Quantum chaos in the spectrum of operators used in Shor's algorithm.

Full Abstract

We provide compelling evidence for the presence of quantum chaos in the unitary part of the operator usually employed in Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the eigenangles as well as the distribution of the eigenvector components follow the circular unitary ensemble of random matrices, of relevance to quantized chaotic systems that violate time-reversal symmetry. However, as the algorithm tracks the evolution of a single state, it is possible to employ other operators; in particular, it is possible that the generic quantum chaos found above becomes of a nongeneric kind such as is found in the quantum cat maps and in toy models of the quantum baker's map.

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Author information

Author/s: Maity, Krishnendu (K); Lakshminarayan, Arul (A);

Affiliation: Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India.

Journal and publication information

Publication Type: Journal Article

Journal: Physical review. E, Statistical, nonlinear, and soft matter physics (Phys Rev E Stat Nonlin Soft Matter Phys), published in United States. (Language: eng)

Reference: 2006-Sep; vol 74 (issue 3 Pt 2) : pp 035203

Dates: Created 2006/10/09; Completed 2007/01/11;

PMID: 17025692, status: PubMed-not-MEDLINE (last retrieval date: 12/26/2008)

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