Analysis of the shortest vector problems with the quantum annealing to search the excited states
arXiv:2209.03721 · doi:10.35848/1347-4065/acba21
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.
References in corpus (4)
- Mathematical Foundation of Quantum Annealing
- Quantum annealing with capacitive-shunted flux qubits
- Preparing ground states of the XXZ model using the quantum annealing with inductively coupled superconducting flux qubits
- Experimental Demonstrations of Native Implementation of Boolean Logic Hamiltonian in a Superconducting Quantum Annealer