Fast non-Abelian geometric gates via transitionless quantum driving

TL;DR

This paper introduces a method to implement fast, high-fidelity non-Abelian geometric quantum gates using transitionless driving, enhancing speed and robustness for practical quantum computing in superconducting circuits.

Contribution

It presents a novel approach combining transitionless quantum driving with non-Abelian geometric phases to accelerate holonomic quantum gates.

Findings

Achieves faster quantum gates with high fidelity.

Maintains geometric noise-tolerance features.

Bridges adiabatic and non-adiabatic holonomic approaches.

Abstract

A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.