More period finding with adiabatic quantum computation

TL;DR

This paper explores extending adiabatic quantum computation techniques to solve problems like Bernstein-Vazirani, Simon's, and factoring, using Ising model-based Hamiltonians, and discusses potential for implementing Shor's algorithm.

Contribution

It introduces a method to formulate various problems within the adiabatic quantum computing framework using Ising objective functions and Hamiltonians.

Findings

Hamiltonians for small problem instances are explicitly constructed

Extension of adiabatic methods to Bernstein-Vazirani and Simon's problems

Discussion of potential implementation of Shor's algorithm in adiabatic quantum computing

Abstract

We extend the work of Hen for the Bernstein-Vazirani problem and Simon's problem on an adiabatic quantum computer. Our results are based on the Ising objective function for quantum annealing. For each problem we determine its objective function, describe its Hamiltonian matrix, and show the Hamiltonian matrix for a small problem. Following the pattern of Hen, we discuss factoring of integers, particularly Shor's factoring algorithm in an adiabatic quantum computing environment.