|
| related topics |
| {algorithm, log, probability} |
| {qubit, qubits, gate} |
| {group, space, representation} |
| {let, theorem, proof} |
| {operator, operators, space} |
| {equation, function, exp} |
|
The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum
Computer
Michele Mosca, Artur Ekert
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9903071
- categories:
- quant-ph
- comments:
- 16 pages, 3 figures, LaTeX2e, to appear in Proceedings of the 1st
NASA International Conference on Quantum Computing and Quantum Communication
(Springer-Verlag)
- arxiv_id:
- quant-ph/9903071
- created:
- 1999-03-20
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