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arXiv:2609.00939 · Chinese Physics B

Robust CZ gate against flux line memory

Yao Song, Xiu-Hao Deng

quant-phSubmitted Sep 1, 2026• Announced Sep 2, 2026• 0 citations
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Abstract

High-fidelity CZ gates are central to superconducting quantum processors, but implementations based on flux tuning are still sensitive to pulse distortion. Conventional predistortion, typically used for an isolated gate, can recover the desired flux at the chip but it fails if the flux line memory exists, causing the fidelity of repeated CZ gates to drop rapidly. To address this issue, we model the flux line distortion as the dynamics of a stateful classical actuator coupled to a quantum system. Using a first-order Dyson expansion, we derive the error generators induced by variations in the initial flux-line state. We then design a robust CZ gate by optimizing the flux pulse to suppress these generators and minimize the residual flux line state at the gate exit. A one-pole flux line model shows the expected first-order robustness plateau. For a more practical three-pole model, the optimized CZ pulse achieves $F_{\mathrm{avg}}=99.998\%$, suppresses all first-order error generators, and brings the residual flux line state close to zero. With no additional waiting time between gates, our robust pulse achieves $F_{\mathrm{avg}}=99.97\%$ for the complete ten-gate sequence and reduces the sequence infidelity by a factor of about $2.3\times10^{3}$ relative to the baseline under the same predistortion protocol. These results show that explicitly accounting for flux line memory maintains high-fidelity CZ operation across repeated gate sequences and addresses a key limitation of conventional predistortion.

Comments
13 pages and 6 figures

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High-fidelity CZ gates are central to superconducting quantum processors, but implementations based on flux tuning are still sensitive to pulse distortion. Conventional predistortion, typically used for an isolated gate, can recover the desired flux at the chip but it fails if the flux line memory exists, causing the fidelity of repeated CZ gates to drop rapidly. To address this issue, we model the flux line distortion as the dynamics of a stateful classical actuator coupled to a quantum system. Using a first-order Dyson expansion, we derive the error generators induced by variations in the initial flux-line state. We then design a robust CZ gate by optimizing the flux pulse to suppress these generators and minimize the residual flux line state at the gate exit. A one-pole flux line model shows the expected first-order robustness plateau. For a more practical three-pole model, the optimized CZ pulse achieves Favg=99.998%F_{\mathrm{avg}}=99.998\%Favg​=99.998%, suppresses all first-order error generators, and brings the residual flux line state close to zero. With no additional waiting time between gates, our robust pulse achieves Favg=99.97%F_{\mathrm{avg}}=99.97\%Favg​=99.97% for the complete ten-gate sequence and reduces the sequence infidelity by a factor of about 2.3×1032.3\times10^{3}2.3×103 relative to the baseline under the same predistortion protocol. These results show that explicitly accounting for flux line memory maintains high-fidelity CZ operation across repeated gate sequences and addresses a key limitation of conventional predistortion.
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High-fidelity quantum gates are essential for scalable quantum computation. However, at short durations, short-timescale waveform distortions break the time-reflection symmetry of control pulses, preventing the precise closure of cyclic evolution. This mechanism renders conventional symmetric protocols intrinsically over-constrained. Conventional strategies typically rely on smoothing the pulse envelopes or embedding the interaction pulse within a longer qubit pulse to bypass short-timescale distortions, which inevitably leads to a persistent speed-fidelity trade-off. To overcome this limitation, we introduce a cyclic control strategy based on parameter-space expansion, which restores controllability by incorporating an additional degree of freedom. We experimentally demonstrate this approach in a superconducting controlled-Z gate, achieving robust suppression of coherent errors without increasing gate duration, reducing the average coherent error from 0.27% to 0.12% across multiple two-qubit gates, as validated by cross-entropy benchmarking. Our results establish a general route to fast, high-fidelity cyclic quantum gates beyond the conventional speed-fidelity trade-off.
Conditional-phase (cz) gates in transmons can be realized by flux pulsing computational states towards resonance with noncomputational ones. We present a 40 ns cz gate based on a bipolar flux pulse suppressing leakage (0.1%) by interference and approaching the speed limit set by exchange coupling. This pulse harnesses a built-in echo to enhance fidelity (99.1%) and is robust to long-timescale distortion in the flux-control line, ensuring repeatability. Numerical simulations matching experiment show that fidelity is limited by high-frequency dephasing and leakage by short-timescale distortion.