2000/05/02 by Bertrand Georgeot, B. Georgeot, Dima L. Shepelyansky +1 · 125 citations
Computer Science · Mathematics · Physics and Astronomy · #Hamiltonian (control theory) #Mathematics #Open quantum system #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum chaos #Quantum chaos and dynamical systems #Quantum computer #Quantum dynamics #Quantum error correction #Quantum information #Quantum mechanics #Quantum state #Qubit #Statistical physics #cond-mat #quant-ph
paper · pdf · doi:10.1103/physreve.62.6366
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 62(5), 6366-6375 (American Physical Society) · revtex, 10 pages, 18 figures
arxiv created 2000/05/02 · openalex publication_date 2000/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the standard generic quantum computer model, which describes a realistic isolated quantum computer with fluctuations in individual qubit energies and residual short-range interqubit couplings. It is shown that in the limit where the fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure, and a renormalized Hamiltonian is obtained which describes the eigenstate properties inside one band. Studies are concentrated on the central band of the computer ("core") with the highest density of states. We show that above a critical interqubit coupling strength, quantum chaos sets in, leading to a quantum ergodicity of the computer eigenstates. In this regime the ideal qubit structure disappears, the eigenstates become complex, and the operability of the computer is quickly destroyed. We confirm that the quantum chaos border decreases only linearly with the number of qubits n, although the spacing between multiqubit states drops exponentially with n. The investigation of time evolution in the quantum computer shows that in the quantum chaos regime, an ideal (noninteracting) state quickly disappears, and exponentially many states become mixed after a short chaotic time scale for which the dependence on system parameters is determined. Below the quantum chaos border an ideal state can survive for long times, and an be used for computation. The results show that a broad parameter region does exist where the efficient operation of a quantum computer is possible.