The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer

Details The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer

1999-03-20

arxiv.org/abs/quant-ph/9903071v1

Physics

Quantum Physics

16 pages, 3 figures, LaTeX2e, to appear in Proceedings of the 1st NASA International Conference on Quantum Computing and Quant

Scientific paper

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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