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arXiv:2610.00783

Real-Time Adaptive Filtering and the Boxcar Limit in Superconducting Qubit Readout

Hans Johnson, Tanay Roy, Leonardo Bove, David van Zanten, Silvia Zorzetti, Jafar Saniie

quant-pheess.SPSubmitted Sep 30, 2026• Announced Oct 2, 2026• 0 citations
v1 · Sep 30, 2026v2 · Oct 2, 2026v3 · Oct 16, 2026
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Abstract

In dispersive readout of superconducting qubits, the common baseline is a boxcar averager: a uniformly weighted average over a fixed window followed by threshold-based state assignment. We ask when additional digital processing improves fidelity. We evaluated an adaptive finite-impulse-response (FIR) filter trained in real time by the least-mean-squares (LMS) algorithm on an FPGA quantum controller, and analyzed measured readout shots offline to compare the frozen filter with boxcar averaging and to test per-sample weighting and sequential detection. For the fixed FIR filters tested, summing the filtered samples gives the boxcar sum multiplied by one complex number, apart from a small edge correction (the kernel collapse). This scales state separation and noise equally, so discrimination cannot improve (the boxcar limit). The frozen LMS filter reduces trace noise without a resolved fidelity improvement at the tested readout lengths. Replayed on the same shots offline, each filtered shot carries 99.4% of the boxcar shot's discrimination signal-to-noise ratio at the 8 $μ$s operating point of the 2D transmon qubit (Q1). On Q1, optimizing the readout window's start and duration improves contrast readout fidelity by +2.4% to +5.6% across four readout lengths. Per-sample weighting adds up to +3.0% over full-window integration, and only +0.33% beyond the tuned window at 8 $μ$s. Remaining results are from a 3D ancilla qubit (Q2), which sits above the early-decision crossover that Q1 sits below. Hardware sweeps locate the crossover window near 1 $μ$s. Offline, the sequential test decided most shots early, with fidelity within 0.5 percentage points of the boxcar. About 30 labeled shots per class build a matched-filter template nearly as good as one from hundreds. The results form an operating-point record that separates waveform denoising from decision improvement.

Comments
16 pages, 12 figures, 2 tables, 27 equations

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In dispersive readout of superconducting qubits, the common baseline is a boxcar averager: a uniformly weighted average over a fixed window followed by threshold-based state assignment. We ask when additional digital processing improves fidelity. We evaluated an adaptive finite-impulse-response (FIR) filter trained in real time by the least-mean-squares (LMS) algorithm on an FPGA quantum controller, and analyzed measured readout shots offline to compare the frozen filter with boxcar averaging and to test per-sample weighting and sequential detection.
For the fixed FIR filters tested, summing the filtered samples gives the boxcar sum multiplied by one complex number, apart from a small edge correction (the kernel collapse). This scales state separation and noise equally, so discrimination cannot improve (the boxcar limit).
The frozen LMS filter reduces trace noise without a resolved fidelity improvement at the tested readout lengths. Replayed on the same shots offline, each filtered shot carries 99.4% of the boxcar shot's discrimination signal-to-noise ratio at the 8 μμμs operating point of the 2D transmon qubit (Q1).
On Q1, optimizing the readout window's start and duration improves contrast readout fidelity by +2.4% to +5.6% across four readout lengths. Per-sample weighting adds up to +3.0% over full-window integration, and only +0.33% beyond the tuned window at 8 μμμs.
Remaining results are from a 3D ancilla qubit (Q2), which sits above the early-decision crossover that Q1 sits below. Hardware sweeps locate the crossover window near 1 μμμs. Offline, the sequential test decided most shots early, with fidelity within 0.5 percentage points of the boxcar. About 30 labeled shots per class build a matched-filter template nearly as good as one from hundreds.
The results form an operating-point record that separates waveform denoising from decision improvement.
Advancements in quantum computing underscore the critical need for sophisticated qubit readout techniques to accurately discern quantum states. This abstract presents our research intended for optimizing readout pulse fidelity for 2D and 3D Quantum Processing Units (QPUs), the latter coupled with Superconducting Radio Frequency (SRF) cavities. Focusing specifically on the application of the Least Mean Squares (LMS) adaptive filtering algorithm, we explore its integration into the FPGA-based control systems to enhance the accuracy and efficiency of qubit state detection by improving Signal-to-Noise Ratio (SNR). Implementing the LMS algorithm on the Zynq UltraScale+ RFSoC Gen 3 devices (RFSoC 4x2 FPGA and ZCU216 FPGA) using the Quantum Instrumentation Control Kit (QICK) open-source platform, we aim to dynamically test and adjust the filtering parameters in real-time to characterize and adapt to the noise profile presented in quantum computing readout signals. Our preliminary results demonstrate the LMS filter's capability to maintain high readout accuracy while efficiently managing FPGA resources. These findings are expected to contribute to developing more reliable and scalable quantum computing architectures, highlighting the pivotal role of adaptive signal processing in quantum technology advancements.
Abstract Fast, high-fidelity single-shot readout is a prerequisite for real-time feedback in superconducting-qubit processors, yet the matched filter that remains the field standard discards the temporal structure of the dispersive readout signal and degrades in the presence of energy decay, leakage, and slow parameter drift. We study neural-network discriminators that can run inside the readout feedback loop on a field-programmable gate array (FPGA). Using a physically motivated simulation of dispersive readout that includes cavity ring-up, T1 decay during measurement, leakage to the second excited state, slow IQ drift, and finite signal-to-noise ratio, we benchmark four classical baselines (boxcar integration, matched filtering, linear discriminant analysis, and a Gaussian mixture model) against a floating-point convolutional neural network (CNN), a quantization-aware CNN trained with QKeras, and a new hybrid architecture, the Trace–IQ Fusion Network (TIF-Net), that fuses a learned temporal feature extractor with an integrated-IQ skip path. TIF-Net reachesan assignment fidelity of 0.9962 with only 686 trainable parameters, roughlyan order of magnitude fewer than the 7194-parameter CNN, while exceedingthe matched-filter baseline by 2.3 percentage points. The architecture is constructed to be synthesis-safe: the two pooling operations are realised as fixed-weight convolutions, which we show avoids a scaling pathology of the pooling primitives in our high-level-synthesis (HLS) toolchain. A weight bit-width sweep shows that both networks retain near-peak fidelity down to 4-bit weights, indicating a small multiplier budget for on-board deployment.
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.
Real-time control and readout are pivotal in superconducting quantum computing, given the imperative for numerous algorithms to perform quantum operations as much as possible within the qubit coherent time. Here, we specifically address the qubit readout, recognized as the most time-consuming operation within our experimental platform, and propose a dynamic adaptive readout method (DARM) to improve the performance of qubit readout. In contrast to a standard readout method (SRM) employing Gaussian Naïve Bayes as a discriminator, the DARM can demonstrate a 22.76% relative improvement on readout fidelity when the readout duration time of both methods is set to be consistent. Furthermore, the DARM can also terminate measurement pulse ahead with a 9.93% relative reduction of measurement pulse length on statistical average. The DARM is implemented on a field-programmable-gate-array-based system, and the electronic processing latency, from the digital processing unit getting the qubit signal to the valid output information, is 52 ns, which is only 4 ns longer than the SRM. Compared with the feedforward neural network readout method, the DARM can work in a pipeline mode with shorter electronic processing latency and lower electronic utilization.
Fast and accurate qubit-state assignment is essential for feedback, calibration, and error correction in quantum processors. In superconducting platforms, frequency-multiplexed readout makes this task intrinsically multivariate as measured traces can encode crosstalk, qubit-state relaxation events, and other transient nonidealities that are not fully captured by conventional matched filtering. Here, we introduce spiking neural network (SNN) discriminators for superconducting qubit readout. By processing the measurement window in successive time chunks, the networks exploit temporal structure and update classification scores as data arrive, rather than waiting until the end of the readout window. The spiking networks outperform matched-filter discrimination and approach the accuracy of a full-trace artificial neural network. Beyond reaching the performance of artificial neural networks, the key advantage of SNNs is that they provide a streaming, time-resolved estimate of the qubit state that evolves as the readout signal is acquired. Using quantisation-aware training and hls4ml synthesis, we further demonstrate that each FPGA inference update can be completed before the next readout chunk arrives. These results establish spiking neural networks as a promising route to low-latency, real-time qubit readout on FPGA hardware, with broader implications for time-critical quantum-control and scientific-inference applications.