dorsal/arxiv
View SchemaEfficient Preparation of Quantum States With Exponential Precision
| Authors | Peter Jaksch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512238 |
| URL | https://arxiv.org/abs/quant-ph/0512238 |
Abstract
It has been shown that, starting from the state |0>, in the general case, an arbitrary quantum state |\psi> cannot be prepared with exponential precision in polynomial time. However, we show that for the important special case when |\psi> represents discrete values of some real, continuous function \psi(x), efficient preparation is possible by applying the eigenvalue estimation algorithm to a Hamiltonian which has \psi(x) as an eigenstate. We construct the required Hamiltonian explicitly and present an iterative algorithm for removing unwanted superpositions from the output state in order to reach |\psi> within exponential accuracy. The method works under very general conditions and can be used to provide the quantum simulation algorithm with very accurate and general starting states.
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"abstract": "It has been shown that, starting from the state |0\u003e, in the general case, an\narbitrary quantum state |\\psi\u003e cannot be prepared with exponential precision in\npolynomial time. However, we show that for the important special case when\n|\\psi\u003e represents discrete values of some real, continuous function \\psi(x),\nefficient preparation is possible by applying the eigenvalue estimation\nalgorithm to a Hamiltonian which has \\psi(x) as an eigenstate. We construct the\nrequired Hamiltonian explicitly and present an iterative algorithm for removing\nunwanted superpositions from the output state in order to reach |\\psi\u003e within\nexponential accuracy. The method works under very general conditions and can be\nused to provide the quantum simulation algorithm with very accurate and general\nstarting states.",
"arxiv_id": "quant-ph/0512238",
"authors": [
"Peter Jaksch"
],
"categories": [
"quant-ph"
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"title": "Efficient Preparation of Quantum States With Exponential Precision",
"url": "https://arxiv.org/abs/quant-ph/0512238"
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