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Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardized for the postquantum era, and a significant proportion of these rely on the hardness of problems like the shortest-vector problem to a quantum adversary. In this paper we describe two variants of a quantum Ising algorithm to solve this problem. One variant is spatially efficient, requiring only O(N log 2 N ) qubits, where N is the lattice dimension, while the other variant is more robust to noise. Analysis of the algorithms' performance on a quantum annealer and in numerical simulations shows that the more qubit-efficient variant will outperform in the long run, while the other variant is more suitable for near-term implementation.

Since quantum computers are known to break the vast majority of currently-used cryptographic protocols, a variety of new protocols are being developed that are conjectured, but not proven to be safe against quantum attacks. Among the most promising is lattice-based cryptography, where security relies upon problems like the shortest vector problem. We analyse the potential of adiabatic quantum computation for attacks on lattice-based cryptography, and give numerical evidence that even outside the adiabatic regime such methods can facilitate the solution of the shortest vector and similar problems. I. B. Quantum Computing in Lattice-Based CryptographySo far, most efforts towards quantum attacks on cryptographic protocols have concentrated on gate model quantum algorithms and their applications as subrou-arXiv:1910.10462v2 [quant-ph]

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