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Genetic and Evolutionary Computation Conference (GECCO)

Performance analysis of derandomized evolution strategies in quantum control experiments

Ofer M. Shir, Jonathan Roslund, Thomas Bäck, HERSCHEL A. RABITZ

Published Jul 12, 2008• 4 citations
Publisher

Abstract

Genetic Algorithms (GAs) are historically the most commonly used optimization method in Quantum Control (QC) experiments. We transfer specific Derandomized Evolution Strategies (DES) that have performed well on noise-free theoretical Quantum Control calculations, including the Covariance Matrix Adaptation (CMA-ES) algorithm, into the noisy environment of Quantum Control experiments. We study the performance of these DES variants in laboratory experiments, and reveal the underlying strategy dynamics of first- versus second-order landscape information.

DOI
10.1145/1389095.1389193

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Genetic Algorithms (GAs) are historically the most commonly used optimization method in Quantum Control (QC) experiments. We transfer specific Derandomized Evolution Strategies (DES) that have performed well on noise-free theoretical Quantum Control calculations, including the Covariance Matrix Adaptation (CMA-ES) algorithm, into the noisy environment of Quantum Control experiments. We study the performance of these DES variants in laboratory experiments, and reveal the underlying strategy dynamics of first- versus second-order landscape information.
Optimization of quantum systems by closed-loop adaptive pulse shaping offers a rich domain for the development and application of specialized evolutionary algorithms. Derandomized evolution strategies (DESs) are presented here as a robust class of optimizers for experimental quantum control. The combination of stochastic and quasi-local search embodied by these algorithms is especially amenable to the inherent topology of quantum control landscapes. Implementation of DES in the laboratory results in efficiency gains of up to $\ensuremath{\sim}9$ times that of the standard genetic algorithm, and thus is a promising tool for optimization of unstable or fragile systems. The statistical learning upon which these algorithms are predicated also provide the means for obtaining a control problem's Hessian matrix with no additional experimental overhead. The forced optimal covariance adaptive learning (FOCAL) method is introduced to enable retrieval of the Hessian matrix, which can reveal information about the landscape's local structure and dynamic mechanism. Exploitation of such algorithms in quantum control experiments should enhance their efficiency and provide additional fundamental insights.
Abstract We present the results of a comprehensive study of optimization algorithms for the calibration of quantum devices. As part of our ongoing efforts to automate bring-up, tune-up, and system identification procedures, we investigate a broad range of optimizers within a simulated environment designed to closely mimic the challenges of real-world experimental conditions. Our benchmark includes widely used algorithms such as Nelder–Mead and the state-of-the-art covariance matrix adaptation evolution strategy (CMA-ES). We evaluate performance in both low-dimensional settings, representing simple pulse shapes used in current optimal control protocols with a limited number of parameters, and high-dimensional regimes, which reflect the demands of complex control pulses with many parameters. Based on our findings, we recommend the CMA-ES algorithm and provide empirical evidence for its superior performance across all tested scenarios.
Variational quantum algorithms (VQAs) offer a promising path toward using near-term quantum hardware for applications in academic and industrial research. These algorithms aim to find approximate solutions to quantum problems by optimizing a parametrized quantum circuit using a classical optimization algorithm. A successful VQA requires fast and reliable classical optimization algorithms. Understanding and optimizing how off-the-shelf optimization methods perform in this context is important for the future of the field. In this work, we study the performance of four commonly used gradient-free optimization methods [sequential least-squares quadratic programming, constrained optimization by linear approximations, the covariance matrix adaptation evolutionary strategy (CMA-ES), and the simultaneous perturbation stochastic approximation (SPSA)] to find ground-state energies of a range of small chemistry and material science problems. We test a telescoping sampling scheme (where the accuracy of the cost-function estimate provided to the optimizer is increased as the optimization converges) for all methods, demonstrating mixed results across our range of optimizers and problems chosen. We further hyperparameter tune two of the four optimizers (CMA-ES and SPSA) across a large range of models and demonstrate that with appropriate hyperparameter tuning, CMA-ES is competitive with and sometimes outperforms SPSA (which is not observed in the absence of hyperparameter tuning). Finally, we investigate the ability of an optimizer to beat the ``sampling-noise floor'' given by the sampling noise of each cost-function estimate provided to the optimizer. Our results demonstrate the necessity for tailoring and hyperparameter tuning known optimization techniques for inherently noisy variational quantum algorithms and that the variational landscape that one finds in a VQA is highly problem and system dependent. This provides guidance for future implementations of these algorithms in experiments.
Quantum control landscape is generally a physical objective defined as a functional of the control field and plays an important role for the analysis and manipulation of quantum systems. In this paper, we focus on typical learning methods (i.e., gradient decent method, genetic algorithm and deferential evolution) for the landscape control of open quantum systems and explores the characteristics of these different types of learning algorithms. Taking a two-level open quantum system as an example, the optimal value of the control landscape can be obtained under varying Lindblad operators that reflect the system's interactions with the environment. Numerical experiments demonstrate the learning performances to acquire the optimal control strategy by exploring the control landscape of this two-level open quantum system.
The laboratory closed-loop optimal control of quantum phenomena, expressed as minimizing a suitable cost functional, is currently implemented through an optimization algorithm coupled to the experimental apparatus. In practice, the most commonly used search algorithms are variants of genetic algorithms. As an alternative choice, a direct search deterministic algorithm is proposed in this paper. For the simple simulations studied here, it outperforms the existing approaches. An additional algorithm is introduced in order to reveal some properties of the cost functional landscape.
The exploration of a quantum control landscape, which is the physical observable as a function of the control variables, is fundamental for understanding the ability to perform observable optimization in the laboratory. For high control variable dimensions, trajectory-based methods provide a means for performing such systematic explorations by exploiting the measured gradient of the observable with respect to the control variables. This paper presents a practical, robust, easily implemented statistical method for obtaining the gradient on a general quantum control landscape in the presence of noise. In order to demonstrate the method's utility, the experimentally measured gradient is utilized as input in steepest-ascent trajectories on the landscapes of three model quantum control problems: spectrally filtered and integrated second harmonic generation as well as excitation of atomic rubidium. The gradient algorithm achieves efficiency gains of up to approximately three times that of the standard genetic algorithm and, as such, is a promising tool for meeting quantum control optimization goals as well as landscape analyses. The landscape trajectories directed by the gradient should aid in the continued investigation and understanding of controlled quantum phenomena.