Quantum Computation and Lattice Problems

We present the first explicit connection between quantum computation and lattice problems. Namely, we show 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. Moreover, we solve the hidden subgroup problem on the dihedral group by using an average case subset sum routine. By combining the two results, we get a quantum reduction from /spl Theta//spl tilde/(n/sup 2. 5/)-unique-SVP to the average case subset sum problem. This is a better connection than the known classical results.

Authors

• Oded Regev 0001

Keywords

• Quantum computing
• Lattices
• Vectors
• Cryptography
• Polynomials
• Physics computing
• Pervasive computing
• Sampling methods
• Computational modeling
• Application software
• Lattice Problems
• Quantum Lattice
• Average Sum
• Hidden Problem
• Classification Algorithms
• Black Box
• Phase Difference
• Vector Of Length
• Regulon
• Abelian Group
• Orthonormal Basis
• Phase Sequence
• Elements In Order
• Point Problem
• Unique Problems
• Lattice Points
• Symmetric Group
• Unique Vector
• Quantum Algorithms
• Graph Isomorphism