Period Finding with Adiabatic Quantum Computation

TL;DR

This paper presents an efficient adiabatic quantum algorithm for Simon's problem, demonstrating exponential speedup over classical methods and discussing implications for adiabatic Shor's algorithm and computational complexity equivalence.

Contribution

It introduces a quantum-adiabatic algorithm for Simon's problem with exponential speedup and explores its implications for the equivalence of adiabatic and circuit-based quantum computation.

Findings

The adiabatic algorithm matches the complexity of circuit-based algorithms for Simon's problem.

Supports conjecture that adiabatic and circuit models are computationally equivalent.

Highlights potential for an adiabatic Shor's algorithm with similar efficiency.

Abstract

We outline an efficient quantum-adiabatic algorithm that solves Simon's problem, in which one has to determine the `period', or xor-mask, of a given black-box function. We show that the proposed algorithm is exponentially faster than its classical counterpart and has the same complexity as the corresponding circuit-based algorithm. Together with other related studies, this result supports a conjecture that the complexity of adiabatic quantum computation is equivalent to the circuit-based computational model in a stronger sense than the well-known, proven polynomial equivalence between the two paradigms. We also discuss the importance of the algorithm and its theoretical and experimental implications for the existence of an adiabatic version of Shor's integer factorization algorithm that would have the same complexity as the original algorithm.