dorsal/arxiv
View SchemaEffects of dynamical phases in Shor's factoring algorithm with operational delays
| Authors | L. F. Wei, Xiao Li, Xuedong Hu, Franco Nori |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305039 |
| URL | https://arxiv.org/abs/quant-ph/0305039 |
| DOI | 10.1103/PhysRevA.71.022317 |
| Journal | Phys. Rev. A 71, 022317 (2005) |
Abstract
Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum computing process. During these delays, coherent "errors" will accumulate from the dynamical phases of the superposed wave functions. Here we explore the sensitivity of Shor's quantum factoring algorithm to such errors. Our results clearly show a severe sensitivity of Shor's factorization algorithm to the presence of delay times between successive unitary transformations. Specifically, in the presence of these {\it coherent "errors"}, the probability of obtaining the correct answer decreases exponentially with the number of qubits of the work register. A particularly simple phase-matching approach is proposed in this paper to {\it avoid} or suppress these {\it coherent errors} when using Shor's algorithm to factorize integers. The robustness of this phase-matching condition is evaluated analytically or numerically for the factorization of several integers: $4, 15, 21$, and 33.
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"abstract": "Ideal quantum algorithms usually assume that quantum computing is performed\ncontinuously by a sequence of unitary transformations. However, there always\nexist idle finite time intervals between consecutive operations in a realistic\nquantum computing process. During these delays, coherent \"errors\" will\naccumulate from the dynamical phases of the superposed wave functions. Here we\nexplore the sensitivity of Shor\u0027s quantum factoring algorithm to such errors.\nOur results clearly show a severe sensitivity of Shor\u0027s factorization algorithm\nto the presence of delay times between successive unitary transformations.\nSpecifically, in the presence of these {\\it coherent \"errors\"}, the probability\nof obtaining the correct answer decreases exponentially with the number of\nqubits of the work register. A particularly simple phase-matching approach is\nproposed in this paper to {\\it avoid} or suppress these {\\it coherent errors}\nwhen using Shor\u0027s algorithm to factorize integers. The robustness of this\nphase-matching condition is evaluated analytically or numerically for the\nfactorization of several integers: $4, 15, 21$, and 33.",
"arxiv_id": "quant-ph/0305039",
"authors": [
"L. F. Wei",
"Xiao Li",
"Xuedong Hu",
"Franco Nori"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.022317",
"journal_ref": "Phys. Rev. A 71, 022317 (2005)",
"title": "Effects of dynamical phases in Shor\u0027s factoring algorithm with operational delays",
"url": "https://arxiv.org/abs/quant-ph/0305039"
},
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