Plug-and-Play Approach to Non-adiabatic Geometric Quantum Gates

TL;DR

This paper introduces an extensible nonadiabatic geometric quantum gate method, NHQC{ h}, that enhances robustness against noise and integrates various optimal control techniques, applicable across different quantum platforms.

Contribution

The paper presents NHQC{ h}, a flexible framework for constructing robust nonadiabatic geometric quantum gates that incorporates existing control methods and improves noise resilience.

Findings

Numerical simulations show improved noise robustness in experimental setups.

The approach is compatible with platforms like superconducting qubits and NV centers.

It combines geometric phase robustness with optimal control techniques.

Abstract

Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive conditions, reducing the robustness of the resulting geometric gates against control errors. Here we show that nonadiabatic geometric gates can be constructed in an extensible way, called NHQC{\th}, for maintaining both flexibility and robustness against certain types of noises. Consequently, this approach makes it possible to incorporate most of the existing optimal control methods, such as dynamical decoupling, composite pulses, and a shortcut to adiabaticity, into the construction of single-looped geometric gates. Furthermore, this extensible approach of geometric quantum computation can be applied to various physical platforms such as superconducting qubits and nitrogen-vacancy centers. Specifically, we performed numerical simulation to show how the noise robustness in recent experimental implementations [Phys. Rev. Lett. 119, 140503 (2017); Nat. Photonics 11, 309 (2017)] can be significantly improved by our NHQC{\th}.approach. These results cover a large class of new techniques combing the noise robustness of both geometric phase and optimal control theory.