Quantum Computation and Lattice Problems

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. Key words. lattices, quantum computation, shortest vector problem, hidden subgroup problem AMS subject classifications. 81P68, 68Q25, 68W25, 11H06

• Type: Conference
• Year: 2002
• Where: FOCS
• Authors: Oded Regev
• Keywords: FOCS 2002, Hidden Subgroup Problem, Quantum Computation, Shortest Vector Problem, Theoretical Computer Science