ABSTRACT
In the last chapter, we saw that it is theoretically possible to switch a logically reversible gate without dissipating any energy at all (recall the proof of the Landauer-Shannon result). If there is no dissipation, then no information is ever being discarded; therefore, if we know the state of the system completely at any instant of time, we should be able to infer its state at any previous instant. This is consistent with the equations of quantum mechanics (e.g., the Schro¨dinger equation, or the Pauli equation) which are reversible in time. This property of quantum mechanical systems, known as “time reversal symmetry”, guarantees that if we know the state of a system at a time t0, we can tell what the state was at any time t < t0. Because of this fundamental connection between physical reversibility, logical reversibility, and the equations of quantum mechanics, we would expect logically reversible gates to behave as non-classical (quantum mechanical) computing machinery.∗ This will bring us to the topic of quantum computing and quantum logic gates, but before we get there, let us explore reversible logic in a little more detail.
