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The key for realizing fault-tolerant quantum computation lies in maintainingthe coherence of all qubits so that high-fidelity and robust quantummanipulations on them can be achieved. One of the promising approaches is touse geometric phases in the construction of universal quantum gates, due totheir intrinsic robustness against certain types of local noises. However, dueto limitations in previous implementations, the noise-resilience feature ofnonadiabatic holonomic quantum computation (NHQC) still needs to be improved.Here, combining with the dynamical correction technique, we propose a generalprotocol of universal NHQC with simplified control, which can greatly suppressthe effect of the accompanied X errors, retaining the main merit of geometricquantum operations. Numerical simulation shows that the performance of our gatecan be much better than previous protocols. Remarkably, when incorporating adecoherence-free subspace encoding for the collective dephasing noise, ourscheme can also be robust against the involved Z errors. In addition, we alsooutline the physical implementation of the protocol that is insensitive to bothX and Z errors. Therefore, our protocol provides a promising strategy forscalable fault-tolerant quantum computation.

Dynamically Corrected Nonadiabatic Holonomic Quantum Gates