Experimental Tests for Stochastic Reduction Models

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。

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

A model of state reduction in relativistic quantum field theory involving a nonlinear stochastic extension of Schrödinger's equation is outlined. The eigenstates of the annihilation operator are chosen as the preferred basis onto which reduction occurs. These are the coherent states which saturate the bound of the Heisenberg uncertainty relation, exhibiting classical-like behavior. The quantum harmonic oscillator is studied in detail before generalizing to relativistic scalar quantum field theory. The infinite rates of increase in energy density which have plagued recent relativistic proposals…

Quantum noise and stochastic reduction

In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schrodinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this article, two such models are investigated: one that …

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。