Quadratic Models for Engineered Control of Open Quantum Systems

TL;DR

This paper presents a quadratic modeling framework for open quantum systems with periodically evolving environments, enabling analysis of system-environment correlations and steady states in quantum thermalization and qubit initialization.

Contribution

It introduces a novel quadratic model framework that generalizes repeated interactions and captures correlations, with applications to thermalization and quantum state preparation.

Findings

Framework effectively models open quantum system evolution.

Preserves system-environment correlations in the formalism.

Applicable to thermalization and qubit initialization scenarios.

Abstract

We introduce a framework to model the evolution of a class of open quantum systems whose environments periodically undergo an instantaneous non-unitary evolution stage. For the special case of quadratic models, we show how this approach can generalise the formalism of repeated interactions to allow for the preservation of system-environment correlations. Furthermore, its continuous zero-period limit provides a natural description of the evolution of small systems coupled to large environments in negligibly perturbed steady states. We explore the advantages and limitations of this approach in illustrative applications to thermalisation in a simple hopping ring and to the problem of initialising a qubit chain via environmental engineering.