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A Low-Resource Quantum Factoring Algorithm

  • Daniel J. BernsteinEmail author
  • Jean-François BiasseEmail author
  • Michele MoscaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10346)

Abstract

In this paper, we present a factoring algorithm that, assuming standard heuristics, uses just \((\log N)^{2/3+o(1)}\) qubits to factor an integer N in time \(L^{q+o(1)}\) where \(L = \exp ((\log N)^{1/3}(\log \log N)^{2/3})\) and \(q=\root 3 \of {8/3}\approx 1.387\). For comparison, the lowest asymptotic time complexity for known pre-quantum factoring algorithms, assuming standard heuristics, is \(L^{p+o(1)}\) where \(p>1.9\). The new time complexity is asymptotically worse than Shor’s algorithm, but the qubit requirements are asymptotically better, so it may be possible to physically implement it sooner.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  2. 2.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands
  3. 3.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA
  4. 4.Institute for Quantum Computing and Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  5. 5.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  6. 6.Canadian Institute for Advanced ResearchTorontoCanada

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