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arXiv · 2401.11579

Elliptic Curves in Continuous-Variable Quantum Systems

Maxwell Aifer·Evan Sheldon
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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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Maxwell Aifer, Evan Sheldon. 2024-01-21. Elliptic Curves in Continuous-Variable Quantum Systems. https://arxiv.org/abs/2401.11579

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