dorsal/arxiv
View SchemaClassical versus quantum errors in quantum computation of dynamical systems
| Authors | Davide Rossini, Giuliano Benenti, Giulio Casati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405189 |
| URL | https://arxiv.org/abs/quant-ph/0405189 |
| DOI | 10.1103/PhysRevE.70.056216 |
| Journal | Phys. Rev. E 70, 056216 (2004) |
Abstract
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 analogue. 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.
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"abstract": "We analyze the stability of a quantum algorithm simulating the quantum\ndynamics of a system with different regimes, ranging from global chaos to\nintegrability. We compare, in these different regimes, the behavior of the\nfidelity of quantum motion when the system\u0027s parameters are perturbed or when\nthere are unitary errors in the quantum gates implementing the quantum\nalgorithm. While the first kind of errors has a classical limit, the second one\nhas no classical analogue. It is shown that, whereas in the first case\n(``classical errors\u0027\u0027) the decay of fidelity is very sensitive to the dynamical\nregime, in the second case (``quantum errors\u0027\u0027) it is almost independent of the\ndynamical behavior of the simulated system. Therefore, the rich variety of\nbehaviors found in the study of the stability of quantum motion under\n``classical\u0027\u0027 perturbations has no correspondence in the fidelity of quantum\ncomputation under its natural perturbations. In particular, in this latter case\nit is not possible to recover the semiclassical regime in which the fidelity\ndecays with a rate given by the classical Lyapunov exponent.",
"arxiv_id": "quant-ph/0405189",
"authors": [
"Davide Rossini",
"Giuliano Benenti",
"Giulio Casati"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"nlin.CD"
],
"doi": "10.1103/PhysRevE.70.056216",
"journal_ref": "Phys. Rev. E 70, 056216 (2004)",
"title": "Classical versus quantum errors in quantum computation of dynamical systems",
"url": "https://arxiv.org/abs/quant-ph/0405189"
},
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