dorsal/arxiv
View SchemaGrover's algorithm on a Feynman computer
| Authors | Diego de Falco, Dario Tamascelli |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0610130 |
| URL | https://arxiv.org/abs/quant-ph/0610130 |
| DOI | 10.1088/0305-4470/37/3/025 |
| Journal | J. Phys. A: Math. Gen. 37 (2004) 909-930 |
Abstract
We present an implementation of Grover's algorithm in the framework of Feynman's cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover's algorithm to be performed using a single, time-independent Hamiltonian. We examine issues of locality and resource usage in implementing such a Hamiltonian. In the familiar language of Heisenberg spin-spin coupling, the clocking mechanism appears as an excitation of a basically linear chain of spins, with occasional controlled jumps that allow for motion on a planar graph: in this sense our model implements the idea of "timing" a quantum algorithm using a continuous-time random walk. In this context we examine some consequences of the entanglement between the states of the input/output register and the states of the quantum clock.
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"abstract": "We present an implementation of Grover\u0027s algorithm in the framework of\nFeynman\u0027s cursor model of a quantum computer. The cursor degrees of freedom act\nas a quantum clocking mechanism, and allow Grover\u0027s algorithm to be performed\nusing a single, time-independent Hamiltonian. We examine issues of locality and\nresource usage in implementing such a Hamiltonian. In the familiar language of\nHeisenberg spin-spin coupling, the clocking mechanism appears as an excitation\nof a basically linear chain of spins, with occasional controlled jumps that\nallow for motion on a planar graph: in this sense our model implements the idea\nof \"timing\" a quantum algorithm using a continuous-time random walk. In this\ncontext we examine some consequences of the entanglement between the states of\nthe input/output register and the states of the quantum clock.",
"arxiv_id": "quant-ph/0610130",
"authors": [
"Diego de Falco",
"Dario Tamascelli"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/37/3/025",
"journal_ref": "J. Phys. A: Math. Gen. 37 (2004) 909-930",
"title": "Grover\u0027s algorithm on a Feynman computer",
"url": "https://arxiv.org/abs/quant-ph/0610130"
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