Classical and Quantum Ensembles via Multiresolution. I. BBGKY Hierarchy

BBGKY 层级用于量子错误缓解

BBGKY hierarchy for quantum error mitigation

本文提出一种基于BBGKY层级方程作为补充约束的ZNE量子错误缓解新方案，在格点Schwinger模型模拟中，对粒子数和电荷测量的误差平均降低18.2%和52.8%，计算成本随系统规模多项式增长。

On Evolution Equations for Marginal Correlation Operators

This paper is devoted to the problem of the description of nonequilibrium correlations in quantum many-particle systems. The nonlinear quantum BBGKY hierarchy for marginal correlation operators is rigorously derived from the von Neumann hierarchy for correlation operators that give an alternative approach to the description of states in comparison with the density operators. A nonperturbative solution of the Cauchy problem of the nonlinear quantum BBGKY hierarchy for marginal correlation operators is constructed.

The BBGKY hierarchy for ultracold bosonic systems

We establish a theoretical framework for exploring the quantum dynamics of finite ultracold bosonic ensembles based on the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations of motion for few-particle reduced density matrices (RDMs). The theory applies to zero as well as low temperatures and is formulated in a highly efficient way by utilizing dynamically optimized single-particle basis states and representing the RDMs in terms of permanents with respect to those. An energy, RDM compatibility and symmetry conserving closure approximation is developed on the basis of a recursive…

Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy

Time-resolved measurement techniques are opening a window on nonequilibrium quantum phenomena that is radically different from the traditional picture in the frequency domain. The simulation and interpretation of nonequilibrium dynamics is a conspicuous challenge for theory. This paper presents a novel approach to quantum many-body dynamics that is based on a Hamiltonian formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations of motion for reduced density matrices. These equations have an underlying symplectic structure, and we write them in the form of the classi…

Groups of Operators for Evolution Equations of Quantum Many-Particle Systems

The aim of this work is to study the properties of groups of operators for evolution equations of quantum many-particle systems, namely, the von Neumann hierarchy for correlation operators, the BBGKY hierarchy for marginal density operators and the dual BBGKY hierarchy for marginal observables. We show that the concept of cumulants (semi-invariants) of groups of operators for the von Neumann equations forms the basis of the expansions for one-parametric families of operators for evolution equations of infinitely many particles.

用于量子误差缓解的费曼时钟与层次信息采样

Feynman's clock and hierarchy-informed sampling for quantum error mitigation

针对近期量子算法物理实现中降低量子噪声的需求，提出将BBGKY - ISM方案从自旋链量子模拟扩展到任意量子电路的新方法，利用费曼时钟哈密顿量映射，经数值模拟验证其能有效降低量子误差。

Dynamics of Correlations of Bose and Fermi Particles

We discuss the origin of the microscopic description of correlations in quantum many-particle systems obeying Fermi-Dirac and Bose-Einstein statistics. For correlation operators that give the alternative description of the quantum state evolution of Bose and Fermi particles, we deduce the von Neumann hierarchy of nonlinear equations and construct the solution of its initial-value problem in the corresponding spaces of sequences of trace class operators. The links of constructed solution both with the solution of the quantum BBGKY hierarchy and with the nonlinear BBGKY hierarchy for marginal co…

通过层级感知采样实现量子误差缓解：Schwinger模型中的手性动力学

Quantum error mitigation by hierarchy-informed sampling: chiral dynamics in the Schwinger model

本文提出一种基于BBGKY层级方程的量子误差缓解方案，用于缓解Schwinger模型中手性磁效应的模拟，实现了噪声的有效抑制。

Quantum multiresolution: tower of scales

We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like equations. The numerical simulation demonstrates the formation of various (meta) stable patterns or orbits generated by internal hidden symmetry from generic high-localized fundamental modes. In addition, we can control the type of behavior on the pure algebraic level by means of properly reduced algebraic systems (generalized dispersion relations).

Pattern Formation in Quantum Ensembles

We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from basic localized modes in various collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal-Lindblad equations, which are the result of ``wignerization'' procedure of classical BBGKY hierarchy. We present the explicit desc…

面向高阶量子动力学BBGKY方程构建的面向对象编程能力

Capabilities of object-oriented programming for the construction of quantum-kinetic BBGKY equations of high orders

提出基于Python的面向对象框架，通过实现量子力学原理与算符代数，高效构建BBGKY层级中高阶关联矩阵的运动方程，不到一分钟即可完成四阶推导。

Localization and Pattern Formation in Quantum Physics. II. Waveletons in Quantum Ensembles

In this second part we present a set of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. The key points demonstrating advantages of this approach are: (i) effects of localization of possible quantum states; (ii) effects of non-perturbative multiscales which cannot be calculated by means of perturbation approaches; (iii) effects of formation of complex/collective quantum patterns from localized modes and classification and possible contro…