Quantum computation and lattice problems

Research output: Contribution to journalArticle

Abstract

We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is a solution to the unique shortest vector problem (SVP) under the assumption that there exists an algorithm that solves the hidden subgroup problem on the dihedral group by coset sampling. Additionally, we present an approach to solving the hidden subgroup problem on the dihedral group by using an average case subset sum routine.

Original languageEnglish (US)
Pages (from-to)738-760
Number of pages23
JournalSIAM Journal on Computing
Volume33
Issue number3
DOIs
StatePublished - 2004

Fingerprint

Quantum computers
Quantum Computation
Sampling
Dihedral group
Subgroup
Subset Sum
Coset

Keywords

  • Hidden subgroup problem
  • Lattices
  • Quantum computation
  • Shortest vector problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Quantum computation and lattice problems. / Regev, Oded.

In: SIAM Journal on Computing, Vol. 33, No. 3, 2004, p. 738-760.

Research output: Contribution to journalArticle

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