Recursive Weak- and Strong Coupling Expansions in a Cosine Potential

Recursive approach for non-Markovian time-convolutionless master equations

We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which pro- vides an useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We…

Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator

In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniqu…

Large-D Expansion from Variational Perturbation Theory

We derive recursively the perturbation series for the ground-state energy of the D-dimensional anharmonic oscillator and resum it using variational perturbation theory (VPT). From the exponentially fast converging approximants, we extract the coefficients of the large-D expansion to higher orders. The calculation effort is much smaller than in the standard field-theoretic approach based on the Hubbard-Stratonovich transformation.

Mixed Precision Fermi-Operator Expansion on Tensor Cores From a Machine Learning Perspective

We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia's A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bia…

密度矩阵微扰理论的磁化率公式

Susceptibility Formulation of Density Matrix Perturbation Theory

提出密度矩阵微扰理论的对偶磁化率公式，通过计算观测量的静态磁化率高效获取任意Hamiltonian微扰下的线性响应，支持稀疏矩阵代数并兼容AI硬件加速。

时间卷积无主方程的递归微扰方法：任意开放系统的广义Lindblad生成元的显式构造

Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems

本文发展了一种递归微扰展开方法，将开放量子系统的时间卷积无（TCL）生成元表示为广义Lindblad形式，并在任意阶保持Lindblad-like结构，同时满足最小耗散条件，显式计算至四阶以验证其对非马尔可夫动力学和强耦合效应的有效性。

基于递归预言扩展的确定性量子搜索

Deterministic Quantum Search via Recursive Oracle Expansion

本文提出一种基于递归预言扩展的确定性量子搜索算法，通过标记目标前两比特前缀的四分之一搜索空间逐步缩减叠加态，以约 O(N^0.7925) 的查询复杂度实现确定性成功，并显著减少双量子比特门数量，适合硬件实现且支持部分数据库搜索。

1/N-expansions in non-relativistic quantum mechanics

An extensive number of numerical computations of energy 1/$N$ series using a recursive Taylor series method are presented in this paper. The series are computed to a high order of approximation and their behaviour on increasing the order of approximation is examined.

基于递归变分级数方法的近期量子算法，用于计算分子与材料性质

Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods

针对近期有缺陷的量子计算机如何解决实用问题的痛点，提出基于递归变分级数的量子算法，将算子展开为Chebyshev多项式后用变分量子算法计算各项，经格林函数与自相关函数计算验证有效，可用于分子与材料性质估算。

Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism

Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for simple single-particle systems, in this paper we present a full extension of this formalism to a general quantum system with many degrees of freedom in a time-dependent potential. Furthermore, we also present a recursive approach for the velocity-independent part of the effective potential, which is necessary for calculating diagonal amplitudes and partition functions, as well as an extension from th…