Simplified Factoring Algorithms for Validating Small-Scale Quantum Information Processing Technologies

TL;DR

This paper introduces simplified, compiled versions of Shor's factoring algorithm for validating small-scale quantum devices, reducing resource requirements and enabling practical experimental implementation.

Contribution

It presents new compiled circuits for Shor's algorithm and a classical compilation layer to minimize qubits and gates needed for quantum validation.

Findings

New compiled circuits for Shor's algorithm provided

Classical compilation reduces qubit and gate requirements

Enables near-term experimental validation of quantum devices

Abstract

Tomography has reached its practical limits in characterization of new quantum devices, and there is a need for a new means of characterizing and validating new technological advances in this field. We propose a different verification scheme based on compiled versions of Shor's factoring algorithm that may be extended to large circuits in the future. The general version Shor's algorithm has been experimentally elusive due to bottlenecks associated with the modular exponentiation operation. Experiments to date have only been able to execute compiled versions of the latter operation. We provide some new compiled circuits for experimentalists to use in the near future. We also demonstrate that an additional layer of compilation can be added using classical operations, that will reduce the number of qubits and gates needed in a given compiled circuit.