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Optimal Control of two-level quantum systems via Chopped RAndom Basis algorithm

Luna Cesari

Published Mar 1, 2020• 0 citations
OpenAlex

Abstract

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

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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
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.
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.
This thesis discusses the application of numerical methods to different complex quantum systems. I present the successful application of the chopped random basis optimal control algorithm (CRAB) to these systems. This includes the optimization of the dynamics of quantum many body systems. For this purpose the possibility of the application of modern tensor network algorithms such as DMRG with the CRAB algorithm is exploited. In all these cases a direct connection to experimental implementations is important to keep. Furthermore, we use these numerical methods to implement a very generic formulation of quantum gauge theories and perform ground state calculations as well as, for the first time, extended dynamical simulations.
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.
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.
Integer factorization remains a significant challenge for classical computers and is fundamental to the security of RSA encryption. Adiabatic quantum algorithms present a promising solution, yet their practical implementation is limited by the short coherence times of current noisy intermediate-scale quantum devices and quantum simulators. In this work, we apply the chopped random-basis (CRAB) optimization technique to enhance adiabatic quantum factorization algorithms. We demonstrate the effectiveness of CRAB by applying it to factor the integers ranging from 21 to 2479, achieving significantly improved fidelity of the target state when the evolution time exceeds the quantum speed limit. Notably, this performance improvement shows resilience in the presence of dephasing noise, highlighting CRAB's practical utility in noisy quantum systems. Our findings suggest that CRAB optimization can serve as a powerful tool for advancing adiabatic quantum algorithms, with broader implications for quantum information processing tasks.