Join gate with memory in token-conserving Brownian circuits and the thermodynamic cost

TL;DR

This paper proposes a quantum dot-based implementation of a conservative join in Brownian circuits, analyzing its thermodynamic cost and particle emission bounds using stochastic thermodynamics and speed limit relations.

Contribution

It introduces a theoretical model of a quantum dot circuit with internal memory for Brownian computation, and analyzes its thermodynamic and dynamical bounds.

Findings

The thermodynamic cost is bounded by work for resets minus entropy reduction.

The number of emitted particles is tightly bounded by entropy production and activity rates.

A quantum dot implementation of CJoin with internal memory is proposed.

Abstract

The token-based Brownian circuit harnesses the Brownian motion of particles for computation. The conservative join (CJoin) is a circuit element that synchronizes two Brownian particles, and its realization using repelling particles, such as magnetic skyrmions or electrons, is key to building the Brownian circuit. Here, a theoretical implementation of the CJoin using a simple quantum dot circuit is proposed, incorporating an internal state-a double quantum dot that functions as a one-bit memory, storing the direction of two-particle transfer. A periodic reset protocol is introduced, allowing the CJoin to emit particles in a specific direction. The stochastic thermodynamics under periodic resets identifies the thermodynamic cost as the work done for resets minus the entropy reduction due to resets, with its lower bound remaining within a few multiples of $k_{\rm B} T$ at temperature $T$. Applying the speed limit relation to a subsystem in bipartite dynamics, the number of emitted particles is shown to be relatively tightly bounded from above by an expression involving the subsystem's irreversible entropy production rate and dynamical activity rate.