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arXiv:2503.04610 · Physical Review Research

Calibrating magnetic flux control in superconducting circuits by compensating distortions on timescales from nanoseconds up to tens of microseconds

Christoph Hellings, Nathan Lacroix, Ants Remm, Richard Boell, J. Herrmann, Stefania Lazar, Sebastian Krinner, François Swiadek, Christian Kraglund Andersen, Christopher Eichler, Andreas J. Wallraff

Published Nov 7, 2025• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/1qhb-r4fb

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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.
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.
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.
Superconducting qubits have achieved exceptional gate fidelities, exceeding the error-correction threshold in recent years. One key ingredient of such improvement is the introduction of tunable couplers to control the qubit-to-qubit coupling through frequency tuning. Moving toward fault-tolerant quantum computation, increasing the number of physical qubits is another step toward effective error correction codes. Under a multiqubit architecture, flux control (Z) lines are crucial in tuning the frequency of the qubits and couplers. However, dense flux lines result in magnetic flux crosstalk, wherein magnetic flux applied to one element inadvertently affects neighboring qubits or couplers. This crosstalk obscures the idle frequency of the qubit when flux bias is applied, which degrades gate performance and calibration accuracy. In this study, we characterize flux crosstalk and suppress it in a multiqubit-coupler chip with multi-Z lines without adding additional readout for couplers. By quantifying the mutual flux-induced frequency shifts of qubits and couplers, we construct a cancellation matrix that enables precise compensation of non-local flux, demonstrating a substantial reduction in Z-line crosstalk from 56.5‰ to 0.13‰, which is close to statistical error. Flux compensation corrects the CZ SWAP measurement, leading to a symmetric map with respect to flux bias. Compared with a crosstalk-free calculated CZ SWAP map, the measured map indicates that our approach provides a near-zero crosstalk for the coupler-transmon system. These results highlight the effectiveness of our approach in enhancing flux crosstalk-free control and supporting its potential for scaling superconducting quantum processors.
Flux-activated two-qubit gates in superconducting processors require correction of line distortion, which otherwise produces residual detuning, conditional-phase error, and leakage. Prior demonstrations of cryoscope-based distortion calibration have generally used commercial solutions that specify the filter models but not their FPGA implementation. These details matter for custom and open-source systems, where the fixed-point coefficient and datapath formats set how accurately the correction is realized, and the IIR feedback loop in its standard form does not meet timing at the required clock rate. We derive the coefficient formats of the correction filters from a step response error tolerance, using bounds on the quantization-induced displacement of the poles and zeros over the physical parameter range of each distortion, and the accumulator format from the smallest input change that must remain resolvable at the output. The same analysis gives the conditions under which quantization preserves filter stability. We implement the resulting FIR/IIR cascade on the QubiC platform at a fabric clock rate of \SI{500}{MHz}, using a super-sample-rate structure with scattered look-ahead pipelining, which removes the feedback recursion from the critical path without changing the target transfer function. A representative cascade for our \SI{1}{GS/s} flux lines, comprising an integrator, a second-order section, and a 20-tap FIR, consumes 88 DSP slices and adds \SI{162}{ns} of latency. We confirm the hardware implementation by correcting characteristic bias-tee distortion, an intermediate step toward full cryoscope-based calibration.
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.