Dynamically Corrected Nonadiabatic Holonomic Quantum Gates

TL;DR

This paper introduces a dynamical correction method for nonadiabatic holonomic quantum gates, significantly enhancing their noise resilience and robustness against X and Z errors, advancing fault-tolerant quantum computing.

Contribution

It presents a universal NHQC protocol with simplified control and dynamical correction, improving noise robustness and incorporating decoherence-free subspaces for enhanced fault tolerance.

Findings

Numerical simulations show improved gate performance over previous protocols.

The scheme is robust against both X and Z errors when using decoherence-free subspace encoding.

The protocol is feasible for physical implementation and scalable quantum computation.

Abstract

The key for realizing fault-tolerant quantum computation lies in maintaining the coherence of all qubits so that high-fidelity and robust quantum manipulations on them can be achieved. One of the promising approaches is to use geometric phases in the construction of universal quantum gates, due to their intrinsic robustness against certain types of local noises. However, due to limitations in previous implementations, the noise-resilience feature of nonadiabatic holonomic quantum computation (NHQC) still needs to be improved. Here, combining with the dynamical correction technique, we propose a general protocol of universal NHQC with simplified control, which can greatly suppress the effect of the accompanied X errors, retaining the main merit of geometric quantum operations. Numerical simulation shows that the performance of our gate can be much better than previous protocols. Remarkably, when incorporating a decoherence-free subspace encoding for the collective dephasing noise, our scheme can also be robust against the involved Z errors. In addition, we also outline the physical implementation of the protocol that is insensitive to both X and Z errors. Therefore, our protocol provides a promising strategy for scalable fault-tolerant quantum computation.