Billiard balls and quantum computers.

 

A single billiard ball could simulate a universal Turing machine (UTM). That machine could simulate any other Turing machine. This is one of the most interesting things in the world. We think that. The billiard ball is the program. And the table is the platform. That drives the program. When we make input to that ball, it selects a certain route. That route can take our system to the right solutions. Or it can fail, and the system must retry that thing. Another way to think of the billiard ball as a computer is this. When the billiard ball spins anticlockwise, the value is zero. When it spins clockwise, the value is one. The change in the axle angle determines the empty spaces between one and zero. That is important. When. There are two ones or two zeros. One. After another. The big problem in the binary computer is this. The system must separate. When there. Are two ones. 

Or two zeros one after another. The other thing this kind of system must solve is. The system must determine if the electricity is cut. And separate that thing from the zeros. The answer is the base voltage. The system floats the bit. And if the voltage goes too low. Or below the minimum. That means the system thinks that electricity is cut. But if we want to make a system that uses two billiard balls. One color and two colors, the system can put them to travel through it. When the one-color ball spins or changes its angle. That is, a one-color ball spins. The value is zero. Or a two-color ball spins, which means the value is one. 

We must remember that simulations must not be possible to copy in the real world. But what if we can create things like quantum computers in 2D models? That means the qubit travels on a lattice. 

A graph representation of a Turing machine (left) and its billiard equivalent (right). (Miranda & Ramos, PNAS, 2026) (ScienceAlert, A Single Ball on a Billiard Table Can Theoretically Perform Any Computation)

Researchers created a mathematical 'billiard' – the word they use to describe their system – in which the ball's position can encode information. While. The carefully designed walls and their shape determine what happens to that information next.

ScienceAlert magazine. Describes this situation like this: As the ball travels from one part of the billiard to another, its trajectory advances the computation, just as a Turing machine works through its instructions one step at a time.

What if we replace billiard balls with atoms? 

“An AI-generated illustration depicting the Kondo effect. Conducting electrons in a metal are shown interacting with the spin of an embedded magnetic atom impurity. Credit: AI-generated artwork by Linqing Peng. A new computational approach uses the real electronic structure of materials to predict a classic quantum effect far more accurately than simplified models. Seven magnetic atoms embedded one at a time in copper have given physicists a new way to test whether computers can predict the behavior of real quantum materials without first reducing them to simplified models.” (ScitechDaily, Physicists Tackle a Classic Quantum Problem With a Powerful New Computational Method)

Billiards have been linked to computation before this new model. But those models needed additional complexity, such as multiple interacting balls, three-dimensional structures, or moving walls. Those walls are gates that control information. 

Researchers stripped all of that away. They created a 2D system. Their system needs just one particle moving in two dimensions between fixed walls.

We can think. Time arrow and computing. We. Can think about a situation. There, a billiard ball is a computer program. It travels past another billiard ball. Every. Standing ball in the line is one step of a mathematical formula. The system is solved. The system solves the mathematical formula step by step. After each step, it stores the answer into the mass memory. That. The system is based on the idea that mathematical formulas must be used in a certain order. The order of the calculations is always the same. 

In that scenario, each billiard ball is one step or stage of the mathematical formula. The idea is that. Every mathematical formula can be solved by using strict orders. The machine generates an answer by using mathematical orders. And that means the system can take every step backward directly when the machine is done. This makes the system more effective. Because. It must not make a complete calculation backward. If. It checks. Those steps that it takes one by one directly when it finishes. But in that case, the billiard ball must transfer information to the standing ball. That could be done. By. Putting a domino brick at a right angle between those balls. And when the billiard ball, or qubit. That travels past the standing ball. That domino brick acts as the gate. 

Maybe. Previously, we could not create a universal Turing machine using billiard balls. But what if we replace those balls with qubits? It can turn. The quantum systems. Into the next level. These systems can turn into universal computers. 

https://www.sciencealert.com/a-single-ball-on-a-billiard-table-can-theoretically-perform-any-computation

https://scitechdaily.com/physicists-tackle-a-classic-quantum-problem-with-a-powerful-new-computational-method/

https://en.wikipedia.org/wiki/Kondo_effect