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.
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.
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.
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%.
With the advancement of quantum physics and deeper exploration of atomic systems, the integration of atoms into communication systems has garnered significant attention. Among these efforts, the use of Rydberg atoms as a communication receiver has emerged as a prominent area of research. In this work, we introduce a new mathematical modeling approach to more accurately establish the input-output relationship of a Rydberg atomic receiver. We categorize this relationship into three segments: one linear region and two nonlinear regions, facilitating a comprehensive analysis of the nonlinear challenges associated with Rydberg atomic receiver. Our findings indicate that adjusting the Rabi oscillation frequency of the coupling laser can effectively extend the linear operating range of the receiver. Furthermore, focusing on complex quadrature amplitude modulation, we propose a digital nonlinear distortion compensation method specifically designed for Rydberg atomic receiver. This method demonstrates a significant improvement in performance, enhancing the demodulation bit error rate compared to conventional linearization techniques.
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.
The implementation of high-fidelity quantum gates for spin qubits requires accurate control of exchange interactions between electrons confined in quantum dots, but pulse distortions can limit this control accuracy. Although linear-dynamical distortions can be compensated for by appropriately convolving the control signal, determining the necessary convolution requires detailed knowledge of the distortion's transfer function, and therefore the calibration of numerous parameters. Alternatively, control pulses can be designed to have a net-zero time integral canceling out linear-dynamical pulse distortions. We generalize net-zero pulse designs to quasi-zero pulses allowing net-positive but reduced time integrals. Using these pulse designs, we systematically develop complete gate sets for exchange-only qubits, and study the resulting tradeoffs between pulse duration, fidelity, and the required number of tunable parameters, both in simulation and experiment. We benchmark the optimized gate pulses on Intel's Tunnel Falls six-dot device and show they achieve fidelities similar to those obtained with a full filtering approach, with identical pulse durations and fewer tuning parameters. This reduction in complexity opens the door to fast and easily automated calibration schemes compatible with large-scale commercial quantum devices.
A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.