  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.
