A quantum circuit for shor's factoring algorithm using 2n + 2 qubits

  • Authors:
  • Yasuhiro Takahashi;Noboru Kunihiro

  • Affiliations:
  • NTT Communications Science Laboratories, NTT Corporation Atsugi, Kanagawa, Japan;The University of Electro-Communications Chofu, Tokyo, Japan

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2006

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Abstract

We construct a quantum circuit for Shor's factoring algorithm that uses 2n + 2 qubits,where n is the length of the number to be factored. The depth and size of the circuitare O(n3) and O(n3 log n), respectivel). The number of qubits used in the circuit is lessthan that in any other quantum circuit ever constructed for Shor's factoring algorithm.Moreover, the size of the circuit is about half the size of Beauregard's quantum circuitfor Shor's factoring algorithm, which uses 2n + 3 qubits.