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A Subexponential Time Algorithm for the Dihedral Hidden Subgroup Problem with Polynomial Space

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arxiv quant-ph/0406151 v1 pith:U4U5YCT6 submitted 2004-06-21 quant-ph

Oded Regev This is my paper · ORCID
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keywords algorithmspacesubexponentialtimedihedralhiddenpolynomialproblem
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In a recent paper, Kuperberg described the first subexponential time algorithm for solving the dihedral hidden subgroup problem. The space requirement of his algorithm is super-polynomial. We describe a modified algorithm whose running time is still subexponential and whose space requirement is only polynomial.

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    A new construction shows exact in-place addition of two n-bit quantum registers can be done in O(log^2 n) depth with O(n log n) classical reversible gates and zero ancilla qubits.

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