and localized coherence are affected by acceleration and coupling strength. Our analysis reveals that both total and collective coherence significantly decrease with increasing acceleration and coupling strength, ultimately vanishing at high levels of acceleration. This underscores the profound impact of Unruh thermal noise. Conversely, localized coherence exhibits relative stability, decreasing to zero only under the extreme condition of infinite acceleration. Moreover, we demonstrate that collective, localized, and basis-independent coherence collectively satisfy the triangle inequality. These findings are crucial for enhancing our understanding of quantum information dynamics in environments subjected to high acceleration and offer valuable insights on the behavior of quantum coherence under relativistic conditions., Comment: 7 pages, 3 figures

The causal modelling of Bell experiments relies on three fundamental assumptions: locality, freedom of choice, and arrow-of-time. It turns out that nature violates Bell inequalities, which entails the failure of at least one of those assumptions. Since rejecting any of them - even partially - proves to be enough to explain the observed correlations, it is natural to ask about the cost in each case. This paper follows up on the results in PNAS 118 e2020569118 (2021), showing the equivalence between the locality and free choice assumptions, adding to the picture retro-causal models explaining the observed correlations. Here, we consider more challenging causal scenarios which allow only single-arrow type violations of a given assumption. The figure of merit chosen for the comparison of the causal cost is defined as the minimal frequency of violation of the respective assumption required for a simulation of the observed experimental statistics., Comment: 14 pages, 4 figures

In the realm weak force sensing, an important issue is to suppress fundamental noise (quantum noise and thermal noise), as they limit the accuracy of force measurement. In this paper, we investigate a weak force sensing scheme that combines a degenerate optical parametric amplifier (OPA) and an auxiliary mechanical oscillator into a cavity optomechanical system to reduce quantum noise. We demonstrate that the noise reduction of two coupled oscillators depends on their norm mode splitting. and provide a classic analogy and quantum perspective for further clarification. Besides, the noise reduction mechanism of OPA is to reduce the fluctuation of photon number and enhance the squeezing of the cavity field. We propose a specific design aimed at enhancing the joint effect of both, beyond what can be achieved using OPA alone or two series coupled oscillators. This scheme provides a new perspective for deeper understanding of cavity field squeezing and auxiliary oscillator in force sensing., Comment: 9 pages,10 figures

It is well-known from the representation theory of particle physics that the tensor product of two fundamental representation of SU(2) and SU(3) group can be decomposed to obtain the desired spectrum of the physical states. In this paper, we apply this tenet in case of two {\it non-local} qubits and qutrits, which leads the complete spectrum of their entangled states in their respective basis. For qutrit system, the study of their properties reveals the existence of a new $\sqrt{2}$ inequality, in addition to usual Bell-CHSH type $2\sqrt{2}$ inequality, which is significant from the experimental point of view., Comment: 14 pages, Replaces the withdrawn manuscript (arXiv:quant-ph:1911.03628)

The analysis of empirical data through model-free inequalities leads to the conclusion that violations of Bell-type inequalities by empirical data cannot have any significance unless one believes that the universe operates according to the rules of a mathematical model., Comment: Expanded version of the paper published in Annals of Physics 469 (2024) 169742. arXiv admin note: text overlap with arXiv:2304.03962

Context: The emergence of quantum computing proposes a revolutionary paradigm that can radically transform numerous scientific and industrial application domains. The ability of quantum computers to scale computations beyond what the current computers are capable of implies better performance and efficiency for certain algorithmic tasks. Objective: However, to benefit from such improvement, quantum computers must be integrated with existing software systems, a process that is not straightforward. In this paper, we propose a unified execution model that addresses the challenges that emerge from building hybrid classical-quantum applications at scale. Method: Following the Design Science Research methodology, we proposed a convention for mapping quantum resources and artifacts to Kubernetes concepts. Then, in an experimental Kubernetes cluster, we conducted experiments for scheduling and executing quantum tasks on both quantum simulators and hardware. Results: The experimental results demonstrate that the proposed platform Qubernetes (or Kubernetes for quantum) exposes the quantum computation tasks and hardware capabilities following established cloud-native principles, allowing seamless integration into the larger Kubernetes ecosystem. Conclusion: The quantum computing potential cannot be realised without seamless integration into classical computing. By validating that it is practical to execute quantum tasks in a Kubernetes infrastructure, we pave the way for leveraging the existing Kubernetes ecosystem as an enabler for hybrid classical-quantum computing.

The multi-particle Arnol'd cat is a generalization of the Hamiltonian system, both classical and quantum, whose period evolution operator is the renown map that bears its name. It is obtained following the Joos-Zeh prescription for decoherence, by adding a number of scattering particles in the configuration space of the cat. Quantization follows swiftly, if the Hamiltonian approach, rather than the semiclassical, is adopted. I have studied this system in a series of previous works, focusing on the problem of quantum-classical correspondence. In this paper I test the dynamics of this system by two related yet different indicators: the time autocorrelation function of the canonical position and the out of time correlator of position and momentum.

Weak-value amplification (WVA) is a metrological protocol that effectively amplifies ultra-small physical effects, making it highly applicable in the fields of quantum sensing and metrology. However, the amplification effect is achieved through post-selection, which leads to a significant decrease in signal intensity. Consequently, there is a heated debate regarding the trade-off between the amplification effect and the success probability of post-selection, questioning whether WVA surpasses conventional measurement (CM) in terms of measurement precision. Extensive research indicates that the specific theoretical assumptions and experimental conditions play crucial roles in determining the respective advantages of WVA and CM. WVA provides new perspectives for recognizing the important role of post-selection in precision metrology. It demonstrates significant advantages in two aspects: (i) WVA based on the phase space interaction provides feasible strategies to practically achieve the Heisenberg-scaling precision using only classical resources. (ii) WVA exhibits robustness against certain types of technical noise and imperfections of detectors. Moreover, WVA allows for various modifications to extend the applicable scope and enhance the metrological performance in corresponding situations. Despite substantial progress in recent years, the inherent connection between the advantages of WVA and its unique features remains incompletely understood. In this paper, we systematically review the recent advances in the WVA scheme, with a particular focus on the ultimate precision of WVA under diverse conditions. Our objective is to provide a comprehensive perspective on the benefits of WVA in precision measurement and facilitate the realization of its full potential., Comment: 34 pages, 15 figures

In this paper, using the Lewis-Riesenfeld method, we determine the explicit form of the wavefunctions of one- and three-dimensional harmonic oscillators with time-dependent mass and frequency within the framework of the Dunkl derivative, which leads to the derivation of a parity-dependent of the invariant and auxiliary equation., Comment: 11 pages

We study the recent gravitational analogue of the Aharonov-Bohm effect for a classical system, namely a complex scalar field. We use this example to demonstrate that the Aharonov-Bohm effect in principle has nothing to do with quantum-mechanics. We then discuss how this classical field description can be connected to the standard one particle quantum description of the Aharonov-Bohm effect., Comment: Preprint version of paper accepted in Modern Physics Letters A. Comments are welcome

The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades., Comment: 36 pages. 2 figures

In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is the coupling between the particle and an ancillary spin-1/2 degree of freedom. This allows us to reconstruct tomographically the scattering amplitudes, which are in general complex numbers, from the readout of one qubit. Applications of our results are discussed., Comment: 9+4 pages, 8+6 figures. v2: corrections, according to referee suggestions: version published in the journal

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational tasks, these noisy-intermediate scale quantum (NISQ) processors are still too small and non-robust to be directly useful for any real-world applications. In this paper, we describe NASA's work in assessing and advancing the potential of quantum computing. We discuss advances in algorithms, both near- and longer-term, and the results of our explorations on current hardware as well as with simulations, including illustrating the benefits of algorithm-hardware co-design in the NISQ era. This work also includes physics-inspired classical algorithms that can be used at application scale today. We discuss innovative tools supporting the assessment and advancement of quantum computing and describe improved methods for simulating quantum systems of various types on high-performance computing systems that incorporate realistic error models. We provide an overview of recent methods for benchmarking, evaluating, and characterizing quantum hardware for error mitigation, as well as insights into fundamental quantum physics that can be harnessed for computational purposes., Comment: 27 pages, 0 figures

Matrix product state (MPS) offers a framework for encoding classical data into quantum states, enabling the efficient utilization of quantum resources for data representation and processing. This research paper investigates techniques to enhance the efficiency and accuracy of MPS representations specifically designed for encoding classical data. Based on the observations that MPS truncation error depends on the pattern of the classical data, we devised an algorithm that finds optimal qubit mapping for given classical data, thereby improving the efficiency and fidelity of the MPS representation. Furthermore, we evaluate the impact of the optimized MPS in the context of quantum classifiers, demonstrating their enhanced performance compared to the conventional mapping. This improvement confirms the efficacy of the proposed techniques for encoding classical data into quantum states. MPS representation combined with optimal qubit mapping can pave a new way for more efficient and accurate quantum data representation and processing., Comment: 11 pages, 15 figures, The current version represents the initial submission and differs significantly from the final published version. Please check the official publication in Physics Letters A for the most up-to-date and comprehensive content

Many-body quantum dynamics defined on a spatial lattice and in discrete time -- either as stroboscopic Floquet systems or quantum circuits -- has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with $q$ states per site, defined on the square lattice by a complex partition function and paremeterized in terms of $q\times q$ Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata [J. Math. Phys. 49, 112104 (2008)] and in the $q\to\infty$ limit to the classical spatiotemporal cat model of many body chaos [Nonlinearity 34, 2800 (2021)]. We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper [Phys. Rev. B 105, 144306 (2022)] can be reinterpreted in purely graphical terms and directly applied here.

There is a growing demand for quantum computing across various sectors, including finance, materials and studying chemical reactions. A promising implementation involves semiconductor qubits utilizing quantum dots within transistors. While academic research labs currently produce their own devices, scaling this process is challenging, requires expertise, and results in devices of varying quality. Some initiatives are exploring the use of commercial transistors, offering scalability, improved quality, affordability, and accessibility for researchers. This paper delves into potential realizations and the feasibility of employing off-the-shelf commercial devices for qubits. It addresses challenges such as noise, coherence, limited customizability in large industrial fabs, and scalability issues. The exploration includes discussions on potential manufacturing approaches for early versions of small qubit chips. The use of state-of-the-art transistors as hosts for quantum dots, incorporating readout techniques based on charge sensing or reflectometry, and methods like electron shuttling for qubit connectivity are examined. Additionally, more advanced designs, including 2D arrays and crossbar or DRAM-like access arrays, are considered for the path toward accessible quantum computing.

The paper develops a methodology for the design of coherent equalizing filters for quantum communication channels. Given a linear quantum system model of a quantum communication channel, the aim is to obtain another quantum system which, when coupled with the original system, mitigates degrading effects of the environment. The main result of the paper is a systematic equalizer synthesis algorithm which relies on methods of state-space robust control design via semidefinite programming.

The Ising model is defined by an objective function using a quadratic formula of qubit variables. The problem of an Ising model aims to determine the qubit values of the variables that minimize the objective function, and many optimization problems can be reduced to this problem. In this paper, we focus on optimization problems related to permutations, where the goal is to find the optimal permutation out of the $n!$ possible permutations of $n$ elements. To represent these problems as Ising models, a commonly employed approach is to use a kernel that utilizes one-hot encoding to find any one of the $n!$ permutations as the optimal solution. However, this kernel contains a large number of quadratic terms and high absolute coefficient values. The main contribution of this paper is the introduction of a novel permutation encoding technique called dual-matrix domain-wall, which significantly reduces the number of quadratic terms and the maximum absolute coefficient values in the kernel. Surprisingly, our dual-matrix domain-wall encoding reduces the quadratic term count and maximum absolute coefficient values from $n^3-n^2$ and $2n-4$ to $6n^2-12n+4$ and $2$, respectively. We also demonstrate the applicability of our encoding technique to partial permutations and Quadratic Unconstrained Binary Optimization (QUBO) models. Furthermore, we discuss a family of permutation problems that can be efficiently implemented using Ising/QUBO models with our dual-matrix domain-wall encoding., Comment: 26 pages, 9 figures

Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen-Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods - whose complexity does not scale up with the dimension - for generating such non-Kochen-Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure., Comment: 19 pages, 5 figures, 1 table; 8-dim part of Fig. 3 has been corrected ((h) and (i) are not isomorphic); Nothing else in the rest of the paper is affected by this correction; The correction is published in Entropy 2024, 26(2), 100; https://doi.org/10.3390/e26020100

The interaction energy between two atoms is crucially dependent on the quantum state of the two-atom system. In this paper, it is demonstrated that a steady resonance interaction energy between two atoms exists when the atoms are in a certain type of coherent superposition of single-excitation states. The interaction is tree-level classical in the sense of the Feynman diagrams. A quantity called quantum classicality is defined in the present paper, whose nonzero-ness ensures the existence of this interaction. The dependence of the interatomic interaction on the quantum nature of the state of the two-atom system may potentially be tested with Rydberg atoms., Comment: 6 pages, 0 figure, published version

Over the past few decades, significant progress has been made in quantum information technology, from theoretical studies to experimental demonstrations. Revolutionary quantum applications are now in the limelight, showcasing the advantages of quantum information technology and becoming a research hotspot in academia and industry. To enable quantum applications to have a more profound impact and wider application, the interconnection of multiple quantum nodes through quantum channels becomes essential. Building an entanglement-assisted quantum network, capable of realizing quantum information transmission between these quantum nodes, is the primary goal. However, entanglement-assisted quantum networks are governed by the unique laws of quantum mechanics, such as the superposition principle, the no-cloning theorem, and quantum entanglement, setting them apart from classical networks. Consequently, fundamental efforts are required to establish entanglement-assisted quantum networks. While some insightful surveys have paved the way for entanglement-assisted quantum networks, most of these studies focus on enabling technologies and quantum applications, neglecting critical network issues. In response, this paper presents a comprehensive survey of entanglement-assisted quantum networks. Alongside reviewing fundamental mechanics and enabling technologies, the paper provides a detailed overview of the network structure, working principles, and development stages, highlighting the differences from classical networks. Additionally, the challenges of building wide-area entanglement-assisted quantum networks are addressed. Furthermore, the paper emphasizes open research directions, including architecture design, entanglement-based network issues, and standardization, to facilitate the implementation of future entanglement-assisted quantum networks., Comment: 58 pages,34 figures, published in IEEE Communications Surveys & Tutorials 2023 (URL: https://ieeexplore.ieee.org/abstract/document/10177948)

In a recent paper (arXiv:2206.05152v4), using the exact diagonalization technique, I calculated the energy and other physical properties (electron density, pair correlation function) of a system of $N\le 7$ two-dimensional electrons at the Landau level filling factor $\nu=1/3$, and showed that the variational many-body wave function proposed for this filling factor by Laughlin is far from the true ground state. In this paper I continue to study exact properties of a small ($N\le 7$) system of two-dimensional electrons lying on the lowest Landau level. I analyze the energies and electron densities of the systems with $N\le 7$ electrons continuously as a function of the magnetic field in the range $1/4\lesssim\nu<1$. The physical mechanisms of the appearance of energy gaps in many-particle electron spectra are elucidated. The results obtained clarify the true nature of the ground and excited states of the considered systems., Comment: 22 pages, 15 figures, 10 tables. Part II of the theory of the fractional quantum Hall effect; for the first part see arXiv:2206.05152v4

An AdS eternal black hole in equilibrium with a finite temperature bath presents a Hawking-like information paradox due to a continuous exchange of radiation with the bath. The non-perturbative gravitational effect, the replica wormhole, cures this paradox by introducing a non-trivial entanglement wedge for the bath after Page time. In this paper, we analyse the theory dependence of this non-perturbative effect by randomising the boundary conditions of some of the bulk matter fields. We explicitly analyse this in JT gravity by introducing a matter CFT in the AdS region with random boundary conditions at the AdS boundary that are drawn from a distribution. Using the island formula and the extended strong subadditivity due to Carlen and Lieb, we show that at late times the black hole interior is contained inside the entanglement wedge of a reference Hilbert space that encodes the information about the random boundary conditions. Consequently, the reconstruction of the black hole interior from the radiation, in particular the region near the singularity, requires a detailed knowledge of the theory., Comment: Arguments in the previous version depended crucially on an assumption in section 4, which may not hold in general. In this version without resorting to any assumptions, we use the extended strong subadditivity due to Carlen and Lieb and reach the same conclusion. The title and the entire presentation of the paper has been changed

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost as compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understanding how energy is dissipated in realistic open quantum system dynamics.

Dynamical decoupling (DD) is a promising technique for mitigating errors in near-term quantum devices. However, its effectiveness depends on both hardware characteristics and algorithm implementation details. This paper explores the synergistic effects of dynamical decoupling and optimized circuit design in maximizing the performance and robustness of algorithms on near-term quantum devices. By utilizing eight IBM quantum devices, we analyze how hardware features and algorithm design impact the effectiveness of DD for error mitigation. Our analysis takes into account factors such as circuit fidelity, scheduling duration, and hardware-native gate set. We also examine the influence of algorithmic implementation details, including specific gate decompositions, DD sequences, and optimization levels. The results reveal an inverse relationship between the effectiveness of DD and the inherent performance of the algorithm. Furthermore, we emphasize the importance of gate directionality and circuit symmetry in improving performance. This study offers valuable insights for optimizing DD protocols and circuit designs, highlighting the significance of a holistic approach that leverages both hardware features and algorithm design for the high-quality and reliable execution of near-term quantum algorithms.

We consider a quantum system of large size $N$ and its subsystem of size $L$ assuming that $N$ is much larger than $L$, which can also be sufficiently large, i.e., $1 \ll L \lesssim N $. A widely accepted mathematical version of this heuristic inequality is the asymptotic regime of successive limits: first the macroscopic limit $N \to \infty$, then an asymptotic analysis of the entanglement entropy as $L \to \infty$. In this paper, we consider another version of the above heuristic inequality: the regime of asymptotically proportional $L$ and $N$, i.e., the simultaneous limits $L \to \infty,\; N \to \infty, L/N \to \lambda >0$. Specifically, we consider the system of free fermions which is in its ground state and such that its one-body Hamiltonian is a large random matrix, that is often used to model the long-range hopping. By using random matrix theory, we show that in this case, the entanglement entropy obeys the volume law known for systems with short-ranged hopping but described either by a mixed state or a pure strongly excited state of the Hamiltonian. We also give a streamlined proof of Page's formula for the entanglement entropy of the black hole radiation for a wide class of typical ground states, thereby proving the universality of the formula.

We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. In this paper we suggest that the two components of the wave function represent the system described by the Hamiltonian H in two different asymptotic regions of spacetime and we show that the non-linear terms can be viewed as giving rise to gravitational effects., Comment: 1+17 pages; 1 figure; conforms to published version

Variational quantum circuits are one of the promising ways to exploit the advantages of quantum computing in the noisy intermediate-scale quantum technology era. The design of the quantum circuit architecture might greatly affect the performance capability of the quantum algorithms. The quantum architecture search is the process of automatically designing quantum circuit architecture, aiming at finding the optimal quantum circuit composition architecture by the algorithm for a given task, so that the algorithm can learn to design the circuit architecture. Compared to manual design, quantum architecture search algorithms are more effective in finding quantum circuits with better performance capabilities. In this paper, based on the deep reinforcement learning, we propose an approach for quantum circuit architecture search. The sampling of the circuit architecture is learnt through reinforcement learning based controller. Layer-based search is also used to accelerate the computational efficiency of the search algorithm. Applying to data classification tasks we show that the method can search for quantum circuit architectures with better accuracies. Moreover, the circuit has a smaller number of quantum gates and parameters., Comment: Comments are welcome

We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with the non-perturbative behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1) dimensions. Our results show the existence of two types of boundary conditions which give rise to two different asymptotic exponential decay regimes of the Casimir energy at large distances. The two families are distinguished by the feature that the boundary conditions involve or not interrelations between the behaviour of the fields at the two boundaries. Non-perturbative numerical simulations and analytical arguments show such an exponential decay for Dirichlet boundary conditions of SU(2) gauge theories. The verification that this behaviour is modified for other types of boundary conditions requires further numerical work. Subdominant corrections in the low-temperature regime are very relevant for numerical simulations, and they are also analysed in this paper.

If an asymmetry in time does not arise from the fundamental dynamical laws of physics, it may be found in special boundary conditions. The argument normally goes that since thermodynamic entropy in the past is lower than in the future according to the Second Law of Thermodynamics, then tracing this back to the time around the Big Bang means the universe must have started off in a state of very low thermodynamic entropy: the Thermodynamic Past Hypothesis. In this paper, we consider another boundary condition that plays a similar role, but for the decoherent arrow of time, i.e. the quantum state of the universe is more mixed in the future than in the past. According to what we call the Entanglement Past Hypothesis, the initial quantum state of the universe had very low entanglement entropy. We clarify the content of the Entanglement Past Hypothesis, compare it with the Thermodynamic Past Hypothesis, and identify some challenges and open questions for future research., Comment: 10 pages, no figures

Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to change the physical Hilbert-space norm. Thus, in a preselected Hamiltonian $H(\lambda)=H_0+\lambda\,H_1$ the size (and, hence, influence) of the perturbation cannot always be kept under a reliable control. Often, an enhanced sensitivity to perturbations is observed, for this reason, in open quantum systems. Second, even when we consider just a closed quantum system in which the influence of $H_1\neq H_1^\dagger$ is guaranteed to be small, the correct probabilistic interpretation of the system remains ambiguous, mainly due to the non-uniqueness of the physical Hilbert-space inner-product metric~$\Theta$. Third, even if we decide to ignore the ambiguity and if we pick up just any one of the eligible metrics (which reduces the scope of the theory of course), such a choice would still vary with $\lambda$. In our paper it is shown that all of these three obstacles can be circumvented via just a mild amendment of the Rayleigh-Schr\"{o}dinger perturbation-expansion approach. The flexibility of $\Theta=\Theta(\lambda)$ is shown to remain tractable while opening several new model-building horizons including the study of generic random perturbations and/or of multiple specific non-Hermitian toy models. In parallel, several paradoxes and open questions are shown to survive., Comment: 33 pp

Although quantum entanglement is an important resource, its characterization is quite challenging. The partial transposition is a common method to detect bipartite entanglement. In this paper, the authors study the partial-transpose(PT)-moments of two-qubit states,and completely describe the whole region, composed of the second and third PT-moments, for all two-qubit states. Furthermore, they determine the accurate region corresponding to all entangled two-qubit states. The states corresponding to those boundary points of the whole region, and to the border lines between separable and entangled states are analyzed. As an application, they characterize the entangled region of PT-moments for the two families of Werner states and Bell-diagonal states. The relations between entanglement and the pairs of PT-moments are revealed from these typical examples. They also numerically plot the whole region of possible PT-moments for all two-qubit X-states, and find that this region is almost the same as the whole region of PT-moments for all two-qubit states. Moreover, they extend their results to detect the entanglement of multiqubit states. By utilizing the PT-moment-based method to characterize the entanglement of the multiqubit states mixed by the GHZ and W states, they propose an operational way of verifying the genuine entanglement in such states., Comment: 31 pages, LaTeX, 9 figures

Secret key exchange relies on the creation of correlated signals, serving as the raw resource for secure communication. Thermal states, exhibit Hanbury Brown and Twiss correlations, which offer a promising avenue for generating such signals. In this paper, we present an experimental implementation of a central broadcast thermal state quantum key distribution (QKD) protocol in the microwave region. Our objective is to showcase a straightforward method of QKD utilizing readily available broadcasting equipment. Unlike conventional approaches to thermal state QKD, we leverage displaced thermal states. These states enable us to share the output of a thermal source among Alice, Bob, and Eve via both waveguide channels and free space. Through measurement and conversion into bit strings, our protocol produces key-ready bit strings without the need for specialized equipment. By harnessing the inherent noise in thermal broadcasts, our setup facilitates the recovery of distinct bit strings by all parties involved., Comment: 18 pages, 10 figures

Recent theoretical investigations have revealed unconventional transport mechanisms within high Brilliouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static or energetic confinement observed in traditional wave guides or one-dimensional electron wires. The quantum properties of superwires give rise to elastic dynamical tunneling, linking disjoint regions of the corresponding classical phase space, and enabling the emergence of several parallel channels. This paper provides the underlying theory and mechanisms that facilitate dynamical tunneling assisted by chaos in periodic lattices. Moreover, we show that the mechanism of dynamical tunneling can be effectively conceptualized through the lens of a paraxial approximation. Our results further reveal that superwires predominantly exist within flat bands, emerging from eigenstates that represent linear combinations of conventional degenerate Bloch states. Finally, we quantify tunneling rates across various lattice configurations, and demonstrate the tunneling can be suppressed in a controlled fashion, illustrating potential implications in future nanodevices., Comment: 12 pages, 6 Figures

We investigate nonclassical properties of a state generated by the interaction of a three-level atom with a quantized cavity field and an external classical driving field. In this study, the fields being degenerate in frequency, are highly detuned from the atom. The atom interacts with the quantized field in a dispersive manner. The experimental set-up involves a three-level atom passing through a cavity and interacting dispersively with the cavity field mode. Simultaneously, the atom interacts with an external classical field that is in resonance with the cavity field. The three-level atom can enter the cavity in one of the bare states $\ket{e}$, $\ket{f}$ or $\ket{g}$ or in a superposition of two of these states. In this paper, we consider superposition of $\ket{e}$ and $\ket{f}$. In our analysis, we focus on the statistical properties of the cavity field after interacting with the atom. The state vector $|\psi(t)\rangle$ describes the entire atom-field system but we analyze the properties of the cavity field independently neglecting the atomic component of the system. For this the atom part is traced out from $|\psi(t)\rangle$ to acquire the cavity field state only, denoted by $\ket{\psi_{ f}(t)}$. We evaluate different nonclassical measures including photon number distribution, Mandel's $Q_M$ parameter, squeezing properties $S_x$ and $S_p$, Wigner distribution, $Q_f$ function, second-order correlation function $g^2(0)$ etc. for the obtained cavity field state., Comment: 16 pages, 8 figures, Accepted in Int. J. Mod. Phys. B

The construction of time of arrival (TOA) operators canonically conjugate to the system Hamiltonian entails finding the solution of a specific second-order partial differential equation called the time kernel equation (TKE). In this paper, we provide an exact analytic solution of the TKE for a special class of potentials satisfying a specific separability condition. The solution enables us to investigate the time evolution of the eigenfunctions of the conjugacy-preserving TOA operators (CPTOA) and show that they exhibit unitary arrival at the intended arrival point at a time equal to their corresponding eigenvalues. We also compare the dynamics between the TOA operators constructed by quantization and those independent of quantization for specific interaction potentials. We find that the CPTOA operator possesses smoother and sharper unitary dynamics over the Weyl-quantized one within numerical accuracy., Comment: 23 pages

A spin-photon interface based on the luminescence of a singly charged quantum dot in a micropillar cavity allows for the creation of photonic entangled states. Current devices suffer from cavity birefringence, which limits the generation of spin-photon entanglement. In this paper, we theoretically study the light absorption and emission by the interface with an anisotropic cavity and derive the maximal excitation and spin-photon entanglement conditions. We show that the concurrence of the spin-photon state equal to one and complete quantum dot population inversion can be reached for a micropillar cavity with any degree of birefringence by tuning the quantum dot resonance strictly between the cavity modes. This sweet spot is also valid for generating a multiphoton cluster state, as we demonstrate by calculating the three-tangle and fidelity with the maximally entangled state., Comment: 10 pages, 4 figures