Elliptic Curves in Continuous-Variable Quantum Systems

• URL: http://arxiv.org/abs/2401.11579v2
• Date: Tue, 23 Jan 2024 05:23:01 GMT
• Title: Elliptic Curves in Continuous-Variable Quantum Systems
• Authors: Maxwell Aifer and Evan Sheldon
• Abstract summary: We give an algorithm for computing elliptic curve group addition using a single continuous-variable mode. This result could lead to improvements in the efficiency of elliptic curve discrete logarithms using a quantum device.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute these logarithms using a quantum computer, assuming that the group addition operation can be computed efficiently on a quantum device. Currently, however, thousands of logical qubits are required for elliptic curve group addition, putting this application out of reach for near-term quantum hardware. Here we give an algorithm for computing elliptic curve group addition using a single continuous-variable mode, based on weak measurements of a system with a cubic potential energy. This result could lead to improvements in the efficiency of elliptic curve discrete logarithms using a quantum device.

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