State-independent geometric quantum gates via nonadiabatic and noncyclic evolution

TL;DR

This paper introduces a scheme for universal quantum gates utilizing nonadiabatic, noncyclic geometric phases, enhancing robustness and reducing implementation complexity, with high fidelities demonstrated on superconducting circuits.

Contribution

It proposes a novel approach to geometric quantum gates that fully exploits nonadiabatic, noncyclic geometric phases for improved robustness and experimental feasibility.

Findings

Geometric gates show stronger robustness than dynamical and cyclic geometric gates.

Single-qubit and two-qubit gates achieve fidelities of 99.97% and 99.87%.

The scheme is promising for large-scale fault-tolerant quantum computation.

Abstract

Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not being fully explored in previous investigations. Here, we propose a scheme for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. In our scheme, only geometric phase can be accumulated in a fast way, and thus it not only fully utilizes the local noise resistant property of geometric phase but also reduces the difficulty in experimental realization. Numerical results show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. Furthermore, we propose to construct universal quantum gate on superconducting circuits, with the fidelities of single-qubit gate and nontrivial two-qubit gate can achieve $99.97\%$ and $99.87\%$, respectively. Therefore, these high-fidelity quantum gates are promising for large-scale fault-tolerant quantum computation.