  Bit reset is a basic operation in irreversible computing. This costs work and
dissipates energy in the computer, creating a limit on speeds and energy
efficiency of future irreversible computers. It was recently shown in [Phys.
Rev. Lett. 127, 190602 (2021)] that for a finite-time reset protocol, the
additional work on top of the quasistatic protocol can always be minimized by
considering a two-level system, and then be lower bounded through a
thermodynamical speed limit. An important question is to understand under what
protocol parameters, including bit reset error and maximum energy shift, this
penalty decreases exponentially vs inverse linearly in the protocol time. Here
we provide several analytical results to address this question, as well as
numerical simulations of specific examples of protocols.
