Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental preparations of Gibbs states and excited states of Heisenberg X X and X X Z models by using a 5-qubit programmable superconducting processor.In the experiments,we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits.We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits,which enable us to prepare excited states at arbitrary energy density.We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error.Based on numerical results,we further show that the time complexity of our approach scales polynomially in the number of qubits,revealing its potential in solving large-scale problems.

Improved statistical fluctuation analysis for two decoy-states phase-matching quantum key distribution

Phase-matching quantum key distribution is a promising scheme for remote quantum key distribution,breaking through the traditional linear key-rate bound.In practical applications,finite data size can cause significant system performance to deteriorate when data size is below 1010.In this work,an improved statistical fluctuation analysis method is applied for the first time to two decoy-states phase-matching quantum key distribution,offering a new insight and potential solutions for improving the key generation rate and the maximum transmission distance while maintaining security.Moreover,we also compare the influence of the proposed improved statistical fluctuation analysis method on system performance with those of the Gaussian approximation and Chernoff-Hoeffding boundary methods on system performance.The simulation results show that the proposed scheme significantly improves the key generation rate and maximum transmission distance in comparison with the Chernoff-Hoeffding approach,and approach the results obtained when the Gaussian approximation is employed.At the same time,the proposed scheme retains the same security level as the Chernoff-Hoeffding method,and is even more secure than the Gaussian approximation.

Quantum Statistical Entropy of Five-Dimensional Black Hole

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Fhrther it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole＇s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

Decoy-state reference-frame-independent quantum key distribution with both source errors and statistical fluctuations

Reference-frame-independent quantum key distribution （RFI QKD） can generate secret keys without the alignment of reference frames, which is very robust in real-life implementations of QKD systems. However, the performance of decoy-state RFI QKD with both source errors and statistical fluctuations is still missing until now. In this paper, we investigate the performance of decoy-state RFI QKD in practical scenarios with two kinds of light sources, the heralded single photon source （HSPS） and the weak coherent source （WCS）, and also give clear comparison results of decoy-state RFI QKD with WCS and HSPS. Simulation results show that the secret key rates of decoy-state RFI QKD with WCS are higher than those with HSPS in short distance range, but the secret key rates of RFI QKD with HSPS outperform those with WCS in long distance range.

Statistical Behaviors of Quantum Spectra in Superheavy Nuclei

From the point of view of the interplay between order and chaos, the most regular single-particle motion of neutrons has been found in the superheavy system with and based on the Skyrme–Hartree–Fock model and in the system with and based on the relativistic mean-field model. It has been shown that the statistical analysis of spectra can give valuable information about the stability of suprheavy systems. In addition it may yield deep insight into the single-particle motion in the mean field formed by the superheavy system.

Total Quantum Statistical Entropy of Reissner-Nordstrom Black Holes： in Dirac Field Case

The total quantum statistical entropy of Reissner-Nordstrom black holes inDirac field case is evaluated in this article. The space-time of the black holes is divided intothree regions: region 1 (r 】 r_o), region 2 (r_o 】 r 】 r_i), and region 3 (r_i 】 r 】 0), where r_ois the radius of the outer event horizon, and Ti is the radius of the inner event horizon. The totalquantum statistical entropy of Reissner-Nordstrom black holes is S = S_1 + S_2 + S_3, where S_i (i= 1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S_2 isneglectfully small. S_1 = w_t(π~2/45)k_b(A_o/ε~2β~3), S_3 = -w_t(π~2/45)k_b(A_i/ε~2β~3), whereA_o and A_i are, respectively, the areas of the outer and inner event horizons, w_t = 2~s[1 -2~(-(s+1))], s = d/2, d is the space-time dimension, here d = 4, s = 2. As r_i approaches r_o in theextreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approacheszero.

On the Quantum Statistical Distributions Describing Finite Fermions and Bosons Systems

A century old methodology for deriving statistical distribution using approximate Stirling’s formulation of the factorial becomes questionable. By avoiding the use of exaggerated approximations, a new picture of the energy distribution of fermions and bosons are presented. Energy distribution among fermions (or bosons) in systems with finite degeneracy are found to be degeneracy dependent. The presented point of view explains, successfully, presence of degeneracy pressure in ultra-cooled Fermi gas and predicts the minimum accessible temperature for finite degeneracy fermions system.

Statistical Mechanics for Weak Measurements and Quantum Inseparability

In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system;hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state. We formulated the Quantum Pigeonhole Principle in the language of abstract Hilbert spaces, then generalized it to systems consisting of mixed states. This insight into the fundamentals of quantum statistical mechanics could help us understand the interpretation of quantum mechanics more deeply, and possibly have implication on quantum computing and information theory.

Numerical Study Using Statistical and Quantum Approaches for Solving Energy and Navier Stokes Momentum Equations (PDEs)

Statistical and Quantum numerical method was implemented in this study to solve various cases in partial differential equations (PDEs) in engineering applications. One-dimensional with two lattices arrangements as well as two-dimensional with nine lattices arrangements is employed. The stability and the accuracy have been investigated either using statistical technique or using Euler’s method. The numerical limitations of using LBM method have been obtained and compared with those obtained by Euler’s method finite difference method. The main goal of this study is to investigate the ability of a statistical method in solving various ODEs or PDEs in energy and momentum equations and comparing them with those obtained by a classical numerical technique. The results show the ability of the statistical method for solving ODEs and PDE’s with more stable and accurate results. Therefore, the motivation of utilizing the statistical technique is the stability and it is easy for a complex fluid flow application.

Prestack seismic stochastic inversion based on statistical characteristic parameters

In the conventional stochastic inversion method,the spatial structure information of underground strata is usually characterized by variograms.However,effectively characterizing the heterogeneity of complex strata is difficult.In this paper,multiple parameters are used to fully explore the underground formation information in the known seismic reflection and well log data.The spatial structure characteristics of complex underground reservoirs are described more comprehensively using multiple statistical characteristic parameters.We propose a prestack seismic stochastic inversion method based on prior information on statistical characteristic parameters.According to the random medium theory,this method obtains several statistical characteristic parameters from known seismic and logging data,constructs a prior information model that meets the spatial structure characteristics of the underground strata,and integrates multiparameter constraints into the likelihood function to construct the objective function.The very fast quantum annealing algorithm is used to optimize and update the objective function to obtain the fi nal inversion result.The model test shows that compared with the traditional prior information model construction method,the prior information model based on multiple parameters in this paper contains more detailed stratigraphic information,which can better describe complex underground reservoirs.A real data analysis shows that the stochastic inversion method proposed in this paper can effectively predict the geophysical characteristics of complex underground reservoirs and has a high resolution.

Photon counting statistics in single multi-level quantum system

We theoretically study the statistics of photon emission of single multi-level quantum system by employing the generating functions approach developed recently. The generalized decay constants are included in single multi-level quantum system with quasi-degenerated levels in this work although they are normally neglected in the absence of （quasi-）degeneracies in multi-level quantum system within the rotating wave approximation. The quantum beats, the line shapes and the Mandel＇s Q parameters, etc. are studied.

Statistical Interaction Term of One-Dimensional Anyon Models

A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.

Statistical Mechanical Entropy of a （4 ＋ n）-Dimensional Static Spherically Symmetric Black Hole

Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensions, we calculate the statistical entropy of the scalar field in the higher-dimensional static spherically symmetric black hole spacetime without any artificial cutoff. Calculation shows that the entropy is proportional to the horizon area. The coefficient of proportionality is 1/4 when the minimal length parameter is selected appropriately.

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.

Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.

Quantum Statistics in Physical Chemistry, the Law of Mass Action and Epicatalysis

The law of mass action, based on maxwellian statistics, cannot explain recent epicatalysis experiments but does when generalized to non-maxwellian statistics. Challenges to the second law are traced to statistical heterogeneity that falls outside assumptions of homogeneity and indistinguishability made by Boltzmann, Gibbs, Tolman and Von Neumann in their H-Theorems. Epicatalysis operates outside these assumptions. Hence, H-Theorems do not apply to it and the second law is bypassed, not broken. There is no contradiction with correctly understood established physics. Other phenomena also based on heterogeneous statistics include non-maxwellian adsorption, the field-induced thermoelectric effect and the reciprocal Hall effect. Elementary particles have well known distributions such as Fermi-Dirac and Bose Einstein, but composite particles such as those involved in chemical reactions, have complex intractable statistics not necessarily maxwellian and best determined by quantum modeling methods. A step by step solution for finding the quantum thermodynamic properties of a quantum composite gas, that avoids the computational requirement of modeling a large number of composite particles includes 1) quantum molecular modeling of a few particles, 2) determining their available microstates, 3) producing their partition function, 4) generating their statistics, and 5) producing the epicatalytic parameter for the generalized law of mass action.

Quantum Statistics of Random Walks

The paper dealt with quantum canonical ensembles by random walks, where state transitions are triggered by the connections between labels, not by elements, which are transferred. The balance conditions of such walks lead to emission rates of the labels. The labels with emission rates definitely lower than 1 are like modes. For labels with emission rates very close to 1, the quantum numbers are concentrated around a mean value. As an application I consider the role of the zero label in a quantum gas in equilibrium.

Level Statistics Crossover of Chiral Surface States in a Three-Dimensional Quantum Hall System

Recent experiments have demonstrated the realization of the three-dimensional quantum Hall effect in highly anisotropic crystalline materials, such as ZrTe|_5 and BaMnSb_2. Such a system supports chiral surface states in the presence of a strong magnetic field, which exhibit a one-dimensional metal-insulator crossover due to suppression of surface diffusion by disorder potential. We study the nontrivial surface states in a lattice model and find a wide crossover of the level-spacing distribution through a semi-Poisson distribution. We also discover a nonmonotonic evolution of the level statistics due to the disorder-induced mixture of surface and bulk states.

Full Counting Statistics of Superconductor-Quantum Dot-Superconductor Contacts in the Presence of Interactions

In this paper, we discuss the full counting statistics of superconducting quantum dot contacts. We discuss the effects both of phonon and onsite electronic interaction focusing on the experimentally most relevant case of strong onsite electronic interactions. We find that in general, the Josephson effect and multiple Andreev reflections in these systems are strongly suppressed due to the onsite interaction. However, in case resonant phonons are found, the effect of the onsite interaction can be overcome.

Topological quantum-phase coherence in full counting statistics of transport electrons with two-body interaction

The full counting statistics of electron transport through two parallel quantum dots with antiparallel magnetic fluxes is investigated as a probe to detect the topological quantum-phase coherence （TQPC）, which results in the characteristic oscillation of the zero-frequency cumulants including the shot noise and skewness. We show explicitly the phase transition of cumulant spectrum-patterns induced by the topology change of electron path-loops while the pattern period, which depends only on the topology （or Chern number）, is robust against the variation of Coulomb interaction and interdot coupling strengths. Most importantly we report for the first time on a new type of TQPC, which is generated by the two- particle interaction and does not exist in the single-particle wave function interference. Moreover, the accurately quantized peaks of Fano-factor spectrum, which characterize the super- and sub-Poissonian shot noises, are of fundamental importance in technical applications similar to the superconducting quantum interference device.