  Atomic-scale logic and the minimization of heating (dissipation) are both
very high on the agenda for future computation hardware. An approach to achieve
these would be to replace networks of transistors directly by classical
reversible logic gates built from the coherent dynamics of a few interacting
atoms. As superpositions are unnecessary before and after each such gate
(inputs and outputs are bits), the dephasing time only needs to exceed a single
gate operation time, while fault tolerance should be achieved with low
overhead, by classical coding. Such gates could thus be a spin-off of quantum
technology much before full-scale quantum computation. Thus motivated, we
propose methods to realize the 3-bit Toffoli and Fredkin gates universal for
classical reversible logic using a single time-independent 3-qubit Hamiltonian
with realistic nearest neighbour two-body interactions. We also exemplify how
these gates can be composed to make a larger circuit. We show that trapped ions
may soon be scalable simulators for such architectures, and investigate the
prospects with dopants in silicon.
