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arXiv:1807.01518 · IEEE Transactions on Control Systems Technology

Learning to Calibrate Quantum Control Pulses by Iterative Deconvolution

Xi Cao, Bing Chu, Yu-xi Liu, Zhihui Peng, Re-Bing Wu

Published Mar 5, 2021• 3 citations
arXivHTMLPDF

Abstract

In experimental control of quantum systems, the precision is often hindered by imperfect applied electronics that distort pulses delivered to target quantum devices. To mitigate such error, the deconvolution method is commonly used for compensating the distortion via a convolutional model. However, its effectiveness is limited by model inaccuracies (e.g., imprecise parameters or unmodeled distortion dynamics). In this article, we propose a learning-based scheme to eliminate the residual calibration error by repeatedly applying the deconvolution operations. The resulting iterative deconvolution method is shown by simulation examples to be able to correct both linear and nonlinear model errors to the highest precision allowed by available finite sampling rates, and the intersampling error caused by finite sampling rate can be suppressed by actively introducing nonlinear components in the control electronics. The proposed method is also experimentally applied on a superconducting platform, which demonstrates improved performance than the noniterative deconvolution methods.

DOI
10.1109/tcst.2021.3060321

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In experimental control of quantum systems, the precision is often hindered by imperfect applied electronics that distort pulses delivered to target quantum devices. To mitigate such error, the deconvolution method is commonly used for compensating the distortion via a convolutional model. However, its effectiveness is limited by model inaccuracies (e.g., imprecise parameters or unmodeled distortion dynamics). In this article, we propose a learning-based scheme to eliminate the residual calibration error by repeatedly applying the deconvolution operations. The resulting iterative deconvolution method is shown by simulation examples to be able to correct both linear and nonlinear model errors to the highest precision allowed by available finite sampling rates, and the intersampling error caused by finite sampling rate can be suppressed by actively introducing nonlinear components in the control electronics. The proposed method is also experimentally applied on a superconducting platform, which demonstrates improved performance than the noniterative deconvolution methods.
In experimental manipulation of quantum systems, the control precision is always hindered by pulse distortion induced by the applied electronic system, when signals are delivered to the target that is often placed in a low-temperature and vacuum chamber. To mitigate such errors, deconvolution is effective by compensating the identified linear convolution. However, there is always residual error because the linear model can never be precise and non-linear distortion is also present. In this paper, we propose an iterative deconvolution scheme that repeatedly applies the deconvolution operation using the error signal. Theoretically, such scheme can correct arbitrary residual model errors, whose performance is up to accuracy of the identified models. Simulation results show its effectiveness on correcting model errors.
Predictive design and optimization methods for controlled quantum systems depend on the accuracy of the system model. Any distortion of the input fields in an experimental platform alters the model accuracy and eventually disturbs the predicted dynamics. These distortions can be nonlinear with a strong frequency dependence so that the field interacting with the microscopic quantum system has limited resemblance to the input signal. We present an effective method for estimating these distortions, which is suitable for nonlinear transfer functions of arbitrary lengths and magnitudes provided the available training data has enough spectral components. Using a quadratic estimation, we have successfully tested our approach for a numerical example of a single Rydberg atom system. The transfer function estimated from the presented method is incorporated into an open-loop control optimization algorithm allowing for high-fidelity operations in quantum experiments.
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations on a superconducting transmon qubit, using detailed numerical simulations. We demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of about 99.99%.
In quantum computation, control signals are adversely affected by distortion due to nonidealities in control chains. In order to implement high-fidelity digital and analog quantum operations, one must characterize the distortion and compensate for it. Here, we propose and experimentally verify an extensible method to model the behavior of control lines with the system function and correct it with digital filters. We correct the distortion of the superconducting-qubit flux control lines within a precision of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which ensures gate fidelity free of the limit of pulse distortion. For the purpose of more accurate and scalable parameter extraction of the low-temperature line response, we employ an optimization-based protocol and the convergence is fast by setting the result of adjacent control lines with the same setup as the initial values. The techniques presented here improve distortion calibration efficiency and enable distortion-free operations, which paves the way for high-precision control of quantum computation and quantum simulation.
Model-based quantum optimal control promises to solve a wide range of critical quantum technology problems within a single, flexible framework. The catch is that highly-accurate models are needed if the optimized controls are to meet the exacting demands set by quantum engineers. A practical alternative is to directly calibrate control parameters by taking device data and tuning until success is achieved. In quantum computing, gate errors due to inaccurate models can be efficiently polished if the control is limited to a few (usually hand-designed) parameters; however, an alternative tool set is required to enable efficient calibration of the complicated waveforms potentially returned by optimal control. We propose an automated model-based framework for calibrating quantum optimal controls called Learning Iteratively for Feasible Tracking (LIFT). LIFT achieves high-fidelity controls despite parasitic model discrepancies by precisely tracking feasible trajectories of quantum observables. Feasible trajectories are set by combining black-box optimal control and the bilinear dynamic mode decomposition, a physics-informed regression framework for discovering effective Hamiltonian models directly from rollout data. Any remaining tracking errors are eliminated in a non-causal way by applying model-based, norm-optimal iterative learning control to subsequent rollout data. We use numerical experiments of qubit gate synthesis to demonstrate how LIFT enables calibration of high-fidelity optimal control waveforms in spite of model discrepancies.
Identifying and calibrating quantitative dynamical models for physical quantum systems is important for a variety of applications. Here we present a closed-loop Bayesian learning algorithm for estimating multiple unknown parameters in a dynamical model, using optimised experimental "probe" controls and measurement. The estimation algorithm is based on a Bayesian particle filter, and is designed to autonomously choose informationally-optimised probe experiments with which to compare to model predictions. We demonstrate the performance of the algorithm in both simulated calibration tasks and in an experimental single-qubit ion-trap system. Experimentally, we find that with 60x fewer samples, we exceed the precision of conventional calibration methods, delivering an approximately 93x improvement in efficiency (as quantified by the reduction of measurements required to achieve a target residual uncertainty and multiplied by the increase in accuracy). In simulated and experimental demonstrations, we see that successively longer pulses are selected as the posterior uncertainty iteratively decreases, leading to an exponential improvement in the accuracy of model parameters with the number of experimental queries.