Nonadiabatic corrections to fast dispersive multiqubit gates involving<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Z</mml:mi></mml:math>control

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 ${10}^{\ensuremath{-}2}$, 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.