Gigahertz Sub-Landauer Momentum Computing

The paper’s idealized protocol states that switching to a harmonic computation potential Vcomp(x)=kx^2/2, isolating the system, and waiting a half period τ=π√(m/k) yields x(τ)=−x(0), flipping the memory bit, and that if Vstore is even the net work is zero because the switching work at t=0 cancels that at t=τ (only switching events contribute work) . The candidate solution reproduces exactly this harmonic-oscillator derivation, including τ=π√(m/k), x(τ)=−x0, v(τ)=−v0, and trajectory-level work cancellation under even Vstore. Both rely on the same assumptions (perfect isolation, instantaneous switching, even Vstore). The paper also emphasizes that realistic devices deviate from perfect harmonicity and require period matching, leading to sub‑Landauer but nonzero costs in practice, which is outside the model’s idealized scope .