Pulse Width Modulation method for quantum control design

TL;DR

This paper introduces a PWM-based approximation method for quantum control that transforms continuous and bang-bang controls, enabling faster design and more practical implementation in large quantum systems.

Contribution

The paper proposes a PWM approximation technique for quantum control that efficiently converts between control types and improves design speed in high-dimensional systems.

Findings

PWM effectively transforms control types with high-frequency error components.

The method accelerates quantum control design in large systems.

PWM facilitates implementation of bang-bang protocols with arbitrary waveforms.

Abstract

Illuminated by the Pulse Width Modulation (PWM) technology in classical control engineering, we propose the PWM approximation which transforms continuous and bang-bang control into each other. This method works by squeezing the approximation error into high-frequency components above a prescribed cutoff frequency $\Omega$, which can be tailored by modulating the switch time of the bang-bang control. Because the quantum dynamics under bang-bang control can be efficiently calculated, PWM allows us to speed up quantum control design particularly in large dimensional systems with small number of control variables. Moreover, PWM paves the way to implement various bang-bang control protocols in the literature with an arbitrary waveform, which is more desirable in laboratory.