Theory of open quantum dynamics with hybrid noise

TL;DR

This paper presents a comprehensive theory for the dynamics of open quantum systems interacting with hybrid environments, combining perturbative and exact treatments to derive master equations applicable to systems with small energy gaps.

Contribution

It introduces a novel hybrid approach that integrates Bloch-Redfield and Marcus formulas for open quantum system dynamics, especially useful for systems with complex environmental interactions.

Findings

Derived master equations with convolution-based relaxation rates.

Applied theory to 16-qubit quantum annealing, matching experimental data.

Enabled analysis of systems with extremely small energy gaps.

Abstract

We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components. One part of the system-bath interaction is treated in a perturbative manner, whereas the other part is considered exactly. This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch-Redfield and Marcus formulas. Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment. As an illustration, we apply the theory to the 16-qubit quantum annealing problem with dangling qubits and show good agreement with experimental results.