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Deep Learning of Robust and High-Precision Quantum Controls

Re-Bing Wu, Haijin Ding, Daoyi Dong, Xiaoting Wang

Published Nov 5, 2018• 2 citations
OpenAlex

Abstract

Robust and high-precision quantum control is extremely important but challenging for scalable quantum computation. In this letter, we show that this hard problem can be translated to a supervised machine learning task by treating the time-ordered controlled quantum evolution as a layer-ordered deep neural network (DNN). The finding of robust quantum controls is then equivalent to training a DNN with high generalizability. In this way, powerful DNN tuning skills matured in deep learning (DL) can be employed for the discovery of highly robust and precise quantum controls, which opens up a door through which a large family of learning algorithms can be developed. We exemplify this DL-inspired potential by introducing the commonly used trick of batch-based optimization. The resulting b-GRAPE algorithm is demonstrated to be able to remarkably enhance the control robustness while maintaining high fidelity in the implementation of a three-qubit quantum gate.

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Robust and high-precision quantum control is extremely important but challenging for scalable quantum computation. In this letter, we show that this hard problem can be translated to a supervised machine learning task by treating the time-ordered controlled quantum evolution as a layer-ordered deep neural network (DNN). The finding of robust quantum controls is then equivalent to training a DNN with high generalizability. In this way, powerful DNN tuning skills matured in deep learning (DL) can be employed for the discovery of highly robust and precise quantum controls, which opens up a door through which a large family of learning algorithms can be developed. We exemplify this DL-inspired potential by introducing the commonly used trick of batch-based optimization. The resulting b-GRAPE algorithm is demonstrated to be able to remarkably enhance the control robustness while maintaining high fidelity in the implementation of a three-qubit quantum gate.
Robust and high-precision quantum control is extremely important but challenging for the functionalization of scalable quantum computation. In this paper, we show that this hard problem can be translated to a supervised machine learning task by thinking of the time-ordered quantum evolution as a layer-ordered neural network (NN). The seeking of robust quantum controls is then equivalent to training a highly generalizable NN, to which numerous tuning skills matured in machine learning can be transferred. This opens up a door through which a family of robust control algorithms can be developed. We exemplify such potential by introducing the commonly used trick of batch-based optimization, and the resulting batch-based gradient algorithm is numerically shown to be able to remarkably enhance the control robustness while maintaining high fidelity.
Abstract Emerging reinforcement learning techniques using deep neural networks have shown great promise in control optimization. They harness non-local regularities of noisy control trajectories and facilitate transfer learning between tasks. To leverage these powerful capabilities for quantum control optimization, we propose a new control framework to simultaneously optimize the speed and fidelity of quantum computation against both leakage and stochastic control errors. For a broad family of two-qubit unitary gates that are important for quantum simulation of many-electron systems, we improve the control robustness by adding control noise into training environments for reinforcement learning agents trained with trusted-region-policy-optimization. The agent control solutions demonstrate a two-order-of-magnitude reduction in average-gate-error over baseline stochastic-gradient-descent solutions and up to a one-order-of-magnitude reduction in gate time from optimal gate synthesis counterparts. These significant improvements in both fidelity and runtime are achieved by combining new physical understandings and state-of-the-art machine learning techniques. Our results open a venue for wider applications in quantum simulation, quantum chemistry and quantum supremacy tests using near-term quantum devices.
This paper investigates quantum gate control problems using the deep reinforcement learning algorithm, i.e., a model-free machine learning method. We implement the twin delayed deep deterministic policy gradient (TD3) algorithm to search for piece-wise constant control pulses for quantum gates through the trail interaction with the quantum system. Simulation results on four typical gates, including three one-qubit gates and a two-qubit CNOT gate, demonstrate that deep reinforcement learning exhibits improved performance for quantum gate control tasks. By setting punishment for steps in the reward function, DRL can automatically find a shorter control sequence than the traditional gradient-based algorithm (e.g., GRAPE algorithm) and the evolutionary algorithm (e.g., DE algorithm) while maintaining high control precision.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.
How to implement multi-qubit gates efficiently with high precision is essential for realizing universal fault-tolerant computing. For a physical system with some external controllable parameters, it is a great challenge to control the time dependence of these parameters to achieve a target multi-qubit gate efficiently and precisely. Here we construct a dueling double deep Q-learning neural network (DDDQN) to find out the optimized time dependence of controllable parameters to implement two typical quantum gates: a single-qubit Hadamard gate and a two-qubit CNOT gate. Compared with traditional optimal control methods, this deep reinforcement learning method can realize efficient and precise gate control without requiring any gradient information during the learning process. This work attempts to pave the way to investigate more quantum control problems with deep reinforcement learning techniques.
Real-time adaptive control of quantum systems requires rapid generation of robust, high-fidelity pulses across a continuous range of operating conditions. Standard optimization algorithms such as gradient-ascent pulse engineering (GRAPE) solve each instance independently, discarding information between runs and requiring costly reinitialization when parameters change. We present an approach to robust optimal quantum control based on model-based reinforcement learning, in which a single neural network -- embedding the Hamiltonian directly into the training pipeline -- generates robust gates across an entire family of gate configurations, without pre-computed training data. Demonstrated on a single-spin (two-level) system, the trained networks produce pulses for arbitrary rotation angles over a range of pulse durations, detunings, and field inhomogeneities in milliseconds, at fidelities comparable to multi-seed GRAPE. The framework is inherently adaptable: any parameter entering the Hamiltonian can serve as a network input, extending the approach to different systems and control settings. Beyond speed, the network reveals structure in the control landscape: it discovers the same structured phase profiles that appear in GRAPE solutions -- made identifiable through fidelity-invariant symmetry transformations -- but more consistently than independent optimization. This consistency enables smooth interpolation across the entire trained parameter space.