Coherence-protected nonadiabatic geometric quantum computation

Because of using geometric phases, nonadiabatic geometric gates have robustness against control errors. On the other hand, decoherence still affects nonadiabatic geometric gates, which is a key factor in reducing their fidelities. In this paper, we show that based on the system Hamiltonian that realizes a nonadiabatic geometric gate, one may construct a system Hamiltonian by the use of which not only the geometric feature of the nonadiabatic geometric gate is preserved, but also the system's coherence is protected. As a result, a coherence-protected nonadiabatic geometric gate is realized with this system Hamiltonian, and this gate has robustness against both control errors and decoherence. We further implement our scheme with nitrogen-vacancy centers and show that a universal set of coherence-protected nonadiabatic geometric gates can be realized. Our scheme does not need auxiliary systems or the encoding of logical qubits with physical qubits, which saves resources for the implementation. Due to the robustness against both control errors and decoherence, our scheme provides a promising way to realize high-fidelity quantum gates.