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Collaborative Learning of High-Precision Quantum Control and Tomography

Haijin Ding, Bing Chu, Re-Bing Wu

Published Jan 1, 2019• 2 citations
Publisher

Abstract

High-precision control of quantum states and gate operations is essential to the hardware implementation of quantum computation. Recently, online calibration has become an important tool for correcting errors induced by parameter shifts or environmental noises in the underlying quantum control systems. However, the experimental cost for acquiring information through quantum tomography (for state or gate reconstruction) is very high, especially when many iterations are to be done. In this paper, we propose a novel scheme that integrates the gradient-descent optimization of quantum control pulses with the adaptive learning of quantum tomography as two interactive processes, which updates the control iteratively with the progressively refined state tomography. This scheme, which we call c-GRAPE, can greatly improve the calibration efficiency by substantial reduction the experimental cost for tomography without sacrificing the control precision.

DOI
10.1016/j.ifacol.2019.12.633

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High-precision control of quantum states and gate operations is essential to the hardware implementation of quantum computation. Recently, online calibration has become an important tool for correcting errors induced by parameter shifts or environmental noises in the underlying quantum control systems. However, the experimental cost for acquiring information through quantum tomography (for state or gate reconstruction) is very high, especially when many iterations are to be done. In this paper, we propose a novel scheme that integrates the gradient-descent optimization of quantum control pulses with the adaptive learning of quantum tomography as two interactive processes, which updates the control iteratively with the progressively refined state tomography. This scheme, which we call c-GRAPE, can greatly improve the calibration efficiency by substantial reduction the experimental cost for tomography without sacrificing the control precision.
In the hardware implementation of quantum computation, the control pulses for quantum states and gate operations must be calibrated to correct errors induced by unknown drifts of system parameters. The calibration can be iteratively done by checking the control precision, but the required randomized benchmarking or quantum tomography is experimentally expensive. In this paper, we propose that the control calibration and the quantum tomography can be taken as two separate but collaborative learning processes. Combining the gradient-descent pulse engineering and the adaptive tomography, the resulting c-GRAPE algorithm can substantially reduce the high cost of measurements without sacrificing the control accuracy. The effectiveness is demonstrated by numerical simulation examples.
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.
Quantum control can be employed in quantum metrology to improve the precision limit for the estimation of unknown parameters. The optimal control, however, typically depends on the actual values of the parameters and thus needs to be designed adaptively with the updated estimations of those parameters. Traditional methods, such as gradient ascent pulse engineering (GRAPE), need to be rerun for each new set of parameters encountered, making the optimization costly, especially when many parameters are involved. Here we study the generalizability of optimal control, namely, optimal controls that can be systematically updated across a range of parameters with minimal cost. In cases where control channels can completely reverse the shift in the Hamiltonian due to a change in parameters, we provide an analytical method which efficiently generates optimal controls for any parameter starting from an initial optimal control found by either GRAPE or reinforcement learning. When the control channels are restricted, the analytical scheme is invalid, but reinforcement learning still retains a level of generalizability, albeit in a narrower range. In cases where the shift in the Hamiltonian is impossible to decompose to available control channels, no generalizability is found for either the reinforcement learning or the analytical scheme. We argue that the generalization of reinforcement learning is through a mechanism similar to the analytical scheme. Our results provide insights into when and how the optimal control in multiparameter quantum metrology can be generalized, thereby facilitating efficient implementation of optimal quantum estimation of multiple parameters, particularly for an ensemble of systems with ranges of parameters.
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.
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
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the online choice of optimal measurements allows one to reach the ultimate bounds of precision for state reconstruction. In this article we generalize an adaptive Bayesian approach to the case of process tomography and experimentally show its superiority in the task of learning unknown quantum operations. Our experiments with photonic polarization qubits cover all types of single-qubit channels. We also discuss instrumental errors and the criteria for evaluation of the ultimate achievable precision in an experiment. It turns out that adaptive tomography provides a lower noise floor in the presence of strong technical noise.