Expected Optimal Time for the NMR Implementation of Shor's Algorithm for Factorising 15

TL;DR

This paper estimates the optimal execution time of Shor's algorithm on a quantum computer using NMR technology, highlighting the potential speedup over current implementations and proposing a new analysis method.

Contribution

It introduces a quantum brachistochrone-based Monte Carlo method to calculate expected optimal execution times for Shor's algorithm on NMR quantum computers.

Findings

Experimental NMR quantum computer takes ~1.59 seconds

Optimal time under same energy conditions is ~0.955 milliseconds

Expected time inversely proportional to energy variance

Abstract

In this paper, we briefly discuss the methodology for simulating a quantum computer which performs Shor's algorithm on a 7-qubit system to factorise 15. Using this simulation and the overlooked quantum brachistochrone method, we devised a Monte Carlo algorithm to calculate the expected time a theoretical quantum computer could perform this calculation under the same energy conditions as current working quantum computers. We found that, experimentally, a nuclear magnetic resonance quantum computer would take $1.59 \pm 0.04$ s to perform our simulated computation, whereas the expected optimal time under the same energy conditions is $0.955 \pm 0.004$ ms. Moreover, we found that the expected time is inversely proportional to the energy variance of our qubit states (as expected). Finally, we propose this theoretical method for analysing the time-efficiency of future quantum computing experiments.