Non-Markovian Momentum Computing: Universal and Efficient

The paper constructs a zero-work bit flip by quenching a double-well to a harmonic potential for half a period so that (x,p) ↦ (−x,−p), and argues zero work from evenness of the potentials; it then implements a zero-work Fredkin gate by using normal modes y'=(y−z)/√2 and z'=(y+z)/√2 with frequencies ω and 2ω over a fixed interval, producing a swap when x≥0 and identity when x<0, with work canceling by symmetry; these are exactly the mechanisms the model presents, with slightly more explicit bookkeeping of the two quenches and the no-crossing assumption for x(t) (both noted or implicit in the paper). See the bit-flip dynamics and zero-work argument , the Fredkin construction in normal modes and the piecewise potential (including the swap derivation) , and the work accounting and barrier-crossing caveat .