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arXiv:quant-ph/0411037quant-ph

The Hidden Subgroup Problem - Review and Open Problems

Chris Lomont

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Abstract

An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it easier to absorb the background necessary to begin research on the Hidden Subgroup Problem. Proofs are provided which give very concrete algorithms and bounds for the finite abelian case with little outside references, and future directions are provided for the nonabelian case. This summary is current as of October 2004.

arXiv comments
A thorough introduction to the HSP, with detailed proofs for many results, and an overview of the research literature through 2004. This is designed to bring more people to bear on the problem. 83 pages
Journal reference
DOI
Subjects
quant-phQuantum Physics

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  1. OpenSSH now uses hybrid post-quantum streamlined NTRU Prime X25519 by default 1 comment

    • QC can only solve two problems more efficiently than classical (and this is proven very thoroughly): unstructured search and discrete log problem (well, more accurately, certain hidden subgroup problems). DLP covers factoring, hence RSA. Elliptic curve crypto is directly a…

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