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

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.