A Quantum Adiabatic Algorithm for Factorization and Its Experimental Implementation

TL;DR

This paper introduces an adiabatic quantum algorithm for factorization that requires fewer qubits than Shor's algorithm, demonstrating its experimental implementation on an NMR processor to factorize 21.

Contribution

It presents a novel adiabatic quantum algorithm for factorization with reduced qubit requirements and experimental validation on an NMR system.

Findings

Successfully factorized 21 using the algorithm

Algorithm's running time grows quadratically with qubits

Fewer qubits needed compared to Shor's algorithm

Abstract

We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in an NMR quantum information processor and experimentally factorize the number 21. Numerical simulations indicate that the running time grows only quadratically with the number of qubits.