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Adiabatic quantum computing~(AQC) is based on the adiabatic principle, wherea quantum system remains in an instantaneous eigenstate of the drivingHamiltonian. The final state of the Hamiltonian encodes solution to the problemof interest. While AQC has distinct advantages, recent researches have shownthat quantumness such as quantum coherence in adiabatic processes may be lostentirely due to the system-bath interaction when the evolution time is long,and consequently the expected quantum speedup dose not show up. Here we proposea fast-signal assisted adiabatic quantum algorithm. We find that by applying asequence of fast random or regular signals during the evolution process, theruntime can be reduced greatly, yet advantages of the adiabatic algorithmremain intact. Significantly, we present a \emph{randomized} Trotter formulaand show that the driving Hamiltonian and the sequence of fast signals can beimplemented simultaneously. We apply the algorithm for solving the $3$-bitexact cover problem~(EC$3$) and put forward an approach for implementing theproblem with trapped ions.

Fast quantum algorithm for EC3 problem with trapped ions