dorsal/arxiv
View SchemaThe Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer
| Authors | Michele Mosca, Artur Ekert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9903071 |
| URL | https://arxiv.org/abs/quant-ph/9903071 |
Abstract
A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and `hidden' or `unknown' subgroups of Abelian groups. It is already known how to phrase the first four problems as the estimation of eigenvalues of certain unitary operators. Here we show how the solution to the more general Abelian `hidden subgroup problem' can also be described and analysed as such. We then point out how certain instances of these problems can be solved with only one control qubit, or `flying qubits', instead of entire registers of control qubits.
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"abstract": "A quantum computer can efficiently find the order of an element in a group,\nfactors of composite integers, discrete logarithms, stabilisers in Abelian\ngroups, and `hidden\u0027 or `unknown\u0027 subgroups of Abelian groups. It is already\nknown how to phrase the first four problems as the estimation of eigenvalues of\ncertain unitary operators. Here we show how the solution to the more general\nAbelian `hidden subgroup problem\u0027 can also be described and analysed as such.\nWe then point out how certain instances of these problems can be solved with\nonly one control qubit, or `flying qubits\u0027, instead of entire registers of\ncontrol qubits.",
"arxiv_id": "quant-ph/9903071",
"authors": [
"Michele Mosca",
"Artur Ekert"
],
"categories": [
"quant-ph"
],
"title": "The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer",
"url": "https://arxiv.org/abs/quant-ph/9903071"
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