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Physics Open

Recommender system expedited quantum control optimization

Priya Batra, M. Harshanth Ram, T. S. Mahesh

Published Nov 25, 2022• 1 citation
Publisher

Abstract

Quantum control optimization algorithms are routinely used to synthesize optimal quantum gates or to realize efficient quantum state transfers. The computational resource required for the optimization is an essential consideration in order to scale toward quantum control of larger registers. Here, we propose and demonstrate the use of a machine learning method, specifically the recommender system (RS), to deal with the challenge of enhancing computational efficiency. Given a sparse database of a set of products and their customer ratings, RS is used to efficiently predict unknown ratings. In the quantum control problem, each iteration of a numerical optimization algorithm typically involves evaluating a large number of parameters, such as gradients or fidelities, which can be tabulated as a rating matrix. We establish that RS can rapidly and accurately predict elements of such a sparse rating matrix. Using this approach, we expedite a gradient ascent based quantum control optimization, namely GRAPE, and demonstrate the faster construction of two-qubit CNOT gate in registers with up to 8 qubits. We also describe and implement the enhancement of the computational speed of a hybrid algorithm involving simulated annealing as well as gradient ascent. Moreover, the faster construction of three-qubit Toffoli gates further confirmed the applicability of RS in larger registers.

DOI
10.1016/j.physo.2022.100127

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Quantum control optimization algorithms are routinely used to synthesize optimal quantum gates or to realize efficient quantum state transfers. The computational resource required for the optimization is an essential consideration in order to scale toward quantum control of larger registers. Here, we propose and demonstrate the use of a machine learning method, specifically the recommender system (RS), to deal with the challenge of enhancing computational efficiency. Given a sparse database of a set of products and their customer ratings, RS is used to efficiently predict unknown ratings. In the quantum control problem, each iteration of a numerical optimization algorithm typically involves evaluating a large number of parameters, such as gradients or fidelities, which can be tabulated as a rating matrix. We establish that RS can rapidly and accurately predict elements of such a sparse rating matrix. Using this approach, we expedite a gradient ascent based quantum control optimization, namely GRAPE, and demonstrate the faster construction of two-qubit CNOT gate in registers with up to 8 qubits. We also describe and implement the enhancement of the computational speed of a hybrid algorithm involving simulated annealing as well as gradient ascent. Moreover, the faster construction of three-qubit Toffoli gates further confirmed the applicability of RS in larger registers.
Quantum control optimization algorithms are routinely used to generate optimal quantum gates or efficient quantum state transfers. However, there are two main challenges in designing efficient optimization algorithms, namely overcoming the sensitivity to local optima and improving the computational speed. The former challenge can be dealt with by designing hybrid algorithms, such as a combination of gradient and simulated annealing methods. Here, we propose and demonstrate the use of a machine learning method, specifically the recommender system (RS), to deal with the latter challenge of enhancing computational efficiency. We first describe ways to set up a rating matrix involving gradients or gate fidelities. We then establish that RS can rapidly and accurately predict elements of a sparse rating matrix. Using this approach, we expedite a gradient ascent based quantum control optimization, namely GRAPE and demonstrate the faster performance for up to 8 qubits. Finally, we describe and implement the enhancement of the computational speed of a hybrid algorithm, namely SAGRAPE.
Gradient ascent pulse engineering algorithm (GRAPE) is a typical method to solve quantum optimal control problems. However, it suffers from an exponential resource in computing the time evolution of quantum systems with the increasing number of qubits, which is a barrier for its application in large-qubit systems. To mitigate this issue, we propose an iterative GRAPE algorithm (iGRAPE) for preparing a desired quantum state, where the large-scale, resource-consuming optimization problem is decomposed into a set of lower-dimensional optimization subproblems by disentanglement operations. Consequently these subproblems can be solved in parallel with less computing resources. For physical platforms such as nuclear magnetic resonance (NMR) and superconducting quantum systems, we show that iGRAPE can provide up to 13-fold speedup over GRAPE when preparing desired quantum states in systems within 12 qubits. Using a four-qubit NMR system, we also experimentally verify the feasibility of the iGRAPE algorithm.
Quantum optimal control, a powerful toolbox for engineering an optimal control field modulation that most precisely implements a desired quantum operation in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The gradient ascent pulse engineering (GRAPE) algorithm is a widely used method in quantum optimal control, which has achieved great success in different physical platforms. However, its computational complexity increases exponentially with the number of qubits, making it challenging to be implemented for large-scale quantum systems. To mitigate this issue, we present the iterative GRAPE algorithm (iGRAPE), which reduces the optimization problem into a series of lower-dimensional subproblems by incorporating disentanglement operations. Our numerical simulations on physical platforms such as nuclear magnetic resonance and superconducting quantum systems demonstrate that iGRAPE significantly enhances state preparation speed. Specifically, compared to GRAPE, iGRAPE achieves up to a five-fold acceleration in preparing Greenberger--Horne--Zeilinger states using a 12-qubit implementation, and up to a 13-fold acceleration for arbitrary state preparation with eight qubits. To further validate our findings, we conduct experimental validation of iGRAPE on a four-qubit nuclear magnetic resonance system. Overall, iGRAPE offers an efficient solution for implementing optimal control in large-scale quantum systems, holding great potential for advancing quantum technologies during the noisy intermediate-scale quantum era.
The efficient implementation of quantum computing is contingent upon high-fidelity quantum operations. Nevertheless, the fidelity of these operations is constrained by the precision of quantum system evolution control. The optimization of quantum control pulses is essential for improving the manipulation accuracy of superconducting qubits. Traditional optimization methods, including gradient descent and the gradient ascent pulse engineering algorithm, frequently encounter challenges such as slow convergence and susceptibility to local optima in pulse optimization problems. This study introduces an adaptive open-loop optimization algorithm based on the adaptive moment estimation (Adam) optimizer, capitalizing on the benefits of momentum and adaptive learning rate adjustments inherent in Adam. We conduct experimental analysis on the algorithm’s hyperparameters to achieve optimal solutions with a higher fidelity range at a faster convergence speed, effectively improving the fidelity and optimization efficiency of quantum gate operations. Through numerical simulations on the QuTiP platform, we validate the excellent performance of the Adam algorithm in quantum gate optimization. In optimizing the X and SWAP gates, its fidelity improved by 0.03% and 0.0016%, respectively, compared to the GRAPE algorithm. Compared to the CRAB method, the initial convergence speed of the Adam method increased fivefold, enabling it to achieve the target fidelity more rapidly. Future research will investigate closed-loop optimization strategies, utilizing feedback derived from the fidelity results of actual quantum computers to further augment quantum control performance
In the quest to achieve scalable quantum information processing technologies, gradient-based optimal control algorithms (e.g., grape) are broadly used for implementing high-precision quantum gates, but their performance is often hindered by deterministic or random errors in the system model and the control electronics. In this paper, we show that grape can be taught to be more effective by jointly learning from the design model and the experimental data obtained from process tomography. The resulting data-driven gradient optimization algorithm (d-grape) can in principle correct all deterministic gate errors, with a mild efficiency loss. The d-grape algorithm may become more powerful with broadband controls that involve a large number of control parameters, while other algorithms usually slow down due to the increased size of the search space. These advantages are demonstrated by simulating the implementation of a two-qubit controlled-not gate.
Highly accurate and robust control of quantum operations is vital for the realization of error-correctible quantum computation. In this paper, we show that the robustness of high-precision controls can be remarkably enhanced through sampling-based stochastic optimization of a risk-sensitive (RS) loss function. Following the stochastic gradient-descent direction of this loss function, the optimization is guided to penalize poor-performance uncertainty samples in a tunable manner. We propose two algorithms, which are termed as the RS GRAPE and the adaptive RS GRAPE. Their effectiveness is demonstrated by numerical simulations, which is shown to be able to achieve high-control robustness while maintaining high fidelity.