dorsal/arxiv
View SchemaHitting time for quantum walks on the hypercube
| Authors | Hari Krovi, Todd A. Brun |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510136 |
| URL | https://arxiv.org/abs/quant-ph/0510136 |
| DOI | 10.1103/PhysRevA.73.032341 |
| Journal | Phys. Rev. A 73, 032341 (2006) |
Abstract
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as well as unitary evolution. We derive an expression for hitting time using superoperators, and numerically evaluate it for the discrete walk on the hypercube. The values found are compared to other analogues of hitting time suggested in earlier work. The dependence of hitting times on the type of unitary ``coin'' is examined, and we give an example of an initial state and coin which gives an infinite hitting time for a quantum walk. Such infinite hitting times require destructive interference, and are not observed classically. Finally, we look at distortions of the hypercube, and observe that a loss of symmetry in the hypercube increases the hitting time. Symmetry seems to play an important role in both dramatic speed-ups and slow-downs of quantum walks.
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"abstract": "Hitting times for discrete quantum walks on graphs give an average time\nbefore the walk reaches an ending condition. To be analogous to the hitting\ntime for a classical walk, the quantum hitting time must involve repeated\nmeasurements as well as unitary evolution. We derive an expression for hitting\ntime using superoperators, and numerically evaluate it for the discrete walk on\nthe hypercube. The values found are compared to other analogues of hitting time\nsuggested in earlier work. The dependence of hitting times on the type of\nunitary ``coin\u0027\u0027 is examined, and we give an example of an initial state and\ncoin which gives an infinite hitting time for a quantum walk. Such infinite\nhitting times require destructive interference, and are not observed\nclassically. Finally, we look at distortions of the hypercube, and observe that\na loss of symmetry in the hypercube increases the hitting time. Symmetry seems\nto play an important role in both dramatic speed-ups and slow-downs of quantum\nwalks.",
"arxiv_id": "quant-ph/0510136",
"authors": [
"Hari Krovi",
"Todd A. Brun"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.032341",
"journal_ref": "Phys. Rev. A 73, 032341 (2006)",
"title": "Hitting time for quantum walks on the hypercube",
"url": "https://arxiv.org/abs/quant-ph/0510136"
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