Quantum optimal control theory and dynamic coupling in the spin-boson model

TL;DR

This paper develops a quantum optimal control framework for the spin-boson model, enabling manipulation of dissipation and quantum state transfer through tailored external fields, with applications including quantum gate implementation.

Contribution

It introduces a non-perturbative optimal control approach within the Bloch-Redfield formalism for open quantum systems, specifically applied to the spin-boson model in strong coupling.

Findings

Optimized control fields can suppress or accelerate relaxation.

Multi-component low-frequency fields effectively control dissipation.

Analytic Lamb shift result at zero temperature.

Abstract

A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system--bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control--dissipation correlation and the non-perturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum Z-gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significatively is a multi--component low--frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.