Assessing the security of lattice-based cryptography against near-term quantum attacks is crucial to the development of postquantum cryptography. Existing quantum algorithms for the shortest-vector problem (SVP) typically reformulate the problem as a search for the first excited state of a single fully-connected quantum Ising model. However, as the quantum system scales with the problem size, determining the first excited state becomes intractable due to the exponentially increased complexity for large-scale SVP instances. In this paper we propose a variational quantum Korkin-Zolotarev (VQKZ) algorithm that substantially reduces the qubit requirement for solving the SVP. Specifically, by decomposing the original SVP into a series of subproblems on sublattices, the VQKZ algorithm can significantly expand the scale of problems solvable by near-term quantum devices compared with existing methods. Our numerical simulations demonstrate that for solving $q$-ary lattice-based SVP problems, the VQKZ algorithm outperforms existing methods in terms of both the solution vector length and the number of qubits required.

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• Quantum algorithms
• Quantum algorithms & computation