Efficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Z</mml:mi></mml:math> gates for quantum computing

TLDR

Microwave pulses drive rotations on superconducting qubits, and by tuning the drive phase they can generate zero‑duration virtual Z‑gates that, together with two Xπ/2 gates, enable arbitrary SU(2) operations. The study demonstrates how virtual Z‑gates can improve quantum algorithms and correct pulse errors, providing an alternative to DRAG for correcting unitary rotation errors in weakly anharmonic qubits. The authors benchmarked a Clifford set of Hadamard and Z‑gates, showing.

Abstract

For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. The phase of these drives can be used to generate zero-duration arbitrary "virtual" Z-gates which, combined with two $X_{\pi/2}$ gates, can generate any SU(2) gate. Here we show how to best utilize these virtual Z-gates to both improve algorithms and correct pulse errors. We perform randomized benchmarking using a Clifford set of Hadamard and Z-gates and show that the error per Clifford is reduced versus a set consisting of standard finite-duration X and Y gates. Z-gates can correct unitary rotation errors for weakly anharmonic qubits as an alternative to pulse shaping techniques such as DRAG. We investigate leakage and show that a combination of DRAG pulse shaping to minimize leakage and Z-gates to correct rotation errors (DRAGZ) realizes a 13.3~ns $X_{\pi/2}$ gate characterized by low error ($1.95[3]\times 10^{-4}$) and low leakage ($3.1[6]\times 10^{-6}$). Ultimately leakage is limited by the finite temperature of the qubit, but this limit is two orders-of-magnitude smaller than pulse errors due to decoherence.