Efficient Z-Gates for Quantum Computing

TL;DR

This paper demonstrates how virtual Z-gates can enhance quantum gate performance by reducing errors and leakage in superconducting qubits, offering a practical alternative to pulse shaping techniques like DRAG.

Contribution

It introduces optimized utilization of virtual Z-gates for error correction and algorithm improvement, achieving lower error rates and leakage in superconducting qubits.

Findings

Error per Clifford reduced with virtual Z-gates

Leakage minimized using combined DRAG and Z-gates (DRAGZ)

Achieved low error and leakage in $X_{\pi/2}$ gates

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.