Variational quantum solutions to the Shortest Vector Problem

A fundamental computational problem is to find a shortest non-zero vector in Euclidean lattices, known as the Shortest Vector Problem (SVP). This believed be hard even on quantum computers and thus plays pivotal role post-quantum cryptography. In this work we explore how (efficiently) Noisy Intermediate Scale Quantum (NISQ) devices may used solve SVP. Specifically, map that of finding ground state suitable Hamiltonian. particular, (i) establish new bounds for lattice enumeration, allows us obtain (resp.~estimates) number qubits required per dimension any lattices (resp.~random q-ary lattices) SVP; (ii) exclude zero from optimization space by proposing (a) different classical optimisation loop or alternatively (b) mapping These improvements allow SVP up 28 emulation, significantly more than what was previously achieved, special cases. Finally, extrapolate size NISQ able instances are best algorithms with approximately $10^3$ noisy such can tackled.