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arXiv:2302.02371 · IEEE Transactions on Artificial Intelligence

Model-Free Quantum Gate Design and Calibration Using Deep Reinforcement Learning

Omar Shindi, Qi Yu, Parth Girdhar, Daoyi Dong

Published Feb 8, 2023• 16 citations
arXivHTMLPDF

Abstract

High-fidelity quantum gate design is important for various quantum technologies, such as quantum computation and quantum communication. Numerous control policies for quantum gate design have been proposed given a dynamical model of the quantum system of interest. However, a quantum system is often highly sensitive to noise, and obtaining its accurate modeling can be difficult for many practical applications. Thus, the control policy based on a quantum system model may be unpractical for quantum gate design. Also, quantum measurements collapse quantum states, which makes it challenging to obtain information through measurements during the control process. In this article, we propose a novel training framework using deep reinforcement learning for model-free quantum control. The proposed framework relies only on the measurement at the end of the control process and offers the ability to find the optimal control policy without access to quantum systems during the learning process. The effectiveness of the proposed technique is numerically demonstrated for model-free quantum gate design and quantum gate calibration using off-policy reinforcement learning algorithms.

DOI
10.1109/tai.2023.3243187

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High-fidelity quantum gate design is important for various quantum technologies, such as quantum computation and quantum communication. Numerous control policies for quantum gate design have been proposed given a dynamical model of the quantum system of interest. However, a quantum system is often highly sensitive to noise, and obtaining its accurate modeling can be difficult for many practical applications. Thus, the control policy based on a quantum system model may be unpractical for quantum gate design. Also, quantum measurements collapse quantum states, which makes it challenging to obtain information through measurements during the control process. In this article, we propose a novel training framework using deep reinforcement learning for model-free quantum control. The proposed framework relies only on the measurement at the end of the control process and offers the ability to find the optimal control policy without access to quantum systems during the learning process. The effectiveness of the proposed technique is numerically demonstrated for model-free quantum gate design and quantum gate calibration using off-policy reinforcement learning algorithms.
Higher-dimensional quantum systems, such as qudits, offer architectural and algorithmic advantages over qubits, but their increased spectral crowding and limited controllability render high-fidelity quantum gates particularly challenging. We propose a hybrid optimization framework that integrates optimal control theory methods with contextual deep reinforcement learning to achieve robust controlled-phase gates on two qutrits. Optimal control is first used to design high-fidelity control pulses for a nominal system model. Reinforcement learning is then employed as a calibration stage that learns small residual corrections to these pulses in the presence of static model mismatch, thereby preserving good gate performance under realistic parameter uncertainties. By learning structured, low-dimensional residual corrections conditioned on device-specific parameter variations, reinforcement learning enhances the transfer robustness of nominally optimal but parameter-sensitive control solutions across ensembles of devices. Crucially, the reinforcement learning step in our framework does not compete with the optimal control step but provides the adaptability required for realistic hardware, systematically reducing the sensitivity to parameter fluctuations. Our results establish reinforcement learning as a practical and scalable ingredient for robust calibration of quantum gates in high-dimensional systems.
The design of high-fidelity quantum gates is difficult because it requires the optimization of two competing effects, namely maximizing gate speed and minimizing leakage out of the qubit subspace. We propose a deep reinforcement learning algorithm that uses two agents to address the speed and leakage challenges simultaneously. The first agent constructs the qubit in-phase control pulse using a policy learned from rewards that compensate short gate times. The rewards are obtained at intermediate time steps throughout the construction of a full-length pulse, allowing the agent to explore the landscape of shorter pulses. The second agent determines an out-of-phase pulse to target leakage. Both agents are trained on real-time data from noisy hardware, thus providing model-free gate design that adapts to unpredictable hardware noise. To reduce the effect of measurement classification errors, the agents are trained directly on the readout signal from probing the qubit. We present proof-of-concept experiments by designing X and square root of X gates of various durations on IBM hardware. After just 200 training iterations, our algorithm is able to construct novel control pulses up to two times faster than the default IBM gates, while matching their performance in terms of state fidelity and leakage rate. As the length of our custom control pulses increases, they begin to outperform the default gates. Improvements to the speed and fidelity of gate operations open the way for higher circuit depth in quantum simulation, quantum chemistry and other algorithms on near-term and future quantum devices.
The extreme sensitivity of contemporary hardware to noise, manufacturing variability, and imperfect quantum logic gates are key factors that limit hardware to reliably perform quantum computation at scale. The use of reinforcement learning assisted control techniques for system dynamics optimization in quantum gate control can significantly improve hardware performance and downstream computing power. However, con-trol field noise and Hamiltonian parameter uncertainty can lead to significant deviations from the target quantum gate. As a result, quantum gates lack the generalization ability to the quantum environment, and existing reinforcement learning assisted for quantum state preparation is not suitable for quantum gate control. In this paper, we design QcontrolSR, a state representation for reinforcement learning method, enabling quantum gate control with enhanced generalization ability. It requires no knowledge of a specific Hamiltonian model of the system, or its underlying unknown process. We introduce the state representation of quantum observations and show through demonstrations that QcontrolSR-optimized quantum gate control is insensitive to driving noise of the typical strength in practice. We show thatRx(π/2)R_{x}(\pi/2)Rx​(π/2)gate implemented using QcontrolSR can maintain fidelity greater than 0.95 and 0.99 on dynamical quantum stochastic system. The regions with fidelity greater than 0.99 and 0.999 are 2 and 3 times higher than the model-optimized Quantum gate control, respectively.
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 presents a novel approach to designing adaptive quantum control policies using reinforcement learning (RL). Traditional methods for quantum control often rely on hand-designed pulse shapes or iterative optimization techniques, which can be computationally expensive and may not generalize well to different systems or desired operations. We propose a framework where an RL agent learns to dynamically adjust quantum control parameters in real-time, based on the system's state and the objective of achieving a specific quantum gate with high fidelity. The core of our approach lies in formulating the quantum control problem as a Markov Decision Process (MDP) and utilizing an RL algorithm to train a policy that maps system states to control parameters. We demonstrate the feasibility and effectiveness of this method through a theoretical analysis and a simplified numerical simulation. The resulting adaptive control policies offer a significant advantage over traditional methods, particularly for complex quantum systems and demanding fidelity requirements. The key contributions are the integration of RL for adaptive control and the formalization of the problem as an MDP.
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.