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Physical Review Applied

Universal scalable characterization and correction of pulse distortions in controlled quantum systems

Liang-Liang Guo, Peng Duan, Sheng Zhang, Xin-Xin Yang, Chi Zhang, Lei Du, Hai-Feng Zhang, Haoran Tao, Tian-Le Wang, Zhi-Long Jia, Zhao‐Yun Chen, Guo‐Ping Guo

Published Jun 26, 2024• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physrevapplied.21.064060

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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×\else\texttimes\fi10\ensuremath−31\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}1\ifmmode×\else\texttimes\fi10\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.
Flux-tunable superconducting qubits rely on fast flux control pulses to implement two-qubit entangling quantum gates, a key building block for quantum algorithms. However, distortion effects introduced by non-ideal control electronics, parasitic components, and the cryogenic quantum chip response can all degrade the gate fidelity. We present a digital predistortion (DPD) framework for characterizing and then compensating for these distortions using a combination of infinite impulse response (IIR) and finite impulse response (FIR) filters. Experiments on a flux-tunable quantum processing unit (QPU) demonstrate a successful correction of step-response distortions on the flux-control line, with a compensated control signal showing only sub-percent deviations from the ideal target linear behavior. The demonstrated method enables automated rapid calibration of flux control channels for superconducting QPUs.
Real-time waveform generation supports dynamic quantum circuits without pre-storing complete waveforms for every execution path. However, long-lived distortions in flux-control lines degrade gate fidelity, requiring compensation to account for the actual pulse history. A frequency-domain inversion and time-domain fitting method is proposed for resource-efficient real-time flux distortion compensation. The method fits the reconstructed compensation impulse response with a compact hybrid infinite impulse response (IIR) and finite impulse response (FIR) filter. Look-ahead parallelization enables this filter to process synthesized waveforms at 1.2GSa/s on a field-programmable gate array (FPGA). Two-qubit cross-entropy benchmarking shows that real-time IIR filtering achieves a median controlled-Z Pauli fidelity close to the software-reference value of 99.57%. Numerical analysis and FPGA synthesis indicate approximately logarithmic growth in hardware resource use with compensation timescale. Extending compensation from microsecond to hundred-microsecond timescales increases look-up table (LUT) and digital signal processing (DSP) resource use by only about 14% and 4%, respectively, while maintaining a relative arithmetic error below 10−410^{-4}10−4. This work provides a scalable hardware foundation for high-fidelity flux control in dynamic superconducting quantum circuits.
Fast tuning of the transition frequency of superconducting qubits using magnetic flux is essential, for example, for realizing high-fidelity two-qubit gates with low leakage or for reducing errors in dispersive qubit readout. To apply accurately shaped flux pulses, signal distortions induced by the flux control lines need to be carefully compensated for. This requires their characterization at the reference plane of the qubit. However, many existing approaches are limited in time resolution or in pulse duration. Here, we overcome these limitations and demonstrate accurate flux control with subpermille residual frequency errors on timescales ranging from nanoseconds to tens of microseconds. We achieve this by combining two complementary methods to characterize and compensate for pulse distortions. We have deployed this approach successfully in a quantum error correction experiment calibrating 24 flux-activated two-qubit gates. Reliable calibration methods, as the ones presented here, are essential in experiments scaling up superconducting quantum processors.
For superconducting quantum processors, stable high-fidelity two-qubit operations depend on precise flux control of the tunable coupler. However, the pulse distortion poses a significant challenge to the control precision. Current calibration methods, which often rely on microwave crosstalk or additional readout resonators for coupler excitation and readout, tend to be cumbersome and inefficient, especially when couplers only have flux control. Here, we introduce and experimentally validate a pulse calibration scheme that exploits the strong coupling between qubits and couplers, eliminating the need for extra coupler readout and excitation. Our method directly measures the short-time and long-time step responses of the coupler flux pulse transient, enabling us to apply predistortion to subsequent signals using fast Fourier transformation and deconvolution. This approach not only simplifies the calibration process, but also significantly improves the precision and stability of the flux control. We demonstrate the efficacy of our method through the implementation of diabatic controlled-ZZZ (cz) and iiiswap gates with fidelities of $99.61\mathrm{%}\ifmmode\pm\else\textpm\fi{}0.04\mathrm{%}$ and $99.82\mathrm{%}\ifmmode\pm\else\textpm\fi{}0.02\mathrm{%}$, respectively, as well as a series of diabatic controlled-phase gates with high fidelities characterized by cross-entropy benchmarking. The consistency and robustness of our technique are further validated by the reduction in pulse distortion and phase error observed across multilayer cz gates. These results underscore the potential of our calibration and predistortion method to enhance the performance of two-qubit gates in superconducting quantum processors.
Efforts to scale-up quantum computation have reached a point where the principal limiting factor is not the number of qubits, but the entangling gate infidelity. However, the highly detailed system characterization required to understand the underlying error sources is an arduous process and impractical with increasing chip size. Open-loop optimal control techniques allow for the improvement of gates but are limited by the models they are based on. To rectify the situation, we provide an integrated open-source tool set for control, calibration, and characterization (C3{\mathbb{C}}^{3}C3), capable of open-loop pulse optimization, model-free calibration, model fitting, and refinement. We present a methodology to combine these tools to find a quantitatively accurate system model, high-fidelity gates, and an approximate error budget, all based on a high-performance, feature-rich simulator. We illustrate our methods using simulated fixed-frequency superconducting qubits for which we learn model parameters with less than $1\mathrm{%}$ error and derive a coherence-limited cross-resonance gate that achieves $99.6\mathrm{%}$ fidelity without the need for calibration.
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%.