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arXiv:2609.27456

Precision and resource scaling of real-time flux distortion compensation for superconducting quantum control

Qi Zhou, Zi-Hao Mei, Peng Duan, Peng Wang, Liang-Liang Guo, Hao-Ran Tao, Wei-Cheng Kong, Hui Yang, Guo-Ping Guo, Zhao-Yun Chen

quant-phcs.ARSubmitted Sep 23, 2026• Announced Sep 24, 2026• 0 citations
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Abstract

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 $10^{-4}$. This work provides a scalable hardware foundation for high-fidelity flux control in dynamic superconducting quantum circuits.

AI Summary

Long-lived flux-line distortions make compensation depend on pulse history, complicating instruction-driven control with conditional execution. This paper studies real-time inverse filtering after waveform synthesis, including how arithmetic precision and FPGA cost scale with the compensation timescale. The method reconstructs an inverse impulse response through frequency-domain inversion with Gaussian high-frequency weighting, then fits a compact parallel IIR/FIR model. Look-ahead IIR processing and sliding-window FIR convolution produce six samples per 200 MHz clock, sustaining 1.2 GSa/s. Validation combines room-temperature oscilloscope measurements, cryogenic qubit-based step-response measurements, and two-qubit XEB. A fourth-order, 44-bit IIR filter with a 44-tap FIR branch gives a median estimated CZ Pauli fidelity of 99.53%, versus 99.57% for offline double-precision compensation. Cryogenic compensated-response fluctuations are approximately $10^{-4}$. Fixed-point simulations using compensation models from 147 measured flux channels, together with FPGA synthesis, relate precision to timescale coverage for a three-SOS architecture. At 44 bits, channel-averaged peak arithmetic error stays below one 16-bit DAC LSB up to 35 microseconds; the channel-averaged relative-error criterion of $10^{-4}$ permits over 100 microseconds. Extending coverage from approximately 1 to 138 microseconds increases IIR LUT and DSP use by about 14% and 4%, respectively. The analysis assumes linear time-invariant responses; extended-timescale results use radially shifted model poles rather than measurements across those timescales. Gate fidelity does not improve monotonically with filter precision or order, and the benchmarking suggests incoherent errors dominate. Integration with measurement-dependent feedforward remains future work.

Little sign of AI-generated textIncrementalMissing comparison

Central claim may not hold: The reported relative arithmetic error below 10^-4 is a channel-averaged peak error for step-input tests, not a per-channel guarantee for arbitrary synthesized waveforms. The resource counts and nine-channel capacity estimate cover the IIR engine without budgeting the FIR branch or other controller functions, so they do not establish complete compensation-system capacity. The approximately logarithmic timescale scaling is demonstrated for a fixed-order, synthetically pole-shifted model family, not generally for physical flux responses whose complexity may change with timescale.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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17 pages, 9 figures

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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.
Long-lived flux-line distortions make compensation depend on pulse history, complicating instruction-driven control with conditional execution. This paper studies real-time inverse filtering after waveform synthesis, including how arithmetic precision and FPGA cost scale with the compensation timescale.
The method reconstructs an inverse impulse response through frequency-domain inversion with Gaussian high-frequency weighting, then fits a compact parallel IIR/FIR model. Look-ahead IIR processing and sliding-window FIR convolution produce six samples per 200 MHz clock, sustaining 1.2 GSa/s. Validation combines room-temperature oscilloscope measurements, cryogenic qubit-based step-response measurements, and two-qubit XEB. A fourth-order, 44-bit IIR filter with a 44-tap FIR branch gives a median estimated CZ Pauli fidelity of 99.53%, versus 99.57% for offline double-precision compensation. Cryogenic compensated-response fluctuations are approximately 10−410^{-4}10−4.
Fixed-point simulations using compensation models from 147 measured flux channels, together with FPGA synthesis, relate precision to timescale coverage for a three-SOS architecture. At 44 bits, channel-averaged peak arithmetic error stays below one 16-bit DAC LSB up to 35 microseconds; the channel-averaged relative-error criterion of 10−410^{-4}10−4 permits over 100 microseconds. Extending coverage from approximately 1 to 138 microseconds increases IIR LUT and DSP use by about 14% and 4%, respectively.
The analysis assumes linear time-invariant responses; extended-timescale results use radially shifted model poles rather than measurements across those timescales. Gate fidelity does not improve monotonically with filter precision or order, and the benchmarking suggests incoherent errors dominate. Integration with measurement-dependent feedforward remains future work.
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.
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.
Control architectures that reduce hardware overhead while maintaining high-fidelity operations are essential for the continued scaling of superconducting quantum processors. Here we experimentally realize a unified control architecture for fluxonium qubits, in which both transverse (XYXYXY) and longitudinal (ZZZ) operations are implemented through a single flux-control channel driven by a single arbitrary waveform generator channel. This architecture imposes competing requirements on the shared control channel, which must simultaneously support low-frequency flux transmission for reset operations while strongly attenuating broadband noise near the qubit transition frequency. We address this challenge through frequency-selective cryogenic filtering together with compensated waveform synthesis that corrects the pulse distortion introduced by the filtered control line. Experimentally, this approach preserves coherence times above 100 μμμs while enabling active reset with approximately 98% fidelity and 20-ns single-qubit gates with fidelities exceeding 99.99%. We further demonstrate FPGA-native instruction-level waveform synthesis based on reusable pulse primitives for unified flux control. These results establish unified flux control as a scalable architecture for fluxonium qubits that reduces control hardware overhead while preserving high-fidelity operation.
In quantum computing, control signals are susceptible to distortion during transmission. Transmission distortion introduces residual voltages that degrade fidelity of quantum operations. Conventional pre-storage calibration need prohibitive memory and latency costs. We present a real-time predistortion circuit based on Infinite Impulse Response(IIR) Filter in 28 nm CMOS that synthesizes the corrected waveforms directly on chip, eliminating offline computation. And this architecture downloads input envelopes only instead of complete waveforms. The architecture supports arbitrary durations for specific pulse types such as rectangular pulses at 3 GSa/s wthin acceptable precision, which establishes the foundation for memory-efficient control in quantum computing.
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.
We present a system for generating arbitrary, triaxial magnetic waveforms with a spectral content spanning from DC to tens of kHz, a critical capability for quantum control and spin manipulation. To compensate for amplifier-coil dynamics, we implement a data-driven approach to identify a numerical compensation model. The method parametrizes the system response using a Finite Impulse Response (FIR) filter calibrated on the specific waveform to be generated. The application of a driving signal designed via frequency-domain inversion of the identified model enables the synthesis of complex field sequences with sharp transitions between static and single- or multi-frequency temporal segments. The work is validated with experimental results demonstrating waveform fidelity and transient performance, thereby showcasing the precision and feasibility of the method.