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