dorsal/arxiv
View SchemaQuantum algorithm for finding periodicities in the spectrum of a black-box Hamiltonian or unitary transformation
| Authors | Dominik Janzing, Thomas Beth |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108053 |
| URL | https://arxiv.org/abs/quant-ph/0108053 |
| Journal | Quant. Inf. & Comp. 2 (3):192-197, 2002 |
Abstract
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure eigenvalues of U\otimes U^\dagger even in this case. Running the algorithm several times allows therefore to estimate the autocorrelation function of the density of eigenstates of U. This can be applied to find periodicities in the energy spectrum of a quantum system with unknown Hamiltonian if it can be coupled to a quantum computer.
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"abstract": "Estimating the eigenvalues of a unitary transformation U by standard phase\nestimation requires the implementation of controlled-U-gates which are not\navailable if U is only given as a black box.\n We show that a simple trick allows to measure eigenvalues of U\\otimes\nU^\\dagger even in this case. Running the algorithm several times allows\ntherefore to estimate the autocorrelation function of the density of\neigenstates of U. This can be applied to find periodicities in the energy\nspectrum of a quantum system with unknown Hamiltonian if it can be coupled to a\nquantum computer.",
"arxiv_id": "quant-ph/0108053",
"authors": [
"Dominik Janzing",
"Thomas Beth"
],
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"quant-ph"
],
"journal_ref": "Quant. Inf. \u0026 Comp. 2 (3):192-197, 2002",
"title": "Quantum algorithm for finding periodicities in the spectrum of a black-box Hamiltonian or unitary transformation",
"url": "https://arxiv.org/abs/quant-ph/0108053"
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