Matrix Product States approach to non-Markovian processes

TL;DR

This paper introduces a matrix product state framework to model non-Markovian processes in classical and quantum systems, enabling derivation of master equations from quantum Markovian processes projected onto lower-dimensional spaces.

Contribution

It presents a novel matrix product state method to represent and analyze non-Markovian processes in both classical and quantum contexts.

Findings

Classical processes can be embedded into quantum measurement procedures.

Master equations can be derived by projecting quantum Markovian processes.

The approach unifies classical and quantum non-Markovian process modeling.

Abstract

A matrix product state approach to non-Markovian, classical and quantum processes is discussed. In the classical case, the Radon-Nikodym derivative of all processes can be embedded into quantum measurement procedure. In the both cases, quantum and classical, the master equation can be derived from a projecting a quantum Markovian process onto a lower dimensional subspace.