时间随机约简模型

可计算的无限时间随机模型预测控制用于量子滤波的本征态缩减

Tractable Infinite-Horizon Stochastic Model Predictive Control for Quantum Filtering via Eigenstate Reduction

本文提出了一种基于本征态缩减的可计算无限时间随机模型预测控制框架，用于提高量子滤波的鲁棒性，并通过实验验证了其在多级和异或型系统中的高效性和可扩展性。

随机粒子湮灭：相对论性量子场论中的一种态约化模型

Stochastic particle annihilation: a model of state reduction in relativistic quantum field theory

本文概述了相对论性量子场论中涉及薛定谔方程非线性随机扩展的态约化模型。湮灭算子的本征态被选为首选的基础上发生减少。这些是饱和海森堡测不准关系的束缚的相干态，表现出类似经典的行为。在推广到相对论标量量子场论之前，对量子谐振子进行了详细的研究。能量密度的无限增长率在这个模型中是不存在的，而这种无限增长率一直困扰着最近相对论提出的动力学态简化。这是因为状态演化方程并不驱动粒子从真空中产生。该模型需要一个首选序列的类空超曲面支持类时状态演化的规范。然而，它示出的优选表面的选择有没有影响扰动的结果，二阶耦合参数。它演示了如何减少到一个电荷密度的基础上，可以诱导在费米子物质通过适当的耦合到玻色子场进行这种机制。

量子噪声与随机约化

Quantum noise and stochastic reduction

在标准的非相对论性量子力学中，能量的期望值是一个守恒量。在遵守守恒定律的同时，有可能将与量子态演化相关联的动力学定律一致地扩展到包括非线性随机分量。根据这样获得的动力学，称为基于能量的随机薛定谔方程，任意初始状态自发地坍缩到能量本征态之一，从而描述了量子态还原现象。在这篇文章中，两个这样的模型进行了研究：一个实现状态减少在无限的时间，和其他在有限的时间。详细地讨论了相应的能量期望过程和能量方差过程的性质。通过使用一种新的应用程序的非线性滤波方法，封闭形式的解决方案-代数性质，不涉及集成-这两个模型。在每种情况下，解决方案表示在一个随机变量表示的终端系统的能量，和一个独立的噪声过程。有了这些解，就有可能明确地模拟复杂物理系统的量子态的动力学。

Quantum State Reduction

We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schrödinger equation, and have introduced the density matrix as the expectation of the random pure projection operator associated with the evolving state vector. After working out properties of the reduction process we construct a general solution to the energy-driven stochastic master equation. The solution is obtained by the use of nonlinear filtering theory and takes …

A Variance Reduction Technique for the Stochastic Liouville-von Neuman Equation

The Stochastic Liouville-von Neumann equation provides an exact numerical simulation strategy for quantum systems interacting with Gaussian reservoirs [J.T. Stockburger & H. Grabert, PRL 88, 170407 (2002)]. Its scaling with the extension of the time interval covered has recently improved dramatically through time-domain projection techniques [J.T. Stockburger, EPL 115, 40010 (2016)]. Here we present a sampling strategy which results in a significantly improved scaling with the strength of the dissipative interaction, based on reducing the non-unitary terms in sample propagation through convex …

Quantum coarse-graining for extreme dimension reduction in modelling stochastic temporal dynamics

Stochastic modelling of complex systems plays an essential, yet often computationally intensive role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to exhibit memory advantages for such tasks. Heretofore, the focus has been on lossless memory compression, wherein the advantage is typically in terms of lessening the amount of information tracked by the model, while -- arguably more practical -- reductions in memory dimension are not always possible. Here we address the case of lossy compression for quantum…

切向插值投影用于线性量子随机系统的模型降阶

Tangential Interpolatory Projection for Model Reduction of Linear Quantum Stochastic Systems

本文提出了一种用于线性量子随机系统模型降阶的方法，通过插值投影匹配多点输入输出响应，保持物理可实现性，提供误差界和插值点选择方法，并展示主动和被动系统的示例。

线性量子随机系统的模型降阶结构与变换

Structures and Transformations for Model Reduction of Linear Quantum Stochastic Systems

本文研究线性量子随机系统的降阶理论，探讨子系统截断对物理可实现性及完全被动性的保持，提出准平衡实现概念并给出降阶误差界。