Quantum Statistical Mechanics Research Articles

Gauge Field Marginal of an Abelian Higgs Model

We study the gauge field marginal of an Abelian Higgs model with Villain action defined on a 2D lattice in finite volume. Our first main result, which holds for gauge theories on arbitrary finite graphs and does not assume that the structure group is Abelian, is a loop expansion of the Radon–Nikodym derivative of the law of the gauge field marginal with respect to that of the pure gauge theory. This expansion is similar to the one of Seiler (Gauge theories as a problem of constructive quantum field theory and statistical mechanics, volume 159 of lecture notes in physics, Springer, Berlin, p v+192. https://doi.org/10.1007/3-540-11559-5, 1982) but holds in greater generality and uses a different graph theoretic approach. Furthermore, we show ultraviolet stability for the gauge field marginal of the model in a fixed gauge. More specifically, we show that moments of the Hölder–Besov-type norms introduced in Chevyrev (Commun Math Phys 372(3):1027–1058. https://doi.org/10.1007/s00220-019-03567-5, 2019) are bounded uniformly in the lattice spacing. This latter result relies on a quantitative diamagnetic inequality that in turn follows from the loop expansion and elementary properties of Gaussian random variables.

A hybrid quantum ensemble learning model for malicious code detection

Quantum computing as a new computing model with parallel computing capability and high information carrying capacity, has attracted a lot of attention from researchers. Ensemble learning is an effective strategy often used in machine learning to improve the performance of weak classifiers. Currently, the classification performance of quantum classifiers is not satisfactory enough due to factors such as the depth of quantum circuit, quantum noise, and quantum coding method, etc. For this reason, this paper combined the ensemble learning idea and quantum classifiers to design a novel hybrid quantum machine learning model. Firstly, we run the Stacking method in classical machine learning to realize the dimensionality reduction of high-latitude data while ensuring the validity of data features. Secondly, we used the Bagging method and Bayesian hyperparameter optimization method applied to quantum support vector machine (QSVM), quantum K nearest neighbors (QKNN), variational quantum classifier (VQC). Thirdly, the voting method is used to ensemble the predict results of QSVM, QKNN, VQC as the final result. We applied the hybrid quantum ensemble machine learning model to malicious code detection. The experimental results show that the classification precision (accuracy, F1-score) of this model has been improved to 98.9% (94.5%, 94.24%). Combined with the acceleration of quantum computing and the higher precision rate, it can effectively deal with the growing trend of malicious codes, which is of great significance to cyberspace security.

Quantifying the quantumness of pure-state ensembles via coherence of Gram matrix

The Gram matrix of a set of pure states plays a crucial role in exploring the information content of quantum states. Since the Gram matrix of a pure-state ensemble can be regarded as a quantum state, we can quantify the quantumness of the corresponding quantum ensemble by means of the coherence of the Gram matrix. In particular, we introduce two natural measures of quantumness of an ensemble by means of the coherence of the Gram matrix based on Hilbert-Schmidt distance and skew information, respectively, and investigate their fundamental properties. In addition, notice that the average coherence and the maximum coherence are independent of the choice of a reference basis, we further propose to use the average coherence and the maximum coherence of the Gram matrix to quantify the generalized quantumness of the corresponding ensemble, and find that the generalized quantumness is not only related to the quantum states in the ensemble, but also to the probability distribution. We discuss the validity of these quantumness measures by calculating some important pure-state ensembles in quantum measurement and quantum cryptography. Finally, we compare these quantifiers with other existing quantifiers in the literatures and illustrate that different quantifiers can yield different features and quantumness orderings for quantum ensembles.

Stability Enhancement by Zero‐Point Spin Fluctuations: A Quantum Perspective on Bloch Point Topological Singularities

AbstractBloch points represent singularities within magnetic materials. From a macroscopic viewpoint, their cores are points where the magnetization vector is undefined, resulting in unique topological characteristics that influence the magnetic behavior of their hosts. The picture is very different at the microscopic level, where quantum effects enter the scene. The spin variables' quantum dynamics effect on the BP's stability is revealed. Zero‐point fluctuations, intrinsic fluctuations within the quantum mechanical ground state originating from the uncertainty principle, play a fundamental role. It is found that quantum fluctuations bloom in the vicinity of the singularity, thereby reducing the effective magnetic moment in its neighborhood. This increases the overall stability of the BP. These methods also allow for a characterization of the magnonic eigenmodes surrounding and bound to the singularity. The latter leads to predict on quite general grounds several features of the magnonic spectra, its degeneration structure, and its splitting response under a magnetic field. The last result is coherent with the association of a magnetic moment to the orbital angular momentum of the magnons. This approach allows integration with multiscale algorithms to provide a realistic description of generic topological singularities.

Quantum statistical mechanics from a Bohmian perspective

We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The continuity equation for any closed or open system suggests a natural Bohmian interpretation in terms of microscopic particle trajectories, that make the same measurable predictions as standard quantum theory. The microscopic trajectories are not directly observable, but provide a general, simple and intuitive microscopic interpretation of macroscopic phenomena in quantum statistical mechanics. In particular, we discuss how various notions of entropy, proper and improper mixtures, and thermodynamics are understood from the Bohmian perspective.

Quantum statistical mechanics and the boundary of modular curves

The theory of limiting modular symbols provides a noncommutative geometric model of the boundary of modular curves that includes irrational points in addition to cusps. A noncommutative space associated to this boundary is constructed, as part of a family of noncommutative spaces associated to different continued fractions algorithms, endowed with the structure of a quantum statistical mechanical system. Two special cases of this family of quantum systems can be interpreted as a boundary of the system associated to the Shimura variety of GL2 and an analog for SL2. The structure of equilibrium states for this family of systems is discussed. In the geometric cases, the ground states evaluated on boundary arithmetic elements are given by pairings of cusp forms and limiting modular symbols.

Cellular automaton ontology, bits, qubits and the Dirac equation

Cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its ontological states that evolve by permutations, in this way never creating would-be quantum mechanical superposition states. We review and illustrate this with a classical Ising spin chain. It is shown that it can be related to the Weyl equation in the continuum limit. Yet, the model of discrete spins or bits unavoidably becomes a model of qubits by generating superpositions, if only slightly deformed. We study modifications of its signal velocity which, however, do not relate to mass terms. To incorporate the latter, we consider the Dirac equation in 1+1 dimensions and sketch an underlying discrete deterministic “necklace of necklaces” automaton that qualifies as ontological.

High-pressure high-temperature EXAFS and Debye–Waller factor of platinum

The temperature and pressure effects on the mean-square relative displacement (MSRD) corresponding to the extended X-ray absorption fine structure (EXAFS) Debye–Waller factor of platinum have been studied based on the statistical moment method in quantum statistical mechanics. We implement numerical calculations for platinum up to pressure of 400 GPa. Examining the temperature effects on the EXAFS Debye–Waller factor at ambient pressure we show that theoretical MSRD curve is in good agreement with the previous measurement and calculations up to nearly 800 K. When pressure increases, our pressure-dependent MSRD curve follows very well with the prediction based on the numerical integration along the Hugoniot. Using the theoretical EXAFS Debye–Waller factor, we obtain the Hugoniot temperatures which are highly consistent with recent experimental results. This research advances the correlated Einstein model on the calculation of MSRDs of materials at high temperature and high pressure, specifically, it includes the zero-point vibrations at low temperature and contains the anharmonicity contributions caused by thermal lattice vibrations at high temperature.

Single-Shot Factorization Approach to Bound States in Quantum Mechanics

Single-Shot Factorization Approach to Bound States in Quantum Mechanics

The set of basis functions generated by Pearson type IV distributions and its application to problems of statistical data analysis and quantum mechanics

На примере распределений Пирсона IV типа предложена процедура дополнения классического распределения вероятностей до квантового состояния. Получена волновая функция, отвечающая распределениям Пирсона IV типа, а также построен соответствующий набор базисных функций. Продемонстрировано применение разработанного метода к задачам статистического анализа данных и квантовой механики. Показана эффективность разработанного подхода при аппроксимации статистических распределений с тяжелыми хвостами.

Underpinnings behind the magnetic order-to-disorder transition and property anomaly of disproportionated insulating samarium nickelate

Perovskite nickelates (RNiO3), as benchmark materials for exploring underlying physics of phase transitions in strong correlated systems, are well-known for their rich structural characteristics and physicochemical properties. Understanding phase transition from the spin-ordered antiferromagnetic (AFM) state to the spin-disordered paramagnetic (PM) state of RNiO3 requires accurate models at finite temperatures. Here, we investigate the underpinning physics behind the property anomaly and AFM-to-PM transition in samarium nickelate (SmNiO3) using a thermodynamic zentropy approach, which depicts the temperature-dependent total entropy for a system of interest via a nested formula through integration of quantum mechanics and statistical mechanics. The SmNiO3 displays the ground-state of AFM insulator as well as the PM metal and PM insulator at elevated temperatures. It turns out that the magnetic configurational entropy induced by competition among different spatially fluctuating polymorphous spin configurations, contributes to the specific-heat anomaly and the phase transition of SmNiO3 from AFM to PM state. The predicted Néel temperature of 241±25 K for SmNiO3 is in satisfactory agreement with the experimental value. Unlike empirical interpretations in literature, the present work indicates that the magnetic order-to-disorder transition in SmNiO3 is associated with the magnetic configurational entropy due to thermal mixture of multiple spin configurations at elevated temperatures, which can be quantitively captured by the first-principles based thermodynamic zentropy approach.

Towards the generation of mechanical Kerr-cats: awakening the perturbative quantum Moyal corrections to classical motion

The quantum to classical transition is determined by the interplay of a trio of parameters: dissipation, nonlinearity, and macroscopicity. Why is nonlinearity needed to see quantum effects? And, is not an ordinary pendulum quite nonlinear already? In this manuscript, we discuss the parameter regime where the dynamics of a massive oscillator should be quantum mechanical in the presence of dissipation. We review the outstanding challenge of the dynamical generation of highly quantum mechanical cat states of a massive ‘pendulum’, known as Kerr-cats. We argue that state-of-the-art cold atom experiments may be in a position to reach such a nonlinear regime, which today singles out superconducting quantum circuits. A way to stabilize Schrödinger cat superpositions of a mechanical atomic oscillator via parametric squeezing and further protected by an unusual form of quantum interference is discussed. The encoding of a neutral atom Kerr-cat qubit is proposed.

Generative model for learning quantum ensemble with optimal transport loss

Generative modeling is an unsupervised machine learning framework, that exhibits strong performance in various machine learning tasks. Recently, we find several quantum versions of generative model, some of which are even proven to have quantum advantage. However, those methods are not directly applicable to construct a generative model for learning a set of quantum states, i.e., ensemble. In this paper, we propose a quantum generative model that can learn quantum ensemble, in an unsupervised machine learning framework. The key idea is to introduce a new loss function calculated based on optimal transport loss, which have been widely used in classical machine learning due to its good properties; e.g., no need to ensure the common support of two ensembles. We then give in-depth analysis on this measure, such as the scaling property of the approximation error. We also demonstrate the generative modeling with the application to quantum anomaly detection problem, that cannot be handled via existing methods. The proposed model paves the way for a wide application such as the health check of quantum devices and efficient initialization of quantum computation.

Zentropy theory for accurate prediction of free energy, volume, and thermal expansion without fitting parameters

Based on statistical mechanics, a macroscopically homogeneous system, i.e., a single phase in the present context, is composed of many independent configurations that the system embraces. The macroscopical properties of the system are determined by the properties and statistical probabilities of those configurations with respect to external conditions. The volume of a single phase is thus the weighted sum of the volumes of all configurations. Consequently, the derivative of the volume to temperature of a single phase depends on both the derivatives of the volumes of every configuration to temperature and the derivatives of their statistical probabilities to temperature, with the latter introducing nonlinear emergent behaviors. It is shown that the derivative of the volume to the temperature of the single phase can be negative, i.e., negative thermal expansion, due to the symmetry-breaking non-ground-state configurations with smaller volumes than that of the ground-state configuration and the rapid increase of the statistical probabilities of the former, and negative thermal expansion can be predicted without fitting parameters from the zentropy theory that combines quantum mechanics and statistical mechanics with the free energy of each configuration predicted from quantum mechanics and the partition function of each configuration calculated from its free energy.

Hamiltonian Identification via Quantum Ensemble Classification.

Identifying the Hamiltonian of an unknown quantum system is a critical task in the area of quantum information. In this article, we propose a systematic Hamiltonian identification approach via quantum ensemble multiclass classification (HI-QEMC). This approach is implemented by a three-step iterative refining process, i.e., parameter interval guess, verification, and judgment. In the parameter interval guess step, the parameter interval is divided into several sub-intervals and the true Hamiltonian parameter is guessed in one of them. In the parameter interval verification step, cross verification is applied to verify the accuracy of the guess. In the parameter interval judgment step, an adaptive interval judgment (AIJ) algorithm is designed to determine the sub-interval containing the true Hamiltonian parameter. Numerical results on two typical quantum systems, i.e., two-level quantum systems and three-level quantum systems, demonstrate the effectiveness and superior performance of the proposed approach for quantum Hamiltonian identification.

Theoretical Study of Raman Intensities of p-Nitroaniline in Different Solvent Conditions by Using a Reference Interaction Site Model Self-Consistent Field Explicitly Including Constrained Spatial Electron Density Distribution.

Raman spectroscopy is one of the most powerful tools to understand and characterize the states and structures of systems in several environments. To obtain highly accurate changes in Raman intensities of systems in solution, theoretical treatment, which can deal with not only the states and structures of systems but also the environment around molecules, proves to be significant. Hence, in this study, we developed the calculation of changes in Raman intensities of systems in different solvent conditions by using the reference interaction site model self-consistent field study explicitly including constrained spatial electron density distribution; this model is designed based on elements from both quantum mechanics and statistical mechanics. We showed that our calculation method could reproduce the changes in Raman intensities of p-nitroaniline (pNA) under different solvent conditions, including supercritical water, which has been observed in previous experimental studies. Based on the analysis of the calculation results, we observed that the ratio of the Raman intensity change of pNA in different solvent conditions is strongly correlated with the charge-transfer character of pNA.

Probing Spin-Dependent Ballistic Charge Transport at Single-Nanometer Length Scales.

The coherent transport of charge and spin is a key requirement of future devices for quantum computing and communication. Scattering at defects or impurities may significantly reduce the coherence of quantum-mechanical states, thereby affecting the device functionality. While numerous methods exist to experimentally assess charge transport, the real-space detection of a material's ballistic spin transport properties with nanometer resolution remains a challenge. Here we report on a novel approach that utilizes a combination of spin-polarized scanning tunneling microscopy (SP-STM) and the recently introduced molecular nanoprobe (MONA) technique. It relies on the local injection of spin-polarized charge carriers from a magnetic STM tip and their detection by a single surface-deposited phthalocyanine molecule via reversible electron-induced tautomerization events. Based on the particular electronic structure of the Rashba alloy BiAg2, which is governed by a spin-momentum-locked surface state, we prove that the current direction inverses upon tip magnetization reversal.

Machine learning quantum mechanical ground states based on stochastic mechanics

Machine learning quantum mechanical ground states based on stochastic mechanics

Ehrenfest modeling of cavity vacuum fluctuations and how to achieve emission from a three-level atom

A much-needed solution for the efficient modeling of strong coupling between matter and optical cavity modes is offered by mean-field mixed quantum–classical dynamics, where a classical cavity field interacts self-consistently with quantum states of matter through Ehrenfest’s theorem. We previously introduced a modified mean-field approach, referred to as decoupled mean-field (DC-MF) dynamics, wherein vacuum fluctuations of the cavity field are decoupled from the quantum-mechanical ground state as a means to resolve an unphysical drawing of energy from the vacuum fluctuations by a two-level atom. Here, we generalize DC-MF dynamics for an arbitrary number of (nondegenerate) atomic levels and show that it resolves an unphysical lack of emission from a three-level atom predicted by conventional mean-field dynamics. We furthermore show DC-MF to provide an improved description of reabsorption and (resonant) two-photon emission processes.

States, observables and symmetries in p-adic quantum mechanics

In the framework of quantum mechanics constructed over a quadratic extension of the field of p-adic numbers, we consider an algebraic definition of physical states. Next, the corresponding observables, whose definition completes the statistical interpretation of the theory, are introduced as SOVMs, a p-adic counterpart of the POVMs associated with a quantum system over the complex numbers. Differently from the standard complex setting, the space of all states of a p-adic quantum system has an affine — rather than convex — structure. Thus, a symmetry transformation may be defined, in a natural way, as a map preserving this affine structure. We argue that the group of all symmetry transformations of a p-adic quantum system has a richer structure wrt the case of standard quantum mechanics over the complex numbers.