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arXiv:2104.07687 · Reports on Progress in Physics

One decade of quantum optimal control in the chopped random basis

Matthias M. Müller, Ressa S. Said, Fedor Jelezko, Tommaso Calarco, Simone Montangero

Published May 23, 2022• 110 citations
arXivHTMLPDF

Abstract

The chopped random basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications such as quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraints-while maintaining an access to the usually trap-free control landscape-and to switch from open-loop to closed-loop optimization (including with remote access-or RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.

DOI
10.1088/1361-6633/ac723c

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The chopped random basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications such as quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraints-while maintaining an access to the usually trap-free control landscape-and to switch from open-loop to closed-loop optimization (including with remote access-or RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.
In this work, we describe in detail the chopped random basis (CRAB) optimal control technique recently introduced to optimize time-dependent density matrix renormalization group simulations [P. Doria, T. Calarco, and S. Montangero, Phys. Rev. Lett. 106, 190501 (2011)]. Here, we study the efficiency of this control technique in optimizing different quantum processes and we show that in the considered cases we obtain results equivalent to those obtained via different optimal control methods while using less resources. We propose the CRAB optimization as a general and versatile optimal control technique.
This work is devoted to the study and the application of the Chopped RAndomBasis (CRAB) control algorithm as an efficient, versatile optimal control techniqueto be used for the purpose of enhancing the quality of quantum processes. In orderto show its principal aspects, the method is here applied to different systems, inparticular one-qubit and two-qubit system. Finally, the dressed CRAB algorithmis presented as a valid alternative to the standard method, as it comes with theadditional property of guaranteed convergence to the global optimum
Optimal control of complex quantum systems in theory and experiment is the focus of this thesis. The theoretical aspect of our work was concerned with the development of algorithms that are capable of precisely tailoring the shapes of control pulses to meet various control goals while respecting all physical constraints, both fundamental and problem specific. Having these effective tools at hand, we computed control inputs for a range of physical systems using simulation-based time propagation. We extended the dressed chopped random basis (dCRAB) optimization method, previously developed in our group, such that boundary conditions and other constraints that arise from experimental setups of quantum systems can be regarded. Therefore, we wrote a software suite that enables experimentalists to improve their control pulses by directly interfacing the lab with our control algorithm.
Abstract The mathematics of optimal control of quantum systems is of great interest in connection with fundamental problems of physics as well as with existing and prospective applications to quantum technologies. One important problem is the development of methods for constructing controls for quantum systems. One of the commonly used methods is the Krotov method, which was initially proposed outside of quantum control theory in articles by Krotov and Feldman (1978, 1983). This method was used to develop a novel approach to finding optimal controls for quantum systems in [64] (Tannor, Kazakov, and Orlov, 1992), [65] (Somlói, Kazakov, and Tannor, 1993), and in many other works by various scientists. Our survey discusses mathematical aspects of this method for optimal control of closed quantum systems. It outlines various modifications with different forms of the improvement function (for example, linear or linear-quadratic), different constraints on the control spectrum and on the admissible states of the quantum system, different regularisers, and so on. The survey describes applications of the Krotov method to controlling molecular dynamics and Bose–Einstein condensates, and to quantum gate generation. This method is compared with the GRAPE (GRadient Ascent Pulse Engineering) method, the CRAB (Chopped Random-Basis) method, and the Zhu–Rabitz and Maday–Turinici methods. Bibliography: 158 titles.
We discuss quantum optimal control of Bose-Einstein condensates trapped in magnetic microtraps. The objective is to transfer a condensate from the ground state to the first-excited state. This type of control problem is typically solved using derivative-based methods in a high-dimensional control space such as gradient-ascent pulse engineering (GRAPE) and Krotov's method or derivative-free methods in a reduced control space such as Nelder-Mead with a chopped random basis (CRAB). We discuss how these methods can be combined in gradient optimization using parametrization (GROUP) including the finite bandwidth of the control electronics. We compare these methods and find that GROUP converges much faster than Nelder-Mead with CRAB and achieves better results than GRAPE and Krotov's method on the control problem presented here.