2006/04/30 by Krishnendu Maity, Arul Lakshminarayan
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Chaotic #Computer science #Eigenvalues and eigenvectors #Mathematics #Open quantum system #Operator (biology) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Fourier transform #Quantum Information and Cryptography #Quantum algorithm #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum error correction #Quantum mechanics #Quantum operation #Quantum state #Random matrix #Spectrum (functional analysis) #Statistical physics #Unitary state #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreve.74.035203
published as Phys. Rev. E. vol. 74, 035203(R) (2006). · Title and paper modified to include interesting additional possibilities. Principal results unaffected. Accepted for publication in Phys. Rev. E as Rapid Comm
arxiv created 2006/08/28 · openalex publication_date 2006/09/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.