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Quantum physics modeling is technically complex and often non-descriptive. This article presents some approaches how quantum physical ideas can be represented by haptic models. For this purpose, models made from 3D printers, models made from paper strips, and models made from textiles are compared. A novelty is the use of zippers instead of paper strips, which can be easily ''cut'' and ''glued'' together. The models have been developed primarily with the aim of conveying and visualizing topological ideas with little basic mathematical knowledge., Comment: Translation, original title: Quantenphysik zum Anfassen - Von Papierstreifen zu Rei{\ss}verschl\"ussen. 4 pages, 7 figures

QBism has long recognized quantum states, POVM elements, Kraus operators, and even unitary operations to be cut from the same cloth: They all express aspects of an agent's personal belief system concerning the consequences (for her) of actions she might take on her external world. Such action-consequence pairs have conventionally been called "quantum measurements." The calculus of quantum theory is then viewed as an empirically motivated addition to Bayesian decision theory when brought to this notion of measurement. This radical approach has allowed QBism to eliminate the conceptual problems that plague other interpretations of quantum mechanics. However, one issue has remained elusive: If a QBist agent does not believe in the existence of an ontic (agent-independent) dynamical variable evolving over time, why would there be any constraints on her quantum state assignment in the absence of performing a measurement? Why would she introduce unitary or open-system quantum dynamics at all? Here, we present a representation theorem based on van Fraassen's reflection principle to answer these questions. Simply put, an agent's assignment of quantum dynamics represents her belief that a measurement action she is contemplating would not change her current odds for future gambles. A corollary to this approach is that one can make sense of "open-system dynamics" without ever introducing an "environment with a measurement record" as is common in decoherence accounts of quantum measurement. Instead, the QBist understanding of decoherence rests entirely on an agent's beliefs about the system of interest (not system plus environment) and her judgments about measurements she might perform on that system., Comment: 21 pages, 1 figure

We present the white paper developed during the QEYSSat 2.0 study, which was undertaken between June 2021 and March 2022. The study objective was to establish a technology road-map for a Canada-wide quantum network enabled by satellites. We survey the state-of-art in quantum communication technologies, identify the main applications and architectures, review the technical readiness levels and technology bottlenecks and identify a future mission scenario. We report the findings of a dedicated one-day workshop that included Canadian stakeholders from government, industry and academia to gather inputs and insights for the applications and technical road-map. We also provide an overview of the Quantum EncrYption and Science Satellite (QEYSSat) mission expected to launch in 2024-2025 and its anticipated outcomes. One of the main outcomes of this study is that developing the main elements for a Canada-wide quantum internet will have the highest level of impact, which includes Canada-wide entanglement distribution and teleportation. We present and analyze a possible future mission ('QEYSSat 2.0') that would enable a long range quantum teleportation across Canada as an important step towards this vision., Comment: 108 pages, 38 figures, white paper to be submitted to CJP

NEWFOCUS is an EU COST Action targeted at exploring radical solutions that could influence the design of future wireless networks. The project aims to address some of the challenges associated with optical wireless communication (OWC) and to establish it as a complementary technology to the radio frequency (RF)-based wireless systems in order to meet the demanding requirements of the fifth generation (5G) and the future sixth generation (6G) backhaul and access networks. Only 6G will be able to widely serve the exponential growth in connected devices (i.e., more than 500 billion) in 2030, real-time holographic communication, future virtual reality, etc. Space is emerging as the new frontier in 5 and 6G and beyond communication networks, where it offers high-speed wireless coverage to remote areas both in lands and sees. This activity is supported by the recent development of low-altitude Earth orbit satellite mega-constellations. The focus of this 2nd White Paper is on the use of OWC as an enabling technology for medium- and long-range links for deployment in (i) smart-cities and intelligent transportation systems; (ii) first- and last-mile access and backhaul/fronthaul wireless networks; (iii) hybrid free-space optics/RF adaptive wireless connections; (iv) space-to-ground, inter-satellite, ground-to-air, and air-to-air communications; and (v) underwater communications.

During the last two decades many new insights into the dynamics of strongly coupled quantum many-body systems have been obtained using gauge/gravity duality, with black holes often playing a universal role. In this white paper we summarize the results obtained and offer some outlook for future developments, including the ongoing mutually beneficial feedback loop with the study of more general, not necessarily holographic, quantum many-body systems., Comment: 18+24 pages

Progress in the quantum readout and control of mechanical devices from single atoms to large masses may enable a first generation of experiments probing the gravitational interaction in the quantum regime, conceivably within the next decade. In this Snowmass whitepaper, we briefly outline the possibilities and challenges facing the realization of these experiments. In particular, we emphasize the need for detailed theories of modifications to the usual effective QFT of gravitons in the infrared regime $E/L^3 \ll m_{\rm Pl}/\ell_{\rm Pl}^3$ in which these experiments operate, and relations to possible UV completions., Comment: Short contribution to Snowmass 2021. 5 pages, 1 figure. v2: typo fixed

We present a summary of recent progress and remaining challenges in applying the methods and ideas of quantum information theory to the study of quantum field theory and quantum gravity. Important topics and themes include: entanglement entropy in QFTs and what it reveals about RG flows, symmetries, and phases; scrambling, information spreading, and chaos; state preparation and complexity; classical and quantum simulation of QFTs; and the role of information in holographic dualities. We also highlight the ways in which quantum information science benefits from the synergy between the fields., Comment: 24 + 21 pages; contribution to Snowmass 2021; v2: references added

Quantum computing offers a new paradigm for advancing high-energy physics research by enabling novel methods for representing and reasoning about fundamental quantum mechanical phenomena. Realizing these ideals will require the development of novel computational tools for modeling and simulation, detection and classification, data analysis, and forecasting of high-energy physics (HEP) experiments. While the emerging hardware, software, and applications of quantum computing are exciting opportunities, significant gaps remain in integrating such techniques into the HEP community research programs. Here we identify both the challenges and opportunities for developing quantum computing systems and software to advance HEP discovery science. We describe opportunities for the focused development of algorithms, applications, software, hardware, and infrastructure to support both practical and theoretical applications of quantum computing to HEP problems within the next 10 years., Comment: A contribution to the 2021 Snowmass Proceedings, Computational Frontier, Topical Group on Quantum Computing

Black holes provide a window into the microscopic structure of spacetime in quantum gravity. Recently the quantum information contained in Hawking radiation has been calculated, verifying a key aspect of the consistency of black hole evaporation with quantum mechanical unitarity. This calculation relied crucially on recent progress in understanding the emergence of bulk spacetime from a boundary holographic description. Spacetime wormholes have played an important role in understanding the underpinnings of this result, and the precision study of such wormholes, in this and other contexts, has been enabled by the development of low-dimensional models of holography. In this white paper we review these developments and describe some of the deep open questions in this subject. These include the nature of the black hole interior, potential applications to quantum cosmology, the gravitational explanation of the fine structure of black holes, and the development of further connections to quantum information and laboratory quantum simulation., Comment: 16 + 17 pages. v2: references added

It has recently been theoretically shown that Quantum Memories (QM) could enable truly global quantum networking when deployed in space thereby surpassing the limited range of land-based quantum repeaters. Furthermore, QM in space could enable novel protocols and long-range entanglement and teleportation applications suitable for Deep-Space links and extended scenarios for fundamental physics tests. In this white paper we will make the case for the importance of deploying QMs to space, and also discuss the major technical milestones and development stages that will need to be considered., Comment: Toptical white paper submitted to National Academies of Sciences, Engineering and Medicine's Decadal Survey on Biological and Physical Sciences Research in Space 2023-2032

In the paper "Quantum theory cannot consistently describe the use of itself" by D. Frauchiger and R. Renner an atempt is made at proving a "no-go theorem" that states that either quantum theory cannot be universally applied, even to macroscopic systems, or some very intuitive properties concerning recursive reasoning and uniquenes of physical values must be false. In this paper, we give a concise description of the paper's result, and expose a detail in the proof., Comment: 3 pages

We present an English translation of Erwin Schr\"odinger's paper on "On the Reversal of the Laws of Nature". In this paper Schr\"odinger analyses the idea of time reversal of a diffusion process. Schr\"odinger's paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schr\"odinger also inspired the development of probabilistic interpretations of quantum mechanics by F\'enyes, Nelson and others as well as the notion of "Euclidean Quantum Mechanics" as probabilistic analogue of quantization. In the second part of the paper Schr\"odinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schr\"odinger's intuitions for contemporary developments in statistical nano-physics., Comment: Revised version. 24 pages, 2 figures. Introduction 2 pages, Translation of the german original pag. 3-10, Commentary pag 10-22

On the seminal paper written by Einstein, Podolsky and Rosen [1], a critique to the completeness of quantum mechanics was posed. Part of the critique consisted in the following argument: if quantum mechanics is complete, then, two physical quantities, with non-commuting operators, can have simultaneous reality. In this paper I aim to provide a pedagogical approach to the notions used in the EPR's argument., Comment: 12 pages, 2 figures

An attempt is made to avoid the difficulty of the infinite reaction of the electron on itself, which occurs in quantum electrodynamics, by introducing difference equations instead of differential equations. This vision allows the difficulty of the relativistic wave equation emphasised by Klein, for example, to be essentially eliminated., Comment: 4 pages, translated from: V. Ambarzumian and D. Ivanenko (1930). Zur Frage nach Vermeidung der unendlichen Selbstr\"uckwirkung des Elektrons. Zeitschrift f\"ur Physik, Vol.64: p.563--567

This paper reviews Holevo's contributions to quantum information theory during the 20 century. At that time, he mainly studied three topics, classical-quantum channel coding, quantum estimation with Cramero-Rao approach, and quantum estimation with the group covariant approach. This paper addresses these three topics., Comment: This paper has been acceepted for the publication in International Journal of Quantum Information on Apr 25, 2024

It has been shown that entropy differences between certain states of perturbative quantum gravity can be computed without specifying an ultraviolet completion. This is analogous to the situation in classical statistical mechanics, where entropy differences are defined but absolute entropy is not. Unlike in classical statistical mechanics, however, the entropy differences computed in perturbative quantum gravity do not have a clear physical interpretation. Here we construct a family of perturbative black hole states for which the entropy difference can be interpreted as a relative counting of states. Conceptually, this paper begins with the algebra of mass fluctuations around a fixed black hole background, and points out that while this is a type I algebra, it is not a factor and therefore has no canonical definition of entropy. As in previous work, coupling the mass fluctuations to quantum matter embeds the mass algebra within a type II factor, in which entropy differences (but not absolute entropies) are well defined. It is then shown that for microcanonical wavefunctions of mass fluctuation, the type II entropy difference equals the logarithm of the dimension of the extra Hilbert space that is needed to map one microcanonical window to another using gauge-invariant unitaries. The paper closes with comments on type II entropy difference in a more general class of states, where the von Neumann entropy difference does not have a physical interpretation, but "one-shot" entropy differences do., Comment: 5 pages

This paper presents a novel approach for minimizing the number of teleportations in Distributed Quantum Computing (DQC) using formal methods. Quantum teleportation plays a major role in communicating quantum information. As such, it is desirable to perform as few teleportations as possible when distributing a quantum algorithm on a network of quantum machines. Contrary to most existing methods which rely on graph-theoretic or heuristic search techniques, we propose a drastically different approach for minimizing the number of teleportations through utilizing formal methods. Specifically, the contributions of this paper include: the formal specification of the teleportation minimization problem in Alloy, the generalizability of the proposed Alloy specifications to quantum circuits with $n$-ary gates, the reusability of the Alloy specifications for different quantum circuits and networks, the simplicity of specifying and solving other problems such as load balancing and heterogeneity, and the compositionality of the proposed approach. We also develop a software tool, called qcAlloy, that takes as input the textual description of a quantum circuit, generates the corresponding Alloy model, and finally solves the minimization problem using the Alloy analyzer. We have experimentally evaluated qcAlloy for some of the circuits in the RevLib benchmark with more than 100 qubits and 1200 layers, and have demonstrated that qcAlloy outperforms one of the most efficient existing methods for most benchmark circuits in terms of minimizing the number of teleportations.

In this paper, we propose a quantum computing oriented benchmark for combinatorial optimization. This benchmark, coined as QOPTLib, is composed of 40 instances equally distributed over four well-known problems: Traveling Salesman Problem, Vehicle Routing Problem, one-dimensional Bin Packing Problem and the Maximum Cut Problem. The sizes of the instances in QOPTLib not only correspond to computationally addressable sizes, but also to the maximum length approachable with non-zero likelihood of getting a good result. In this regard, it is important to highlight that hybrid approaches are also taken into consideration. Thus, this benchmark constitutes the first effort to provide users a general-purpose dataset. Also in this paper, we introduce a first full solving of QOPTLib using two solvers based on quantum annealing. Our main intention with this is to establish a preliminary baseline, hoping to inspire other researchers to beat these outcomes with newly proposed quantum-based algorithms., Comment: 15 pages, 3 figures, 1 table

As quantum technology is advancing, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions without assuming a prior background in quantum computing. While this is a well-studied problem, optimization models that minimize the true objective have only been explored recently. This paper introduces a new optimization model and symmetry-breaking constraints that improve solving time by up to two orders of magnitude compared to earlier work when a Constraint Programming solver is used. Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits for well-known benchmarks. Finally, an extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with optimality guarantees.

In this paper, we introduce HamilToniQ, an open-source, and application-oriented benchmarking toolkit for the comprehensive evaluation of Quantum Processing Units (QPUs). Designed to navigate the complexities of quantum computations, HamilToniQ incorporates a methodological framework assessing QPU types, topologies, and multi-QPU systems. The toolkit facilitates the evaluation of QPUs' performance through multiple steps including quantum circuit compilation and quantum error mitigation (QEM), integrating strategies that are unique to each stage. HamilToniQ's standardized score, H-Score, quantifies the fidelity and reliability of QPUs, providing a multidimensional perspective of QPU performance. With a focus on the Quantum Approximate Optimization Algorithm (QAOA), the toolkit enables direct, comparable analysis of QPUs, enhancing transparency and equity in benchmarking. Demonstrated in this paper, HamilToniQ has been validated on various IBM QPUs, affirming its effectiveness and robustness. Overall, HamilToniQ significantly contributes to the advancement of the quantum computing field by offering precise and equitable benchmarking metrics., Comment: 11 pages, 13 figures

In this paper we examine one of the multiple applications of the theta operator xd/dx in quantum mechanics, namely, in the formalism of generalized hypergeometric coherent states (GHG CSs). These states are the most general coherent states, in the sense that from them, through particularization, all coherent states with physical meaning can be obtained. A series of new results were obtained and some already known ones were found / confirmed (the integral representations, as well as the Laplace transform of hypergeometric functions). To support the theoretical considerations presented above, we examined, as example, the quantum systems with a linear energy spectrum. The results obtained in this paper contribute to widening the area of applicability of the theta operator., Comment: 22 pages, NO figures

Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically analyze noisy analogue quantum simulation of geometrically local open quantum systems and provide evidence that this problem is both hard to simulate on classical computers and could be approximately solved on near-term quantum devices. First, given a noiseless quantum simulator, we show that the dynamics of local observables and the fixed-point expectation values of rapidly-mixing local observables in geometrically local Lindbladians can be obtained to a precision of $\varepsilon$ in time that is $\text{poly}(\varepsilon^{-1})$ and uniform in system size. Furthermore, we establish that the quantum simulator would provide an exponential advantage, in run-time scaling with respect to the target precision and either the evolution time (when simulating dynamics) or the Lindbladian's decay rate (when simulating fixed-points) over any classical algorithm for these problems unless BQP = BPP. We then consider the presence of noise in the quantum simulator in the form of additional geometrically-local Linbdladian terms. We show that the simulation tasks considered in this paper are stable to errors, i.e. they can be solved to a noise-limited, but system-size independent, precision. Finally, we establish that there are stable geometrically local Lindbladian simulation problems such that as the noise rate on the simulator is reduced, classical algorithms must take time exponentially longer in the inverse noise rate to attain the same precision unless BQP = BPP.

Quantum Monte Carlo integration (QMCI) provides a quadratic speed-up over its classical counterpart, and its applications have been investigated in various fields, including finance. This paper considers its application to risk aggregation, one of the most important numerical tasks in financial risk management. Risk aggregation combines several risk variables and quantifies the total amount of risk, taking into account the correlation among them. For this task, there exists a useful tool called copula, with which the joint distribution can be generated from marginal distributions with a flexible correlation structure. Classically, the copula-based method utilizes sampling of risk variables. However, this procedure is not directly applicable to the quantum setting, where sampled values are not stored as classical data, and thus no efficient quantum algorithm is known. In this paper, we propose a quantum algorithm for copula-based risk aggregation that is compatible with QMCI. In our algorithm, we first estimate each marginal distribution as a series of orthogonal functions, where the coefficients can be calculated with QMCI. Then, by plugging the marginal distributions into the copula and obtaining the joint distribution, we estimate risk measures using QMCI again. With this algorithm, nearly quadratic quantum speed-up can be obtained for sufficiently smooth marginal distributions.

This is the second in a series of "graphical grokking" papers in which we study how stabiliser codes can be understood using the ZX calculus. In this paper we show that certain complex rules involving ZX diagrams, called spider nest identities, can be captured succinctly using the scalable ZX calculus, and all such identities can be proved inductively from a single new rule using the Clifford ZX calculus. This can be combined with the ZX picture of CSS codes, developed in the first "grokking" paper, to give a simple characterisation of the set of all transversal diagonal gates at the third level of the Clifford hierarchy implementable in an arbitrary CSS code.

In this paper we present a modified version of the proof given Jing-Yang-Zhao's paper titled "Local Unitary Equivalence of Quantum States and Simultaneous Orthogonal Equivalence," which established the correspondance between local unitary equivalence and simultaneous orthogonal equivalence of $2$-qubits. Our modified proof utilizes a hypermatrix algebra framework, and through this framework we are able to generalize this correspondence to $3$-qubits. Finally, we apply a generalization of Specht's criterion (first proved in "Specht's Criterion for Systems of Linear Mappings" by V. Futorney, R. A. Horn, and V. V. Sergeichuk) to reduce the problem of local unitary equivalence of $3$-qubits to checking trace identities and a few other easy-to-check properties. We also note that all of these results can be extended to $2$ and $3$ qudits if we relax the notion of LU equivalence to quasi-LU equivalence, as defined in the aforementioned paper by Jing et. al.

Quantum computing is an exciting field with high disruptive potential, but very difficult to access. For this reason, numerous concepts are being developed worldwide on how quantum computing can be taught. 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 gave 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 platform's purpose is to make computer science education available to everyone free of charge. The nine quantum courses form a self-contained curriculum. A total of 17157 course attendances have been taken by 7413 natural persons, and the number is still rising. This paper presents the course concept and then evaluates the anonymized data on the background of the participants, their behavior in the courses, and their learning success. In the present paper for the first time such a large dataset of MOOC-based quantum computing education is analyzed. 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 correlatatd to following the didactic recommendations. The amount of data from such a large group of quantum computing learners offers numerous starting points for further research in the field of quantum computing education.

In a recent paper (Heras in $\href{https://doi.org/10.1140/epjp/s13360-023-03914-5}{{\rm Eur. Phys. J. Plus\, 138: 329, 2023}}$), we have demonstrated that when a dyon encircles an infinitely long solenoid enclosing electric and magnetic fluxes, its wave function accumulates a quantum phase invariant under electromagnetic duality transformations. In this paper, we show that this phase, in conjunction with the Witten effect, gives rise to a topological phase proportional to the vacuum angle $\theta$ and thereby connected with CP violation. We show that this phase becomes quantised in a vacuum state $\delta_{\theta}=n\theta$ and that the most general vacuum state associated with this quantisation identifies with an Abelian form of the $\theta$-vacua. We discuss two hypothetical interference effects in the vacuum where the angle $\theta$ could manifest., Comment: Published in The European Physical Journal Plus. See the related preceding paper, arXiv:1910.01117

Nonadiabatic holonomic quantum computation has been proposed as a method for implementing quantum logic gates with the same robustness as adiabatic holonomic quantum computation but with shorter execution times. In this paper, we establish an isoholonomic inequality for quantum gates, which provides a lower bound on the lengths of cyclic transformations of the computational space that generate a specific gate. Then, as a corollary, we derive a nonadiabatic execution time estimate for holonomic gates. In addition, we demonstrate that under certain dimensional conditions, the isoholonomic inequality is tight in the sense that every gate on the computational space can be implemented holonomically and unitarily in a time-optimal way. We illustrate the results by showing that the procedures for implementing a universal set of holonomic gates proposed in a pioneering paper on nonadiabatic holonomic quantum computation saturate the isoholonomic inequality and are thus time-optimal., Comment: 9 pages, 1 figure, 1 table, comments are welcome

In two recent papers Khrennikov uses what he calls Ozawa intersubjectivity theorem to claim that intersubjectivity is necessarily verified in quantum mechanics and to criticize QBism and more generally all interpretations that are perspectival. In agreement with two previous QBist papers, I explain here why Khrennikov proof is not valid but in contrast with one of these papers, I criticize the way intersubjectivity is dealt with in QBism.

What happens when an infinite number of players play a quantum game? In this paper, we will answer this question by looking at the emergence of cooperation in the presence of noise in a one-shot quantum Prisoner's dilemma (QuPD). We will use the numerical Agent-based model (ABM) and compare it with the analytical Nash equilibrium mapping (NEM) technique. To measure cooperation, we consider five indicators, i.e., game magnetization, entanglement susceptibility, correlation, player's payoff average, and payoff capacity, respectively. In quantum social dilemmas, entanglement plays a non-trivial role in determining the players' behavior in the thermodynamic limit, and we consider the existence of bipartite entanglement between neighboring players. For the five indicators in question, we observe \textit{first}-order phase transitions at two entanglement values, and these phase transition points depend on the payoffs associated with the QuPD game. We numerically analyze and study the properties of both the \textit{Quantum} and the \textit{Defect} phases of the QuPD via the five indicators. The results of this paper demonstrate that both ABM and NEM, in conjunction with the chosen five indicators, provide insightful information on cooperative behavior in the thermodynamic limit of the one-shot quantum Prisoner's dilemma., Comment: 16 pages, 7 figures

Language processing is at the heart of current developments in artificial intelligence, and quantum computers are becoming available at the same time. This has led to great interest in quantum natural language processing, and several early proposals and experiments. This paper surveys the state of this area, showing how NLP-related techniques including word embeddings, sequential models, attention, and grammatical parsing have been used in quantum language processing. We introduce a new quantum design for the basic task of text encoding (representing a string of characters in memory), which has not been addressed in detail before. As well as motivating new technologies, quantum theory has made key contributions to the challenging questions of 'What is uncertainty?' and 'What is intelligence?' As these questions are taking on fresh urgency with artificial systems, the paper also considers some of the ways facts are conceptualized and presented in language. In particular, we argue that the problem of 'hallucinations' arises through a basic misunderstanding: language expresses any number of plausible hypotheses, only a few of which become actual, a distinction that is ignored in classical mechanics, but present (albeit confusing) in quantum mechanics.

Post Quantum and Quantum Cryptography schemes are feasible quantum computer applications for 7G networks. These schemes could possibly replace existing schemes. These algorithms have been compromised by advances in quantum search algorithms run on quantum computers like Shor algorithm. Shor algorithm is a quantum algorithm for finding the prime factors of an integer which is the basis of existing algorithm. This has become an available quantum computer application putting the use of ESA algorithm at risk. Our recent paper provides a detailed survey of the work on post quantum and quantum cryptography algorithms with focus on their applicability in 7G networks. Since the paper focuses on the cryptography algorithms as a follow up, in this paper, we provide a new framework for quantum network optimization and survey in detail the work on enabling technologies (quantum hardware) for the practical implementation of these algorithms including the most important segments of quantum hardware in 7G. As always in engineering practice practical solutions are a compromise between the performance and complexity of the implementation. For this reason, as the main contribution, the paper presents a network and computer applications optimization framework that includes implementation imperfections. The tools should be useful in optimizing future generation practical computer system design. After that a comprehensive survey of the existing work on quantum hardware is presented pointing out the sources of these imperfections. This enables us to make a fair assessment of how much investment into quantum hardware improvements contributes to the performance enhancement of the overall system. In this way a decision can be made on proper partitioning between the investment in hardware and system level complexity.

This paper introduces Fermihedral, a compiler framework focusing on discovering the optimal Fermion-to-qubit encoding for targeted Fermionic Hamiltonians. Fermion-to-qubit encoding is a crucial step in harnessing quantum computing for efficient simulation of Fermionic quantum systems. Utilizing Pauli algebra, Fermihedral redefines complex constraints and objectives of Fermion-to-qubit encoding into a Boolean Satisfiability problem which can then be solved with high-performance solvers. To accommodate larger-scale scenarios, this paper proposed two new strategies that yield approximate optimal solutions mitigating the overhead from the exponentially large number of clauses. Evaluation across diverse Fermionic systems highlights the superiority of Fermihedral, showcasing substantial reductions in implementation costs, gate counts, and circuit depth in the compiled circuits. Real-system experiments on IonQ's device affirm its effectiveness, notably enhancing simulation accuracy.

This paper outlines an alternative approach to teaching quantum computing at the high school level, tailored for students with limited prior knowledge in advanced mathematics and physics. This approach diverges from traditional methods by building upon foundational concepts in classical computing before gradually introducing quantum mechanics, thereby simplifying the entry into this complex field. The course was initially implemented in a program for gifted high school students under the Hong Kong Education Bureau and received encouraging feedback, indicating its potential effectiveness for a broader student audience. A key element of this approach is the practical application through portable NMR quantum computers, which provides students with hands-on experience. The paper describes the structure of the course, including the organization of the lectures, the integration of the hardware of the portable nuclear magnetic resonance (NMR) quantum computers, the Gemini/Triangulum series, and detailed lecture notes in an appendix. The initial success in the specialized program and ongoing discussions to expand the course to regular high schools in Hong Kong and Shenzhen suggest the viability of this approach for wider educational application. By focusing on accessibility and student engagement, this approach presents a valuable perspective on introducing quantum computing concepts at the high school level, aiming to enhance student understanding and interest in the field., Comment: 10 pages, 6 figures for main manuscript, with an appendix of 183 pages

In this paper, we provide an algebraic condition on any $2n \times 2n$ real symmetric positive definite matrix which is necessary and sufficient for the matrix to be diagonalized by an orthosymplectic matrix in the sense of Williamson's theorem., Comment: This work is going to become part of a bigger project that would contain wider applications of the main result presented in the paper

The recent paper (IEEE Trans. IT 69, 1680) introduced an analytical method for calculating the channel capacity without the need for iteration. This method has certain limitations that restrict its applicability. Furthermore, the paper does not provide an explanation as to why the channel capacity can be solved analytically in this particular case. In order to broaden the scope of this method and address its limitations, we turn our attention to the reverse em-problem, proposed by Toyota (Information Geometry, 3, 1355 (2020)). This reverse em-problem involves iteratively applying the inverse map of the em iteration to calculate the channel capacity, which represents the maximum mutual information. However, several open problems remained unresolved in Toyota's work. To overcome these challenges, we formulate the reverse em-problem based on Bregman divergence and provide solutions to these open problems. Building upon these results, we transform the reverse em-problem into em-problems and derive a non-iterative formula for the reverse em-problem. This formula can be viewed as a generalization of the aforementioned analytical calculation method. Importantly, this derivation sheds light on the information geometrical structure underlying this special case. By effectively addressing the limitations of the previous analytical method and providing a deeper understanding of the underlying information geometrical structure, our work significantly expands the applicability of the proposed method for calculating the channel capacity without iteration.

Space-time dependence of imaginary-time propagators, vital for \textit{ab initio} and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X {\bf 13}, 021015 (2023)]. However, the impact of system parameters, like temperature, on data size remains underexplored. This paper provides a comprehensive numerical analysis of the compactness of local imaginary-time propagators in QTT for one-time/-frequency objects and two-time/-frequency objects, considering truncation in terms of the Frobenius and maximum norms. We employ random pole models to study worst-case scenarios. The numerical analysis reveals several key findings. For one-time/-frequency objects and two-time/-frequency objects, the bond dimensions saturate at low temperatures, especially for truncation in terms of the Frobenius norm. We provide counting-number arguments for the saturation of bond dimensions for the one-time/-frequency objects, while the origin of this saturation for two-time/-frequency objects remains to be clarified. This paper's findings highlight the critical need for further research on the selection of truncation methods, tolerance levels, and the choice between imaginary-time and imaginary-frequency representations in practical applications., Comment: 21 pages, 11 figures

In recent years, there has been tremendous focus on identifying whether effective descriptions of open quantum systems such as master equations, provide the correct steady state in the long time limit. The correct steady state is usually not known, however it can be approximated by means of the Mean Force Hamiltonian up to some fixed order, the reaction coordinate mapping or other pseudo-mode like approaches. A few years ago a controversy arose concerning the thermalization of master equations, namely, whether steady state coherences actually arise in systems with composite interactions or if they are some artifact caused by nonpositivity of the effective description, in this manuscript we confirm the existence of such steady state coherences in numerically exact dynamics, and see reminiscences of it in a CPTP map, while the steady state coherence seems to be real its oscillatory characyer seems to be an artifact of second order approximations, indicating that rather than being steady state coherences as one may think, the equilibrium state of the system is not diagonal in the basis of the system Hamiltonian. This paper also shows evidence than comparing Hamiltonian corrections calculated from the mean force approach and the quasi-steady states of dynamical equations may be deceiving, as dynamics may not tend to the state with the correction as shown in this paper.

Machine learning, particularly deep neural networks, has been widely utilized in high energy physics and has shown remarkable results in various applications. Moreover, the concept of machine learning has been extended to quantum computers, giving rise to a new research area known as quantum machine learning. In this paper, we propose a novel variational quantum circuit model, Quantum Complete Graph Neural Network (QCGNN), designed for learning complete graphs. We argue that QCGNN has a polynomial speedup against its classical counterpart, due to the property of quantum parallelism. In this paper, we study the application of QCGNN through the challenging jet discrimination, where the jets are represented with complete graphs. Subsequently, we conduct a comparative analysis with classical graph neural networks to establish a benchmark.

Great efforts have been dedicated in recent years to explore practical applications for noisy intermediate-scale quantum (NISQ) computers, which is a fundamental and challenging problem in quantum computing. As one of the most promising methods, the variational quantum eigensolver (VQE) has been extensively studied. In this paper, VQE is applied to solve portfolio optimization problems in finance by designing two hardware-efficient Dicke state ansatze that reach a maximum of 2n two-qubit gate depth and n^2/4 parameters, with n being the number of qubits used. Both ansatze are partitioning-friendly, allowing for the proposal of a highly scalable quantum/classical hybrid distributed computing (HDC) scheme. Combining simultaneous sampling, problem-specific measurement error mitigation, and fragment reuse techniques, we successfully implement the HDC experiments on the superconducting quantum computer Wu Kong with up to 55 qubits. The simulation and experimental results illustrate that the restricted expressibility of the ansatze, induced by the small number of parameters and limited entanglement, is advantageous for solving classical optimization problems with the cost function of the conditional value-at-risk (CVaR) for the NISQ era and beyond. Furthermore, the HDC scheme shows great potential for achieving quantum advantage in the NISQ era. We hope that the heuristic idea presented in this paper can motivate fruitful investigations in current and future quantum computing paradigms., Comment: 21 pages, 20 figures

Louis Sica derived Bell's inequalities from the simple hypothesis that the time series of outcomes observed in one station does not change if the setting in the other (distant) station is changed. This derivation is based on arithmetical properties only. It does not involve the controversial definitions of Locality and Realism, it does not require the definition of probabilities, and is valid for series of any length. Although it is not directly testable, Sica's approach puts a decisive criterion for computer codes aimed to explain the violation of Bell's inequalities without violating classical intuition. In this paper, the approach is extended to series with non ideal efficiency and to series recorded at different times. The first extension leads to an interesting relationship involving the entanglement parameter SCHSH and efficiency, what puts the so-called "detection loophole" under a new light. The second extension makes visible that measuring with different settings unavoidably means recording series at different times, and leads to replace "Local Realism" (as the condition for the validity of Bell's inequalities), with the condition that the recorded series can always be arbitrarily reordered. At the end of the paper, promising lines for future research based on Sica's approach are proposed., Comment: 12 pages, 7 figures

The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many complex problems that cannot be solved with conventional computing methods. These problems include modeling quantum mechanics, logistics, chemical-based advances, drug design, statistical science, sustainable energy, banking, reliable communication, and quantum chemical engineering. The last few years have witnessed remarkable advancements in quantum software and algorithm creation and quantum hardware research, which has significantly advanced the prospect of realizing quantum computers. It would be helpful to have comprehensive literature research on this area to grasp the current status and find outstanding problems that require considerable attention from the research community working in the quantum computing industry. To better understand quantum computing, this paper examines the foundations and vision based on current research in this area. We discuss cutting-edge developments in quantum computer hardware advancement and subsequent advances in quantum cryptography, quantum software, and high-scalability quantum computers. Many potential challenges and exciting new trends for quantum technology research and development are highlighted in this paper for a broader debate., Comment: Preprint: 11 pages, 2 figures

In this position paper, we posit that a major Department of Energy (DOE)-funded open-source quantum compilation platform is needed to facilitate: (a) resource optimization at the fault-tolerant layer of the quantum computing software stack, and (b) co-design of that layer of the stack with other layers, and that this platform needs to be extensible and include verification., Comment: 3 pages, 0 figures. This position paper was written for the DOE ASCR Basic Research Needs in Quantum Computing and Networking Workshop that was held on July 11-13, 2023

The paper aims to reveal the relationship between the geometrical features and linear and nonlinear optical properties of InAs quantum dots (QDs). This problem is justified by the extreme variety offered by the recent advances in growth techniques tailored to the attainment of QDs and nanostructures with virtually any shape. To that end, the Finite Element Method in conjunction with the Effective Mass Approximation and Envelope Function Approximation was employed to solve the one-particle eigenproblems in domains with any complex geometries. The paper explores nanoplatelets, spherical QDs, nanocones, nanorods, nanotadpoles, and nanostars. It has been found that there is a clear correlation between the complexity and symmetry of the QDs and their linear and nonlinear absorption spectra for transitions between the electronic ground state and the first three excited states.

Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the ontological content of a proper physical model to the epistemic conditions of the experimental context. More precisely, it is assumed that all knowable distinctions should correspond to distinctions in a proper model. This principle of "ontological completeness" means, for example, that the probabilistic treatment of the double slit experiment with and without path information should differ. Further, it is assumed that the model should rely only on knowable ontological elements, and that failure to fulfill this principle of "ontological minimalism" gives rise to wrong predictions. Consequently, probabilities should be assigned only to observable experimental outcomes. Also, the method to calculate such probabilities should not rely on the existence of a precise path of the observed object if this path is not knowable. A similar principle was promoted by Born, even though he did not apply it to probability. Another crucial assumption is that the proper rule to calculate probabilities should be generally valid. It should be applicable in all experimental contexts, regardless the setup that determines which attributes of the studied object are observed, together with the probability to observe each of the associated attribute values. There is no need to refer to the Hilbert space structure of quantum mechanics in the present treatment. Rather, some elements of this structure emerge from the analysis., Comment: 29 pages, 3 figures. The material in this paper is a further development of preliminary ideas concerning Born's rule expressed in a wider context in arXiv:1601.00680 and arXiv:1703.08543

In this paper, we develop the resource theory of quantum secret key. Operating under the assumption that entangled states with zero distillable key do not exist, we define the key cost of a quantum state, and device. We study its properties through the lens of a quantity that we call the key of formation. The main result of our paper is that the regularized key of formation is an upper bound on the key cost of a quantum state. The core protocol underlying this result is privacy dilution, which converts states containing ideal privacy into ones with diluted privacy. Next, we show that the key cost is bounded from below by the regularized relative entropy of entanglement, which implies the irreversibility of the privacy creation-distillation process for a specific class of states. We further focus on mixed-state analogues of pure quantum states in the domain of privacy, and we prove that a number of entanglement measures are equal to each other for these states, similar to the case of pure entangled states. The privacy cost and distillable key in the single-shot regime exhibit a yield-cost relation, and basic consequences for quantum devices are also provided., Comment: 34 pages, 6 figures, 1 table

In a multi-level quantum system Fano coherences stand for the formation of quantum coherences due to the interaction with the continuum of modes characterizing an incoherent process. When the incoherent source vanishes, Fano coherences tend to disappear. In this paper we propose a V-type three-level quantum system on which we certify the presence of genuinely quantum traits underlying the generation of Fano coherences. We do this by determining work conditions that allows for the loss of positivity of the Kirkwood-Dirac quasiprobability distribution of the stochastic energy variations within the discrete system. We also show the existence of nonequilibrium regimes where the generation of Fano coherences leads to a non-negligible amount of extractable work, however provided the initial state of the discrete system is in a superposition of the energy eigenbasis. We conclude the paper by studying the thermodynamic efficiency of the whole process., Comment: 17 pages, 6 figures. Comments are welcome

The projection postulate is a description of the effect on a quantum system, assumed to be in a pure state, of a measurement of an observable with a discrete spectrum, in nonrelativistic quantum mechanics. It is often called "von Neumann's projection postulate" or "the L\"uders rule". This paper is an examination of the versions of this postulate due to Dirac, von Neumann and L\"uders. It is shown that Dirac, in 1930, proposed what is now generally known as the projection postulate. Von Neumann, in 1932, gave a different theory which only applies in special and rather unusual cases. L\"uders, in 1951, rejected this theory and presented one which is the same as Dirac's. Treatments of observables with continuous spectra by both Dirac and von Neumann are criticised, and the possibility of a generalised version of the projection postulate for this case is considered. The paper concludes with a discussion of the status of the projection postulate (in its various forms) as a separate postulate (independent of the other postulates of quantum mechanics) and as a separate form of time development (in addition to the time-dependent Schr\"odinger equation)., Comment: Unfair criticism of L\"uders removed

This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes particles governed by quantum mechanics for computational purposes, leveraging properties like superposition and entanglement for information representation and manipulation. Quantum machine learning applies these principles to enhance classical machine learning models, potentially reducing network size and training time on quantum hardware. The paper covers basic quantum mechanics principles, including superposition, phase space, and entanglement, and introduces the concept of quantum gates that exploit these properties. It also reviews classical deep learning concepts, such as artificial neural networks, gradient descent, and backpropagation, before delving into trainable quantum circuits as neural networks. An example problem demonstrates the potential advantages of quantum neural networks, and the appendices provide detailed derivations. The paper aims to help researchers new to quantum mechanics and machine learning develop their expertise more efficiently., Comment: Published as a DTIC report under the title "Quantum Computing for Machine Learning - An Introduction". Distribution Statement A: Approved for Public Release. Distribution is Unlimited

This paper explores the application of Quadratic Unconstrained Binary Optimization (QUBO) models in solving the Travelling Salesman Problem (TSP) through Quantum Annealing algorithms and Graph Neural Networks. Quantum Annealing (QA), a quantum-inspired optimization method that exploits quantum tunneling to escape local minima, is used to solve QUBO formulations of TSP instances on Coherent Ising Machines (CIMs). The paper also presents a novel approach where QUBO is employed as a loss function within a GNN architecture tailored for solving TSP efficiently. By leveraging GNN's capability to learn graph representations, this method finds approximate solutions to TSP with improved computational time compared to traditional exact solvers. The paper details how to construct a QUBO model for TSP by encoding city visits into binary variables and formulating constraints that guarantee valid tours. It further discusses the implementation of QUBO-based Quantum Annealing algorithm for TSP (QQA-TSP) and its feasibility demonstration using quantum simulation platforms. In addition, it introduces a Graph Neural Network solution for TSP (QGNN-TSP), which learns the underlying structure of the problem and produces competitive solutions via gradient descent over a QUBO-based loss function. The experimental results compare the performance of QQA-TSP against state-of-the-art classical solvers such as dynamic programming, Concorde, and Gurobi, while also presenting empirical outcomes from training and evaluating QGNN-TSP on various TSP datasets. The study highlights the promise of combining deep learning techniques with quantum-inspired optimization methods for solving NP-hard problems like TSP, suggesting future directions for enhancing GNN architectures and applying QUBO frameworks to more complex combinatorial optimization tasks.