dorsal/arxiv
View SchemaQuantum walks in higher dimensions
| Authors | Troy D. Mackay, Stephen D. Bartlett, Leigh T. Stephenson, Barry C. Sanders |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108004 |
| URL | https://arxiv.org/abs/quant-ph/0108004 |
| DOI | 10.1088/0305-4470/35/12/304 |
| Journal | J. Phys. A: Math. Gen. 35, 2745 (2002) |
Abstract
We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the quantum coin toss in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable.
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"abstract": "We analyze the quantum walk in higher spatial dimensions and compare\nclassical and quantum spreading as a function of time. Tensor products of\nHadamard transformations and the discrete Fourier transform arise as natural\nextensions of the quantum coin toss in the one-dimensional walk simulation, and\nother illustrative transformations are also investigated. We find that\nentanglement between the dimensions serves to reduce the rate of spread of the\nquantum walk. The classical limit is obtained by introducing a random phase\nvariable.",
"arxiv_id": "quant-ph/0108004",
"authors": [
"Troy D. Mackay",
"Stephen D. Bartlett",
"Leigh T. Stephenson",
"Barry C. Sanders"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/35/12/304",
"journal_ref": "J. Phys. A: Math. Gen. 35, 2745 (2002)",
"title": "Quantum walks in higher dimensions",
"url": "https://arxiv.org/abs/quant-ph/0108004"
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