Quantum Information Theory Research Articles

Transformer models for quantum gate set tomography

Quantum computation represents a promising frontier in the domain of high-performance computing, blending quantum information theory with practical applications to overcome the limitations of classical computation. This study investigates the challenges of manufacturing high-fidelity and scalable quantum processors. Quantum gate set tomography (QGST) is a critical method for characterizing quantum processors and understanding their operational capabilities and limitations. This paper introduces Ml4Qgst as a novel approach to QGST by integrating machine learning techniques, specifically utilizing a transformer neural network model. Adapting the transformer model for QGST addresses the computational complexity of modeling quantum systems. Advanced training strategies, including data grouping and curriculum learning, are employed to enhance model performance, demonstrating significant congruence with ground-truth values. We benchmark this training pipeline on the constructed learning model, to successfully perform QGST for 2 and 3 gates on single-qubit and two-qubit systems, with over-rotation error and depolarizing noise estimation with comparable accuracy to pyGSTi. This research marks a pioneering step in applying deep neural networks to the complex problem of quantum gate set tomography, showcasing the potential of machine learning to tackle nonlinear tomography challenges in quantum computing.

Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions.

Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen-Specker and non-Kochen-Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field.

Метод решения задачи безопасного движения транспорта и пешеходов на основе квантовых и нейрокомпьютерных систем

Abstract. The article discusses two problems arising in the theory of optimal processes: 1) controlling a dynamical system under the condition of a minimum of the selected estimate of the intensity ꭓ [u] of the control forces; 2) observation, i.e. calculating the current coordinates — xi (t) of a moving object from the measurable functions yj from these coordinates. The main attention is paid to objects described by linear equations (for which, however, nonlinear laws of optimal control are derived from the minimum conditions ꭓ[u]). The solution of the problems under consideration is given, based on the methods of functional analysis based on the representation of observation problems and decision-making based on the closure of the control circuit based on quantum and neurocomputer technologies. Minimax rules are formulated and substantiated, which determine the optimal control actions or optimal resolving operations in cases of control and observation of a dangerous situation on the road, respectively. The duality between the processes of control and observation is discussed. The connection of the considered problems with the basic concepts of quantum information theory is established. Numerical methods for determining optimal control forces are described. The connection of the considered problems with the basic concepts of quantum information theory is established. Numerical methods for determining optimal control forces are described. The problem of control in a conflict situation of a possible collision of an unmanned controlled object with a pedestrian is considered. To solve this problem, a rule of extreme pedestrian warning is proposed, which provides a minimum of time for an accurate human response. The relationship between the solution of the problem of observation of a linear object and the canonical decomposition by Eigen elements of the motions of a dynamic system with an aftereffect is studied. The problem of calming the disturbed movements of the controlled system with the aftereffect is considered. A solution to one problem of observing the motions of a linear system under random interference is given.

Holographic entanglement negativity for disjoint subsystems in conformal field theories with a conserved charge

In this paper, we extend a holographic construction for the entanglement negativity of two disjoint subsystems in the literature to [Formula: see text]s with a conserved charge dual to bulk [Formula: see text] geometries. This involves an algebraic sum of the areas of bulk RT surfaces for certain appropriate combinations of subsystems. In this context, we compute the holographic entanglement negativity for two disjoint subsystems with long rectangular strip geometries in [Formula: see text]s dual to bulk RN-[Formula: see text] black holes in a perturbative framework. Our results at the leading order reproduce significant features observed earlier in the literature and conform to quantum information theory, which constitute strong substantiation of our construction.

Quantum information reveals that orbital-wise correlation is essentially classical in natural orbitals.

The intersection of quantum chemistry and quantum computing has led to significant advancements in understanding the potential of using quantum devices for the efficient calculation of molecular energies. Simultaneously, this intersection enhances the comprehension of quantum chemical properties through the use of quantum computing and quantum information tools. This paper tackles a key question in this relationship: Is the nature of the orbital-wise electron correlations in wavefunctions of realistic prototypical cases classical or quantum? We address this question with a detailed investigation of molecular wavefunctions in terms of Shannon and von Neumann entropies, common tools of classical and quantum information theory. Our analysis reveals a notable distinction between classical and quantum mutual information in molecular systems when analyzed with Hartree-Fock canonical orbitals. However, this difference decreases dramatically, by ∼100-fold, when natural orbitals are used as reference. This finding suggests that orbital correlations, when viewed through the appropriate basis, are predominantly classical. Consequently, our study underscores the importance of using natural orbitals to accurately assess molecular orbital correlations and to avoid their overestimation.

Enhancing Quantum Entanglement Through Parametric Control of Atom‐Cavity States

AbstractDicke states form a class of entangled states that has attracted much attention for their applications in various quantum algorithms. They emerge as eigenstates of the Tavis–Cummings (TC) Hamiltonian, a simplification of the Dicke model, which describes an assembly of two‐level atoms trapped in an electromagnetic cavity. In this letter, it is showed that in the regime where the field energy is large with respect to the atomic energy splitting, precise control of the ground state can be implemented. Specifically, pure Dicke states can be selected and produced by appropriate tuning of the parameters. This result may have important applications in quantum engineering and quantum information theory.

Nonassociative gauge gravity theories with R-flux star products and Batalin–Vilkovisky quantization in algebraic quantum field theory

Abstract Nonassociative modifications of general relativity, GR, and quantum gravity, QG, models naturally arise as star product and R-flux deformations considered in string/ M-theory. Such nonassociative and noncommutative geometric and quantum information theories were formulated on phase spaces defined as cotangent Lorentz bundles enabled with nonassociative symmetric and nonsymmetric metrics and nonlinear and linear connection structures. We outline the analytic methods and proofs that corresponding geometric flow evolution and dynamical field equations can be decoupled and integrated in certain general off-diagonal forms. New classes of solutions describing nonassociative black holes, wormholes, and locally anisotropic cosmological configurations are constructed using such methods. We develop the Batalin-Vilkovisky, BV, formalism for quantizing modified gravity theories, MGTs, involving twisted star products and semi-classical models of nonassociative gauge gravity with de Sitter/affine/ Poincar'{e} double structure groups. Such theories can be projected on Lorentz spacetime manifolds in certain forms equivalent to GR or MGTs with torsion generalizations etc. We study the properties of the classical and quantum BV operators for nonassociative phase spaces and nonassociative gauge gravity. Recent results and methods from algebraic QFT are generalized to involve nonassociative star product deformations of the anomalous master Ward identity. Such constructions are elaborated in a nonassociative BV perspective and for developing non-perturbative methods in QG.

The enhanced separability criteria based on equiangular tight frames

Abstract The detection of quantum entanglement is an essential issue in the theory of quantum information. Recently, an elegant separability criterion to detect the entanglement of arbitrary-dimensional bipartite states is presented in Shi (2024 J. Phys. A: Math. Theor. 57 075302) by applying the positive operator valued measurements based on the equiangular tight frames (ETFs). Here we derive two enhanced separability criteria for detecting bipartite entanglement in arbitrary-dimensional quantum states using ETFs. Furthermore, we prove that they are not weaker than the criterion proposed in Shi (2024 J. Phys. A: Math. Theor. 57 075302).

Energy preserving evolutions over Bosonic systems

The exponential convergence to invariant subspaces of quantum Markov semigroups plays a crucial role in quantum information theory. One such example is in bosonic error correction schemes, where dissipation is used to drive states back to the code-space – an invariant subspace protected against certain types of errors. In this paper, we investigate perturbations of quantum dynamical semigroups that operate on continuous variable (CV) systems and admit an invariant subspace. First, we prove a generation theorem for quantum Markov semigroups on CV systems under the physical assumptions that (i) the generator is in GKSL form with corresponding jump operators defined as polynomials of annihilation and creation operators; and (ii) the (possibly unbounded) generator increases all moments in a controlled manner. Additionally, we show that the level sets of operators with bounded first moments are admissible subspaces of the evolution, providing the foundations for a perturbative analysis. Our results also extend to time-dependent semigroups and multi-mode systems. We apply our general framework to two settings of interest in continuous variable quantum information processing. First, we provide a new scheme for deriving continuity bounds on the energy-constrained capacities of Markovian perturbations of quantum dynamical semigroups. Second, we provide quantitative perturbation bounds for the steady state of the quantum Ornstein-Uhlenbeck semigroup and the invariant subspace of the photon dissipation used in bosonic error correction.

Entanglement and Mutual Information in Molecules: Comparing Localized and Delocalized Orbitals.

The use of the mutual information (MI) as a measure of the entanglement in quantum systems has gained a consensus in recent years, even if there is an ongoing effort to distinguish the classical and quantum contributions contained therein. This quantity has been first introduced in condensed matter physics, in particular, in studies based on the density matrix renormalization group method. This method has been successfully adapted to quantum chemistry problems, opening the way to compute MI also in molecular systems. A key aspect of this quantity is its dependence on the one-electron (orbital) basis set, even for wave functions that are invariant under unitary transformation of the orbitals. In this work, we investigate the role of the orbital basis set (delocalized or localized, following different strategies) for wave functions expressed as linear combinations of Slater determinants and we give the analytic expression for the MI for a few special cases. This study aims to improve the knowledge of the relationship between the characteristics of the chemical bond (considering a few paradigmatic molecules, H2, F2, N2, and short linear polyenes) and the properties of interest in the field of quantum information theory.

Projective toric designs, quantum state designs, and mutually unbiased bases

Toric t-designs, or equivalently t-designs on the diagonal subgroup of the unitary group, are sets of points on the torus over which sums reproduce integrals of degree t monomials over the full torus. Motivated by the projective structure of quantum mechanics, we develop the notion of t-designs on the projective torus, which have a much more restricted structure than their counterparts on full tori. We provide various new constructions of toric and projective toric designs and prove bounds on their size. We draw connections between projective toric designs and a diverse set of mathematical objects, including difference and Sidon sets from the field of additive combinatorics, symmetric, informationally complete positive operator valued measures and complete sets of mutually unbiased bases (MUBs) from quantum information theory, and crystal ball sequences of certain root lattices. Using these connections, we prove bounds on the maximal size of dense Btmodm sets. We also use projective toric designs to construct families of quantum state designs. In particular, we construct families of (uniformly-weighted) quantum state 2-designs in dimension d of size exactly d(d+1) that do not form complete sets of MUBs, thereby disproving a conjecture concerning the relationship between designs and MUBs (Zhu 2015). We then propose a modification of Zhu's conjecture and discuss potential paths towards proving this conjecture. We prove a fundamental distinction between complete sets of MUBs in prime-power dimensions versus in dimension 6 (and, we conjecture, in all non-prime-power dimensions), the distinction relating to group structure of the corresponding projective toric design. Finally, we discuss many open questions about the properties of these projective toric designs and how they relate to other questions in number theory, geometry, and quantum information.

Entanglement classification – a comparative study of 𝑺𝑼(𝟐) and 𝑺𝑳(𝟐) developed operator model

Entanglement classification is a core aspect of quantum information theory. It ensures successful quantum information processing. This article presents a comparative study of entanglement classification using developed operator models for the special unitary group and special linear group. This study was built upon prior work in entanglement classification in a pure three-qubit quantum system environment, where the operator models for each mathematical group were independently developed. Through extensive analysis, both synthesized models are functionally effective and yield the desired results. However, the comparative analysis reveals that the operator model exhibits certain limitations, particularly in its early phase of development compared to. This study provides significant enlightenments into the practical abilities of the developed operator models in entanglement classification and underlines the theoretical distinction between and paving the path for future research in quantum information theory, specifically entanglement classification.

Quantum advantages in (n,d)↦1 random access codes

Abstract A random access code (RAC), corresponding to a communication primitive with various applications in quantum information theory, is an instance of a preparation-and-measurement scenario. In this work, we consider (n, d)-RACs constituting an n-length string, constructed from a d size set of letters, and send an encoding of the string in a single d-level physical system and present their quantum advantages. We first characterize optimal classical RACs and prove that a known classical strategy, the so-called majority-encoding-identity-decoding, is optimal. We then construct a quantum protocol by exploiting only two incompatible measurements (the minimal requirement) and show the advantages beyond the classical one. We also discuss the generality of our results and whether quantum advantages are valid for all types of (n, d)→1 RACs.

The quantum gravity seeds for laws of nature

We discuss the challenges that the standard (Humean and non-Humean) accounts of laws face within the framework of quantum gravity where space and time may not be fundamental. This paper identifies core (meta)physical features that cut across a number of quantum gravity approaches and formalisms and that provide seeds for articulating updated conceptions that could account for QG laws not involving any spatio-temporal notions. To this aim, we will in particular highlight the constitutive roles of quantum entanglement, quantum transition amplitudes and quantum causal histories. These features also stress the fruitful overlap between quantum gravity and quantum information theory.

Toward a Quantum-Inspired Framework for Modelling Legal Rules

There is a growing demand for the development of computational models of legal rulesets, yet scholars acknowledge an incompatibility between the deterministic nature of current legal coding processes and the indeterminate nature of the law. Previously, legal scholars have identified conceptual links between the indeterminacy of quantum mechanics and the law, but very few have attempted to formally model the law using a framework inspired by the formalism of quantum information. I highlight similarities regarding indeterminacy as it is understood by legal and scientific scholars, motivating the construction of a quantum-inspired framework to model ambiguous legal rules. I outline how multi-qubit systems can be used to represent ambiguous legal rules formally, wherein each state of the system represents competing orthogonal interpretations of the law. I show that the amplitude corresponding to an interpretation state can represent its likelihood of validity and secondary interpretive characteristics, such as jurisprudential alignment. Using measures of classical and quantum information theory, these states can be analysed to yield information relating to forms of ambiguity, intra- and intertextuality, and inconsistencies present in a legal ruleset and interpretations. Finally, I illustrate the potential for generative artificial intelligence to assist in producing these quantum-inspired models of legal rules.

Construction of Optimal Orthogonal Partition

ABSTRACTOrthogonal partitions play a crucial role in orthogonal array theory, design of experiments and quantum information theory. The optimisation of orthogonal partitions can improve the saturation percentages of orthogonal arrays (OAs) obtained by the orthogonal partition method. In particular, optimal orthogonal partitions of strength 1 are of great practical utility. However, there is still a scarcity of results about orthogonal partitions, especially optimal ones. In this paper, the definition of an optimal orthogonal partition is proposed, and we construct optimal orthogonal partitions of OAs by several construction methods, such as orthogonal partition method, difference scheme construction, generalised product construction and construction. As an application, we obtain various optimal orthogonal partitions and OAs with higher saturation percentages.

Quantum blockchain: Trends, technologies, and future directions

AbstractBlockchain technology is a highly developed database system that shares information within a business web. It stores details in blocks connected chronologically, ensuring information integrity through consensus mechanisms that prevent unauthorised alterations. This decentralised system removes the need for a believable mediator, mitigating vulnerabilities and enhancing transaction security. Blockchain’s application spans the energy, finance, media, entertainment, and retail sectors. However, classical blockchain faces threats from quantum computing advancements, necessitating the development of quantum blockchain technology. Quantum blockchain, leveraging quantum computation and information theory, offers enhanced security and immutability. In this paper, different mathematical foundations, practical implementations and effectiveness of lattice‐based cryptography in securing blockchain applications are discussed. Analysis of how the cryptographic techniques can protect blockchain systems against quantum attacks is being done by using mathematical formulations and examples. Quantum computing strengthens blockchain security with advanced encryption and authentication, which is critical for safeguarding diverse sectors from evolving cyber threats. Further study on quantum‐resistant design is necessary if blockchain networks are to be robust and intact in the face of future technological developments.

Can quantum computers do nothing?

AbstractQuantum computing platforms are subject to contradictory engineering requirements: qubits must be protected from mutual interactions when idling (‘doing nothing’), and strongly interacting when in operation. If idling qubits are not sufficiently protected, information ‘leaks’ into neighbouring qubits, becoming ultimately inaccessible. Candidate solutions to this dilemma include many-body localization, dynamical decoupling, and active error correction. However, no protocol exists to quantify this effect in a similar way to e.g. SPAM errors. We develop a scalable, device non-specific, protocol for quantifying idle information loss by exploiting tools from quantum information theory. We implement this protocol in over 3500 experiments carried out across 4 months (Dec 2023–Mar 2024) on IBM’s entire Falcon 5.11 processor series. After accounting for other error sources, we detect information loss to high degrees of statistical significance. This work thus provides a firm quantitative foundation from which the protection-operation dilemma can be investigated and ultimately resolved.

Quantum social network analysis: Methodology, implementation, challenges, and future directions

Quantum social network analysis (QSNA) is a recent advancement in the interdisciplinary field of quantum computing and social network analysis. This manuscript comprehensively reviews QSNA, emphasizing its methodologies, implementation strategies, challenges, and potential applications. It explores the conceptual foundation of key social network analysis research problems, including link prediction, influence maximization, and community detection. The research examines how quantum algorithms can revolutionize such social network tasks by leveraging principles from quantum mechanics and information theory and highlights the advantages of quantum algorithms in handling complex social network structures. The implementation section delves into the practical aspects of QSNA, such as frameworks, experimental setups, and evaluation methods. We assess the capabilities of existing quantum programming language tools and platforms. Various case studies illustrate the potential of quantum computing to enhance the performance of social network analysis. Additionally, we identify several crucial challenges and future research directions for QSNA, including the complexity of developing quantum algorithms, the need for interdisciplinary knowledge, and the challenges of integrating quantum and classical computing resources. This paper aims to serve as a foundational resource for researchers and practitioners, providing insights into the transformative potential of quantum computing in advancing the analysis of social networks and outlining future research directions in this emerging field.

Quantum information for graphene wormholes

Abstract This paper explores the interplay between quantum information theory and the stabilization of graphene wormholes using external magnetic fields. Utilizing Shannon entropy, we analyze how quantum information can be applied to control and stabilize these structures. By studying graphene’s quantum states under different magnetic field strengths and configurations, we gain insights into the entanglement and coherence properties governing their behavior. The findings demonstrate the potential of quantum information metrics to enhance the stability and control of graphene wormholes, with implications for quantum computing and material science innovations.