dorsal/arxiv
View SchemaEffects of imperfections for Shor's factorization algorithm
| Authors | Ignacio Garcia-Mata, Klaus M. Frahm, Dima L. Shepelyansky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701169 |
| URL | https://arxiv.org/abs/quant-ph/0701169 |
| DOI | 10.1103/PhysRevA.75.052311 |
| Journal | Phys. Rev. A 75, 052311 (2007) |
Abstract
We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor's algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show that the width of peaks, which frequencies allow to determine the factors, grow exponentially with the number of qubits. However, the algorithm remains operational up to a critical coupling strength $\epsilon_c$ which drops only polynomially with $\log_2 N$. The numerical dependence of $\epsilon_c$ on $\log_2 N$ is explained by analytical estimates that allows to obtain the scaling for functionality of Shor's algorithm on realistic quantum computers with a large number of qubits.
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"abstract": "We study effects of imperfections induced by residual couplings between\nqubits on the accuracy of Shor\u0027s algorithm using numerical simulations of\nrealistic quantum computations with up to 30 qubits. The factoring of numbers\nup to N=943 show that the width of peaks, which frequencies allow to determine\nthe factors, grow exponentially with the number of qubits. However, the\nalgorithm remains operational up to a critical coupling strength $\\epsilon_c$\nwhich drops only polynomially with $\\log_2 N$. The numerical dependence of\n$\\epsilon_c$ on $\\log_2 N$ is explained by analytical estimates that allows to\nobtain the scaling for functionality of Shor\u0027s algorithm on realistic quantum\ncomputers with a large number of qubits.",
"arxiv_id": "quant-ph/0701169",
"authors": [
"Ignacio Garcia-Mata",
"Klaus M. Frahm",
"Dima L. Shepelyansky"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.052311",
"journal_ref": "Phys. Rev. A 75, 052311 (2007)",
"title": "Effects of imperfections for Shor\u0027s factorization algorithm",
"url": "https://arxiv.org/abs/quant-ph/0701169"
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