A Pseudospectral Method for Optimal Control of Open Quantum Systems

TL;DR

This paper introduces a pseudospectral computational method for designing optimal control pulses in open quantum systems, transforming continuous control problems into finite-dimensional nonlinear programs solvable with standard optimization tools.

Contribution

The paper presents a universal pseudospectral approach for optimal control in open quantum systems, enabling efficient and practical pulse design with extensions for smoothing and energy minimization.

Findings

Excellent agreement with analytical solutions in NMR problems

Method extends to practical control concerns like smoothing and energy minimization

Applicable to all open quantum systems limited by dissipation

Abstract

In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous time optimal control problem, to a finite dimensional constrained nonlinear programming problem. This resulting optimization problem can then be solved using existing numerical optimization suites. We apply the Legendre pseudospectral method to a series of optimal control problems on open quantum systems that arise in Nuclear Magnetic Resonance (NMR) spectroscopy in liquids. These problems have been well studied in previous literature and analytical optimal controls have been found. We find an excellent agreement between the maximum transfer efficiency produced by our computational method and the analytical expressions. Moreover, our method permits us to extend the analysis and address practical concerns, including smoothing discontinuous controls as well as deriving minimum energy controls. The method is not restricted to the systems studied in this article but is universal to every open quantum system whose performance is limited by dissipation.