Minimally dissipative multibit logical operations

Area of Science:

• Physics and Computer Science
• Information Theory
• Thermodynamics

Background:

• Modern computers dissipate significant energy, exceeding theoretical thermodynamic limits.
• There's a need for principled methods to achieve low-dissipation logical operations.

Purpose of the Study:

• To formulate multibit logical gates as optimal transport problems.
• To derive tractable solutions for low-dissipation operations beyond classical limits.
• To establish general energy-speed-accuracy tradeoffs.

Main Methods:

• Formulating multibit logical gates (bit erasure, NAND) as optimal transport problems.
• Utilizing entropically regularized unbalanced optimal transport for tractable solutions.
• Developing algorithms combining optimal transport with generative modeling to construct dynamical controllers.

Main Results:

• Established general energy-speed-accuracy tradeoffs: faster, more accurate operations dissipate more energy.
• Demonstrated that Landauer limits cannot be trivially overcome in higher-dimensional geometries.
• Developed practical protocols achieving near-optimal dissipation for energy-efficient information processing.

Conclusions:

• The developed framework bridges fundamental thermodynamic limits with scalable computational design.
• The proposed protocols offer a path towards practical, energy-efficient computing implementations.
• Optimal transport provides a powerful tool for designing low-dissipation logical operations.