Analysis of the shortest vector problems with the quantum annealing to search the excited states

TL;DR

This paper explores using quantum annealing to find excited states for solving the shortest vector problem, which is crucial for lattice-based cryptography, demonstrating higher solution probabilities than ground-state searches.

Contribution

It introduces a novel excited-state search method in quantum annealing to improve solving the shortest vector problem, addressing limitations of ground-state approaches.

Findings

Excited-state search yields higher solution probability than ground-state search.

Numerical simulations support the effectiveness of the excited-state approach.

Potential implications for post-quantum cryptography.

Abstract

The shortest vector problem (SVP) is one of the lattice problems and is mathematical basis for the lattice-based cryptography, which is expected to be post-quantum cryptography. The SVP can be mapped onto the Ising problem, which in principle can be solved by quantum annealing (QA). However, one issue in solving the SVP using QA is that the solution of the SVP corresponds to the first excited state of the problem Hamiltonian. Therefore, QA, which searches for ground states, cannot provide a solution with high probability. In this paper, we propose to adopt an excited-state search of the QA to solve the shortest vector problem. We numerically show that the excited-state search provides a solution with a higher probability than the ground-state search.