Quantum control with spectral constraints

TL;DR

This paper introduces a method for designing quantum control fields that respect spectral constraints, ensuring robustness and minimal quality loss, demonstrated on a Heisenberg spin chain.

Contribution

A general approach for generating spectral-constrained quantum control pulses using low-pass filtering, applicable to various quantum systems.

Findings

Control quality remains high with spectral constraints

Method is robust and applicable to different quantum interactions

Negligible impact on control performance compared to unconstrained methods

Abstract

Various constraints concerning control fields can be imposed in the realistic implementations of quantum control systems. One of the most important is the restriction on the frequency spectrum of acceptable control parameters. It is important to consider the limitations of experimental equipment when trying to find appropriate control parameters. Therefore, in this paper we present a general method of obtaining a piecewise-constant controls, which are robust with respect to spectral constraints. We consider here a Heisenberg spin chain, however the method can be applied to a system with more general interactions. To model experimental restrictions we apply an ideal low-pass filter to numerically obtained control pulses. The usage of the proposed method has negligible impact on the control quality as opposed to the standard approach, which does not take into account spectral limitations.