Minimally dissipative multibit logical operations

Modern computing architectures are vastly more energy dissipative than fundamental thermodynamic limits suggest, motivating the search for principled approaches to low-dissipation logical operations. We formulate multibit logical gates (bit erasure, nand) as optimal transport problems, extending beyond classical one-dimensional bit erasure to scenarios where existing methods fail. Using entropically regularized unbalanced optimal transport, we derive tractable solutions and establish general energy-speed-accuracy tradeoffs that demonstrate that faster, more accurate operations necessarily dissipate more energy. Furthermore, we demonstrate that the Landauer limits cannot be trivially overcome in higher-dimensional geometries. We develop practical algorithms combining optimal transport with generative modeling techniques to construct dynamical controllers that follow Wasserstein geodesics. These protocols achieve near-optimal dissipation and can, in principle, be implemented in realistic experimentally setups. The framework bridges fundamental thermodynamic limits with scalable computational design for energy-efficient information processing.