Analytical blueprint for 99.999% fidelity X-gates on present superconducting hardware under strong driving

TL;DR

This paper develops an analytical framework for implementing ultra-fast, high-fidelity X-gates on superconducting qubits under strong driving, addressing multi-photon errors and optimizing control parameters.

Contribution

It introduces analytical formulas and calibration strategies to suppress multi-photon errors and phase errors, enabling 7ns π-rotations with infidelity below 10^-5 on superconducting hardware.

Findings

Achieved gate infidelity below 10^-5 for 7ns π-rotation.

Derived analytical formulas for error suppression in strong driving regime.

Optimized control parameters including DRAG prefactor and detuning.

Abstract

Achieving very fast gates that undercut the natural limits set by decoherence requires going into the strong driving limit. Realizing single-qubit control predicted beyond semi-classical, time-dependent modeling has yet to be experimentally realized on superconducting and most other computing platforms. In this regime, the common model of dynamics within a three-level manifold breaks down, and instead, we see new quantum error channels growing abruptly with decreasing time. To identify these error processes we systematically calculate the effect of multi-photon transitions that occur out of the computational space. We then derive analytical formulas to suppress these effects, as well as amplitude and phase errors on the qubit space; we term these R1D for suppressing the $|0\rangle-|2\rangle$ transition and R2D when also suppressing $|1\rangle-|3\rangle$ leakage. We also answer long-standing questions about the optimal values of the DRAG prefactor as well as constant detuning, when accounting for time-ordering, and also show how to calibrate other prefactors for further performance improvement. Upon correcting these varied sources of error, we numerically demonstrate gate infidelities below $10^{-5}$ for a 7ns $\pi$-rotation when incorporating existing decoherence rates.