A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability

TL;DR

This paper numerically investigates the performance of a quantum adiabatic algorithm on satisfiability problems, showing that the required running time grows slowly with problem size in tested instances.

Contribution

It provides the first numerical analysis of quantum adiabatic algorithms on both NP-complete and classically easy problems, demonstrating favorable scaling behavior.

Findings

Running time grows slowly with number of bits for tested instances

Quantum adiabatic algorithm performs well on NP-complete problems in simulations

Classically easy problems also show polynomial-like scaling

Abstract

Quantum computation by adiabatic evolution, as described in quant-ph/0001106, will solve satisfiability problems if the running time is long enough. In certain special cases (that are classically easy) we know that the quantum algorithm requires a running time that grows as a polynomial in the number of bits. In this paper we present numerical results on randomly generated instances of an NP-complete problem and of a problem that can be solved classically in polynomial time. We simulate a quantum computer (of up to 16 qubits) by integrating the Schrodinger equation on a conventional computer. For both problems considered, for the set of instances studied, the required running time appears to grow slowly as a function of the number of bits.