Nonadiabatic corrections to fast dispersive multiqubit gates involving Z control

TL;DR

This paper introduces a time-dependent Schrieffer-Wolff transformation to accurately model nonadiabatic effects in fast multiqubit gates, improving fidelity estimates crucial for fault-tolerant quantum computing.

Contribution

It extends the dispersive regime analysis to time-dependent controls and provides a rigorous application to superconducting two-qubit gates, revealing significant fidelity corrections.

Findings

Fidelity estimates are off by up to 10^{-2} using previous models.

A closed-form expression for nonadiabatic errors is derived.

The method enhances understanding of high-speed quantum gate performance.

Abstract

We review a time-dependent version of the Schrieffer-Wolff transformation that accounts for real-time control of system parameters, soon to be rendered possible on a broad basis due to technical progress. The dispersive regime of $N$ multilevel systems coupled to a cavity via a Jaynes-Cummings interaction is extended to the most general case. As a concrete example we rigorously apply the technique to dispersive two-qubit gates in a superconducting architecture, showing that fidelities based on previous models are off by up to $10^{-2}$, which is certainly relevant for high-fidelity gates compatible with fault-tolerant quantum information devices. A closed analytic form for the error depending on the target evolution closes our work.