Fast quantum algorithm for EC3 problem with trapped ions

TL;DR

This paper introduces a rapid adiabatic quantum algorithm enhanced with fast signals, significantly reducing runtime for solving the EC3 problem using trapped ions, while maintaining quantum advantages.

Contribution

It proposes a novel fast-signal assisted adiabatic quantum algorithm with a randomized Trotter formula, specifically applied to the EC3 problem with trapped ions.

Findings

Runtime is greatly reduced with fast signals.

Quantum advantages are preserved despite faster evolution.

Implementation with trapped ions is feasible.

Abstract

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