Non-Markovian Momentum Computing: Universal and Efficient

TL;DR

This paper introduces non-Markovian momentum computing using continuous-time hidden Markov chains, enabling the modeling of complex, thermodynamically-efficient computations like bit flips and Fredkin gates that are impossible with traditional rate equations.

Contribution

It extends the modeling framework to include non-Markovian dynamics, demonstrating thermodynamically-costless computation of universal logic gates.

Findings

Counterexample of thermodynamically-costless bit flip

Design of a costless Fredkin gate

Necessity of non-Markovian models for physical computation

Abstract

All computation is physically embedded. Reflecting this, a growing body of results embraces rate equations as the underlying mechanics of thermodynamic computation and biological information processing. Strictly applying the implied continuous-time Markov chains, however, excludes a universe of natural computing. We show that expanding the toolset to continuous-time hidden Markov chains substantially removes the constraints. The general point is made concrete by our analyzing two eminently-useful computations that are impossible to describe with a set of rate equations over the memory states. We design and analyze a thermodynamically-costless bit flip, providing a first counterexample to rate-equation modeling. We generalize this to a costless Fredkin gate---a key operation in reversible computing that is computation universal. Going beyond rate-equation dynamics is not only possible, but necessary if stochastic thermodynamics is to become part of the paradigm for physical information processing.