A study of heuristic guesses for adiabatic quantum computation

TL;DR

This paper explores a heuristic approach to adiabatic quantum computation that starts from an educated guess state rather than a uniform superposition, potentially improving efficiency and enabling restart strategies based on measurement outcomes.

Contribution

It introduces a heuristic method for AQC using initial guess states and a restart strategy based on measurements, diverging from conventional uniform initial states.

Findings

Performance depends on Hamming distance of initial guess to solution

Heuristic allows restarting from measured excited states

Numerical results on 6 and 7 bit 3-SAT instances

Abstract

Adiabatic quantum computation (AQC) is a universal model for quantum computation which seeks to transform the initial ground state of a quantum system into a final ground state encoding the answer to a computational problem. AQC initial Hamiltonians conventionally have a uniform superposition as ground state. We diverge from this practice by introducing a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem. With this goal in mind, we explain the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7 bit random instances of the satisfiability problem (3-SAT), we show how this heuristic approach is possible and we identify that the performance of the particular algorithm proposed is largely determined by the Hamming distance of the chosen initial guess state with respect to the solution. Besides the possibility of introducing educated guesses as initial states, the new strategy allows for the possibility of restarting a failed adiabatic process from the measured excited state as opposed to restarting from the full superposition of states as in CAQC. The outcome of the measurement can be used as a more refined guess state to restart the adiabatic evolution. This concatenated restart process is another heuristic that the CAQC strategy cannot capture.