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

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

2006-04-16

arxiv.org/abs/quant-ph/0604111v2

Phys. Rev. E. vol. 74, 035203(R) (2006).

Physics

Quantum Physics

Title and paper modified to include interesting additional possibilities. Principal results unaffected. Accepted for publicati

Scientific paper

10.1103/PhysRevE.74.035203

We provide compelling evidence for the presence of quantum chaos in the unitary part of 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 CUE 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 bakers map.

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