  The potential energy profile of a binary switch is a symmetric double well.
Switching between the wells without energy dissipation requires time-modulating
the potential barrier separating them and tilting the profile towards the
desired well at the precise juncture when the barrier disappears. This demands
perfect timing synchronization and is therefore fault-intolerant, even in the
absence of noise. A fault-tolerant strategy that requires no time modulation of
the barrier (and hence no timing synchronization) switches by tilting the
profile by an amount at least equal to the barrier height and dissipates at
least that amount of energy. Here, we present a third strategy that requires a
time modulated barrier but no timing synchronization. It is therefore
fault-tolerant in the absence of thermal noise and yet it dissipates
arbitrarily small energy since an arbitrarily small tilt is required for slow
and adiabatic switching. This case is exemplified with stress induced switching
of a shape-anisotropic single-domain nanomagnet dipole coupled to a neighbor.
We also show by examining various energy profiles and the corresponding
probability distributions that when thermal noise is present, the minimum
energy dissipated to switch in this scheme is 2kTln(1/p) [p = switching error
probability].
