Mitigating off-resonant error in the cross-resonance gate

TL;DR

This paper investigates off-resonant errors in the cross-resonance quantum gate, focusing on less-studied off-diagonal interactions, and proposes pulse optimization and Y-DRAG pulses to significantly reduce these errors.

Contribution

It introduces methods to suppress off-resonant errors in the cross-resonance gate, including pulse parameter optimization and the use of Y-DRAG pulses, supported by numerical simulations and theoretical analysis.

Findings

Off-resonant error can be reduced from ~10^{-3} to ~10^{-4}.

Optimized pulse parameters align off-resonant frequencies with spectral minima.

Y-DRAG pulses effectively mitigate off-resonant control interactions.

Abstract

Off-resonant error for a driven quantum system refers to interactions due to the input drives having non-zero spectral overlap with unwanted system transitions. For the cross-resonance gate, this includes leakage as well as off-diagonal computational interactions that lead to bit-flip error on the control qubit. In this work, we quantify off-resonant error, with more focus on the less studied off-diagonal control interactions, for a direct CNOT gate implementation. Our results are based on numerical simulation of the dynamics, while we demonstrate the connection to time-dependent Schrieffer-Wolff and Magnus perturbation theories. We present two methods for suppressing such error terms. First, pulse parameters need to be optimized so that off-resonant transition frequencies coincide with the local minima due to the pulse spectrum sidebands. Second, we show the advantage of a $Y$-DRAG pulse on the control qubit in mitigating off-resonant error. Depending on qubit-qubit detuning, the proposed methods can improve the average off-resonant error from approximately $10^{-3}$ closer to the $10^{-4}$ level for a direct CNOT calibration.