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Bulletin of the American Physical Society

High-fidelity controlled-Z gate with maximal intermediate leakage operating at the speed limit in a superconducting quantum processor

Hany A. Ali, Victor Negîrneac, Nandini Muthusubramanian, Francesco Battistel, Ramiro Sagastizabal, M. S. Moreira, Jorge Marques, Wouter Vlothuizen, Marc Beekman, Nadia Haider, Alessandro Bruno, L. DiCarlo

Published Mar 18, 2021• 5 citations
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Simple tuneup of fast two-qubit gates is essential for the scaling of quantum processors. We introduce the sudden variant (SNZ) of the net zero scheme realizing controlled-Z (CZ) gates by flux control of transmon frequency. SNZ CZ gates realized in a multitransmon processor operate at the speed limit of transverse coupling between computational and noncomputational states by maximizing intermediate leakage. Beyond speed, the key advantage of SNZ is tuneup simplicity, owing to the regular structure of conditional phase and leakage as a function of two control parameters. SNZ is compatible with scalable schemes for quantum error correction and adaptable to generalized conditional-phase gates useful in intermediate-scale applications.
Achieving fast and high-fidelity qubit operations is crucial for unlocking the potential of quantum computers. In particular, reaching low gate errors in two-qubit gates has been a long-standing challenge in the field of superconducting qubits due to their typically long duration relative to coherence times. To realize fast gates, we use the hybridization between fixed-frequency superconducting qubits with a strongly interacting coupler mode that is tunable in frequency. To reduce population leakage during required adiabatic passages through avoided level crossings, we employ a sensitivity-adaptive closed-loop optimization method to design complex pulse shapes. We compare the performance of Gaussian-square, Fourier-series, and piecewise-constant-slope pulse parametrizations and are able to reach 99.9% controlled- Z -gate fidelity using a 64-ns-long Fourier-series pulse defined by only seven parameters. These high-fidelity values are achieved by analyzing the optimized pulse shapes to identify and systematically mitigate signal-line distortions in the experiment. To improve the convergence speed of the optimization, we implement an adaptive cost function, which continuously maximizes the sensitivity. The demonstrated method can be used for tune-up and recalibration of superconducting quantum processors.
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.