Minimally dissipative multi-bit logical operations

TL;DR

This paper introduces a novel optimal transport framework for designing multi-bit logical operations that approach thermodynamic limits, revealing fundamental energy-speed-accuracy trade-offs and practical algorithms for low-dissipation computing.

Contribution

It extends optimal transport methods to multi-bit logic gates, providing a principled approach for energy-efficient computation beyond classical limits.

Findings

Faster, more accurate operations dissipate more energy.

Landauer limits are not trivially overcome in higher dimensions.

Proposed algorithms achieve near-optimal dissipation in realistic setups.

Abstract

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 multi-bit 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 trade-offs 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 set-ups. The framework bridges fundamental thermodynamic limits with scalable computational design for energy-efficient information processing.