Dynamics of a two-level system under strong driving: quantum gate optimization based on floquet theory

TL;DR

This paper develops a Floquet theory-based approach to analyze and optimize fast, high-fidelity quantum gates in a two-level system driven by strong pulses, revealing interference effects that suppress unwanted transitions.

Contribution

It introduces the FIESTA protocol, leveraging Floquet interference effects to enhance quantum gate speed and fidelity under strong driving conditions.

Findings

Analytical expressions for quasienergies and Floquet states derived.

Identification of interference effects that suppress nonadiabatic transitions.

Demonstration of a protocol for ultra-fast, high-fidelity quantum gates.

Abstract

We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is non-adiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet Interference Efficient Suppression of Transitions in the Adiabatic basis (FIESTA), that can be used to design ultra-fast high-fidelity single-qubit quantum gates.