Computing Naturally in the Billiard Ball Model

TL;DR

This paper explores a mirrorless approach to the Billiard Ball Model, proposing new gates that reduce the need for fixed reflectors, aiming for more physically realistic collision-based computing.

Contribution

It introduces the m-counting gate, enabling certain circuits to be realized with fewer mirrors in the BBM, advancing the physical plausibility of collision-based computing.

Findings

Proposed the m-counting gate for mirror reduction.

Demonstrated circuits with fewer fixed mirrors.

Enhanced physical realism of the BBM.

Abstract

Fredkin's Billiard Ball Model (BBM) is considered one of the fundamental models of collision-based computing, and it is essentially based on elastic collisions of mobile billiard balls. Moreover, fixed mirrors or reflectors are brought into the model to deflect balls to complete the computation. However, the use of fixed mirrors is "physically unrealistic" and makes the BBM not perfectly momentum conserving from a physical point of view, and it imposes an external architecture onto the computing substrate which is not consistent with the concept of "architectureless" in collision-based computing. In our initial attempt to reduce mirrors in the BBM, we present a class of gates: the m-counting gate, and show that certain circuits can be realized with few mirrors using this gate. We envisage that our findings can be useful in future research of collision-based computing in novel chemical and optical computing substrates.