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arXiv:1712.02211

Pulse Width Modulation method for quantum control design

Qiming Chen, Re-Bing Wu, HERSCHEL A. RABITZ

Published Dec 6, 2017• 0 citations
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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 $Ω$, 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.

DOI
10.48550/arxiv.1712.02211

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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 ΩΩΩ, 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.
This paper proposes a numerical method for solving time-dependent Schrodinger equations with finite spectral bandwidth, which applies to both periodic and non-periodic cases. We introduce the concept of Pulse Width Modulation (PWM), which is broadly used in classical control engineering, to simulate time-dependent quantum dynamics by switching between a finite number of constant Hamiltonians. The switching timings can be programmed to improve the precision and save computational resources. The effectiveness of the PWM method is demonstrated by numerical simulations, which shows that it is faster and more robust than the standard piecewise constant control systems. Moreover, we also propose the realization of PWM method for potential implementation in experimental systems.
This paper focuses on accelerating quantum optimal control design for complex quantum systems. Based on our previous work [{arXiv:1607.04054}], we combine Pulse Width Modulation (PWM) and gradient descent algorithm into solving quantum optimal control problems, which shows distinct improvement of computational efficiency in various cases. To further apply this algorithm to potential experiments, we also propose the smooth realization of the optimized control solution, e.g. using Gaussian pulse train to replace rectangular pulses. Based on the experimental data of the D-Norleucine molecule, we numerically find optimal control functions in 333-qubit and 666-qubit systems, and demonstrate its efficiency advantage compared with basic GRAPE algorithm.
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