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The main challenges in achieving high-fidelity quantum gates are to reducethe influence of control errors caused by imperfect Hamiltonians and theinfluence of decoherence caused by environment noise. To overcome controlerrors, a promising proposal is nonadiabatic holonomic quantum computation,which has attracted much attention in both theories and experiments. While themerit of holonomic operations resisting control errors has been well exploited,an important issue following is how to shorten the evolution time needed forrealizing a holonomic gate so as to avoid the influence of environment noise asmuch as possible. In this paper, we put forward a general approach ofconstructing Hamiltonians for nonadiabatic holonomic quantum computation, whichmakes it possible to minimize the evolution time and might open a new horizonfor the realistic implementation of nonadiabatic holonomic quantum computation.

General approach for constructing Hamiltonians for nonadiabatic holonomic quantum computation