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

• URL: http://arxiv.org/abs/2006.14057v7
• Date: Thu, 4 Mar 2021 11:18:20 GMT
• Title: Two quantum Ising algorithms for the Shortest Vector Problem: one for now and one for later
• Authors: David Joseph, Adam Callison, Cong Ling, Florian Mintert
• Abstract summary: We describe two variants of a quantum Ising algorithm to solve the Shortest Vector Problem. One variant is spatially efficient, requiring only O(NlogN) 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 show that the more qubit-efficient variant will outperform in the long run.
• Score: 19.4417702222583
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardised for the post-quantum 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(NlogN) 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 show that the more qubit-efficient variant will outperform in the long run, while the other variant is more suitable for near-term implementation.

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