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This study uses optimal transport to design low-dissipation logic gates for energy-efficient computing. It reveals fundamental energy-speed-accuracy tradeoffs, showing faster, accurate operations require more energy.

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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.