dorsal/arxiv
View SchemaAn Analog Analogue of a Digital Quantum Computation
| Authors | Edward Farhi, Sam Gutmann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9612026 |
| URL | https://arxiv.org/abs/quant-ph/9612026 |
Abstract
We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >< w|$ where $| w>$ is an unknown (normalized) state. We show how to discover $| w >$ by adding a Hamiltonian (independent of $| w >$) and evolving for a time proportional to $N^{1/2}/E$. We show that this time is optimally short. This process is an analog analogue to Grover's algorithm, a computation on a conventional (!) quantum computer which locates a marked item from an unsorted list of N items in a number of steps proportional to $N^{1/2}$.
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"abstract": "We solve a problem, which while not fitting into the usual paradigm, can be\nviewed as a quantum computation. Suppose we are given a quantum system\ndescribed by an N dimensional Hilbert space with a Hamiltonian of the form $E\n|w \u003e\u003c w|$ where $| w\u003e$ is an unknown (normalized) state. We show how to\ndiscover $| w \u003e$ by adding a Hamiltonian (independent of $| w \u003e$) and evolving\nfor a time proportional to $N^{1/2}/E$. We show that this time is optimally\nshort. This process is an analog analogue to Grover\u0027s algorithm, a computation\non a conventional (!) quantum computer which locates a marked item from an\nunsorted list of N items in a number of steps proportional to $N^{1/2}$.",
"arxiv_id": "quant-ph/9612026",
"authors": [
"Edward Farhi",
"Sam Gutmann"
],
"categories": [
"quant-ph"
],
"title": "An Analog Analogue of a Digital Quantum Computation",
"url": "https://arxiv.org/abs/quant-ph/9612026"
},
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