Quantum computation and lattice problems

Research output: Contribution to journalArticlepeer-review

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

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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