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

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.

arXiv comment6 pages, 2 figures, written as part of a third year group project. [v2] Updated to a more accurate title. [v3] Updated to a more precise abstract, added an acknowledgement, updated second figure for gray-scale print

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• Quantum Brachistochrone
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Cited by in corpus (1)

• Complementarity between quantum entanglement, geometrical and dynamical appearances in N spin-$1/2$ system under all-range Ising model