Effects of dynamical phases in Shor's factoring algorithm with operational delays

Journal Article · Tue Feb 01 04:00:00 EST 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.71.022317· OSTI ID:20650062

Wei, L F ^[1]; Xiao, Li ^[2]; Xuedong, Hu ^[1]; Nori, Franco ^[1]

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1. Frontier Research System, Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama, 351-0198 (Japan)
2. Department of Physics, Shanghai Jiaotong University, Shanghai 200030 (China)

Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum computing process. During these delays, coherent errors will accumulate from the dynamical phases of the superposed wave functions. Here we explore the sensitivity of Shor's quantum factoring algorithm to such errors. Our results clearly show a severe sensitivity of Shor's factorization algorithm to the presence of delay times between successive unitary transformations. Specifically, in the presence of these coherent errors, the probability of obtaining the correct answer decreases exponentially with the number of qubits of the work register. A particularly simple phase-matching approach is proposed in this paper to avoid or suppress these coherent errors when using Shor's algorithm to factorize integers. The robustness of this phase-matching condition is evaluated analytically and numerically for the factorization of several integers: 4, 15, 21, and 33.

• OSTI ID: 20650062
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 71; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ALGORITHMS
ERRORS
FACTORIZATION
INFORMATION THEORY
PROBABILITY
QUANTUM MECHANICS
SENSITIVITY
TRANSFORMATIONS
WAVE FUNCTIONS