dorsal/arxiv
View SchemaAsymptotics of Quantum Random Walk Driven by Optical Cavity
| Authors | Demosthenes Ellinas, Ioannis Smyrnakis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510112 |
| URL | https://arxiv.org/abs/quant-ph/0510112 |
| DOI | 10.1088/1464-4266/7/7/004 |
| Journal | Journal of Optics B: Quantum Semiclass. Opt. 7 (2005) S152 - S157 |
Abstract
We investigate a novel quantum random walk (QRW) model, possibly useful in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behavior expressed in the form of a limit probability distribution of a double horn shape. Questions of robustness and control of that limit distribution are addressed by introducing a quantum optical cavity in which a resonant Jaynes-Cummings type of interaction between the quantum walk coin system realized in the form of a two-level atom and a laser field is taking place. Driving the optical cavity by means of the coin-field interaction time and the initial quantum coin state, we determine two types of modification of the asymptotic behavior of the QRW. In the first one the limit distribution is robustly reproduced up to a scaling, while in the second one the quantum features of the walk, exemplified by enhanced diffusion rate, are washed out and Gaussian asymptotics prevail. Verification of these findings in an experimental setup that involves two quantum optical cavities that implement the driven QRW and its quantum to classical transition is discussed.
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"abstract": "We investigate a novel quantum random walk (QRW) model, possibly useful in\nquantum algorithm implementation, that achieves a quadratically faster\ndiffusion rate compared to its classical counterpart.\n We evaluate its asymptotic behavior expressed in the form of a limit\nprobability distribution of a double horn shape. Questions of robustness and\ncontrol of that limit distribution are addressed by introducing a quantum\noptical cavity in which a resonant Jaynes-Cummings type of interaction between\nthe quantum walk coin system realized in the form of a two-level atom and a\nlaser field is taking place. Driving the optical cavity by means of the\ncoin-field interaction time and the initial quantum coin state, we determine\ntwo types of modification of the asymptotic behavior of the QRW. In the first\none the limit distribution is robustly reproduced up to a scaling, while in the\nsecond one the quantum features of the walk, exemplified by enhanced diffusion\nrate, are washed out and Gaussian asymptotics prevail. Verification of these\nfindings in an experimental setup that involves two quantum optical cavities\nthat implement the driven QRW and its quantum to classical transition is\ndiscussed.",
"arxiv_id": "quant-ph/0510112",
"authors": [
"Demosthenes Ellinas",
"Ioannis Smyrnakis"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/7/7/004",
"journal_ref": "Journal of Optics B: Quantum Semiclass. Opt. 7 (2005) S152 - S157",
"title": "Asymptotics of Quantum Random Walk Driven by Optical Cavity",
"url": "https://arxiv.org/abs/quant-ph/0510112"
},
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