2004/05/31 by Davide Rossini, Giuliano Benenti, Giulio Casati · 3 citations
Computer Science · Physics and Astronomy · #Neural Networks and Reservoir Computing #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #cond-mat.mes-hall #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreve.70.056216
published as Phys. Rev. E 70, 056216 (2004) · 8 pages, 7 figures
arxiv created 2004/05/31 · openalex publication_date 2004/11/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum motion when the system's parameters are perturbed or when there are unitary errors in the quantum gates implementing the quantum algorithm. While the first kind of errors has a classical limit, the second one has no classical analog. It is shown that, whereas in the first case ("classical errors") the decay of fidelity is very sensitive to the dynamical regime, in the second case ("quantum errors") it is almost independent of the dynamical behavior of the simulated system. Therefore, the rich variety of behaviors found in the study of the stability of quantum motion under "classical" perturbations has no correspondence in the fidelity of quantum computation under its natural perturbations. In particular, in this latter case it is not possible to recover the semiclassical regime in which the fidelity decays with a rate given by the classical Lyapunov exponent.