Optimal Control for Open Quantum Systems: Qubits and Quantum Gates

TL;DR

This review discusses recent advances in optimal control strategies for open quantum systems, emphasizing state-independent control methods for quantum information processing in solid-state qubits, including new theoretical extensions and practical applications.

Contribution

The paper introduces novel extensions of Pontryagin's principle to non-Markovian quantum dynamics and compares three approaches for state-independent control in open quantum systems.

Findings

Extended Pontryagin's principle for non-Markovian quantum systems

Development of three approaches for state-independent control

Application to solid-state qubits and quantum gates

Abstract

This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open quantum systems, and quantum information processing is followed by a presentation of recent developments regarding the two main tasks in this context: state-specific and state-independent optimal control. For the former, we present an extension of conventional theory (Pontryagin's principle) to quantum systems which undergo a non-Markovian time-evolution. Owing to its importance for the realization of quantum information processing, the main body of the review, however, is devoted to state-independent optimal control. Here, we address three different approaches: an approach which treats dissipative effects from the environment in lowest-order perturbation theory, a general method based on the time--evolution superoperator concept, as well as one based on the Kraus representation of the time-evolution superoperator. Applications which illustrate these new methods focus on single and double qubits (quantum gates) whereby the environment is modeled either within the Lindblad equation or a bath of bosons (spin-boson model). While these approaches are widely applicable, we shall focus our attention to solid-state based physical realizations, such as semiconductor- and superconductor-based systems. While an attempt is made to reference relevant and representative work throughout the community, the exposition will focus mainly on work which has emerged from our own group.