dorsal/arxiv
View SchemaPhase diagram for the Grover algorithm with static imperfections
| Authors | A. A. Pomeransky, O. V. Zhirov, D. L. Shepelyansky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403138 |
| URL | https://arxiv.org/abs/quant-ph/0403138 |
| DOI | 10.1140/epjd/e2004-00113-4 |
| Journal | Eur. Phys. J. D 31, 131-135 (2004) |
Abstract
We study effects of static inter-qubit interactions on the stability of the Grover quantum search algorithm. Our numerical and analytical results show existence of regular and chaotic phases depending on the imperfection strength $\epsilon$. The critical border $\epsilon_c$ between two phases drops polynomially with the number of qubits $n_q$ as $\epsilon_c \sim n_q^{-3/2}$. In the regular phase $(\epsilon < \epsilon_c)$ the algorithm remains robust against imperfections showing the efficiency gain $\epsilon_c / \epsilon$ for $\epsilon \gtrsim 2^{-n_q/2}$. In the chaotic phase $(\epsilon > \epsilon_c)$ the algorithm is completely destroyed.
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"abstract": "We study effects of static inter-qubit interactions on the stability of the\nGrover quantum search algorithm. Our numerical and analytical results show\nexistence of regular and chaotic phases depending on the imperfection strength\n$\\epsilon$. The critical border $\\epsilon_c$ between two phases drops\npolynomially with the number of qubits $n_q$ as $\\epsilon_c \\sim n_q^{-3/2}$.\nIn the regular phase $(\\epsilon \u003c \\epsilon_c)$ the algorithm remains robust\nagainst imperfections showing the efficiency gain $\\epsilon_c / \\epsilon$ for\n$\\epsilon \\gtrsim 2^{-n_q/2}$. In the chaotic phase $(\\epsilon \u003e \\epsilon_c)$\nthe algorithm is completely destroyed.",
"arxiv_id": "quant-ph/0403138",
"authors": [
"A. A. Pomeransky",
"O. V. Zhirov",
"D. L. Shepelyansky"
],
"categories": [
"quant-ph"
],
"doi": "10.1140/epjd/e2004-00113-4",
"journal_ref": "Eur. Phys. J. D 31, 131-135 (2004)",
"title": "Phase diagram for the Grover algorithm with static imperfections",
"url": "https://arxiv.org/abs/quant-ph/0403138"
},
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