Simulating local measurements on a quantum many body system with stochastic matrix product states

TL;DR

This paper introduces a method to simulate stochastic measurement processes in quantum many-body systems using matrix product states, enabling analysis of local and non-local measurement effects.

Contribution

It develops a general approach for simulating measurement-induced dynamics with matrix product states, including a simple measurement model and its matrix product operator representation.

Findings

Successfully simulated measurement effects on a Heisenberg spin chain.

Demonstrated handling of both local and non-local measurements.

Revealed how measurements induce long-range correlations.

Abstract

We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators is found. The technique is exemplified by numerical simulations of the anti-ferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular we focus on local measurements with small support and non-local measurements which induces long range correlations.