Dynamically Corrected Nonadiabatic Holonomic Quantum Gates

Abstract

The key for realizing fault-tolerant quantum computation lies in maintaining the coherence of all the qubits so that high-fidelity and robust qubit manipulations can be achievable. One of the promising approaches is to use geometric phases in the construction of universal quantum gates, due to the intrinsic robustness against operational errors, i.e., X errors. However, due to the implementation limitations, previous schemes for nonadiabatic holonomic quantum computation (NHQC) do not possess the noise-resilience feature. Here, combining with the dynamical correction technique, we propose a general protocol for universal NHQC, which can greatly suppress X errors, retaining the merit of geometric quantum operations. Numerical simulation shows that our gate performance can be much better than previous protocols. Remarkably, when incorporate a minimum resource decoherence-free subspace encoding, our scheme can also be robust against dephasing error, i.e., the Z error. 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.