Fast Evolution of Single Qubit Gate in Non-Adiabatic Geometric Quantum Computing

TL;DR

This paper demonstrates a fast, single-shot implementation of arbitrary single qubit gates in non-adiabatic geometric quantum computing, reducing gate time and enhancing robustness against errors by optimizing the evolution trajectory.

Contribution

It introduces a generalized model for non-adiabatic holonomic quantum gates that minimizes evolution time and improves robustness, unifying previous schemes as special cases.

Findings

Gate duration can be reduced to ~40% of traditional methods.

Certain pulses show robustness against static detuning and Rabi errors.

The model links detuning and Rabi frequency through a constant related to geometric phase.

Abstract

We implemented arbitrary single qubit gates of geometric quantum computing for a three-level system in a single-shot manner. The evolution time of the gate has been minimized by considering the shortest trajectory of the state on the Bloch sphere. The duration of gates grows from zero with the rotation angle $\gamma$, and the tested T gate time can be reduced to $\sim$40\% of those in the traditional orange-sliced-shaped path non-adiabatic holonomic quantum computing (NHQC) scheme by the parametrization of Rabi frequency. We also demonstrated that certain pulses are robust against static detuning errors and Rabi errors. The time-dependent detuning and Rabi frequency are found to be proportional to each other by a constant which is determined by the geometric phase. In this way, some previous NHQC schemes can be treated as special cases in our generalized model.