We consider the technologically relevant costs of operating a reliable bit
that can be erased rapidly. We find that both erasing and reliability times are
non-monotonic in the underlying friction, leading to a trade-off between
erasing speed and bit reliability. Fast erasure is possible at the expense of
low reliability at moderate friction, and high reliability comes at the expense
of slow erasure in the underdamped and overdamped limits. Within a given class
of bit parameters and control strategies, we define "optimal" designs of bits
that meet the desired reliability and erasing time requirements with the lowest
operational work cost. We find that optimal designs always saturate the bound
on the erasing time requirement, but can exceed the required reliability time
if critically damped. The non-trivial geometry of the reliability and erasing
time-scales allows us to exclude large regions of parameter space as
sub-optimal. We find that optimal designs are either critically damped or close
to critical damping under the erasing procedure.