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Quantum computers are expected to break today's public key cryptographywithin a few decades. New cryptosystems are being designed and standardised forthe post-quantum era, and a significant proportion of these rely on thehardness of problems like the Shortest Vector Problem to a quantum adversary.In this paper we describe two variants of a quantum Ising algorithm to solvethis problem. One variant is spatially efficient, requiring only O(NlogN)qubits where N is the lattice dimension, while the other variant is more robustto noise. Analysis of the algorithms' performance on a quantum annealer and innumerical simulations show that the more qubit-efficient variant willoutperform in the long run, while the other variant is more suitable fornear-term implementation.

Two quantum Ising algorithms for the Shortest Vector Problem: one for now and one for later