  We implement a thermal-fluctuation driven logical bit reset on a
superconducting flux logic cell. We show that the logical state of the system
can be continuously monitored with only a small perturbation to the thermally
activated dynamics at 500 mK. We use the trajectory information to derive a
single-shot estimate of the work performed on the system per logical cycle. We
acquire a sample of $10^5$ erasure trajectories per protocol, and show that the
work histograms agree with both microscopic theory and global fluctuation
theorems. The results demonstrate how to design and diagnose complex,
high-speed, and thermodynamically efficient computing using superconducting
technology.
