Elliptic Curves in Continuous-Variable Quantum Systems

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2401.11579.pdf (551.83 KB)

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https://arxiv.org/abs/2401.11579

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https://doi.org/10.48550/arXiv.2401.11579
 http://hdl.handle.net/11603/31701

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UMBC Physics Department
UMBC Student Collection

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Author/Creator ORCID

https://orcid.org/0000-0003-1936-0877

Date

2024-01-21

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journal articles
preprints
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CC BY 4.0 DEED Attribution 4.0 International

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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.