Making Classical Ground State Spin Computing Fault-Tolerant

TL;DR

This paper demonstrates how classical ground state spin computing can be made fault-tolerant at low temperatures by leveraging fault-tolerant classical computing techniques, linking physical models to computational complexity.

Contribution

It introduces a method to achieve effective error correction in classical ground state spin systems at finite temperatures, connecting physical models to complexity theory.

Findings

Fault-tolerant classical spin systems are achievable below a critical temperature.

The model's partition function maps to probabilistic classical circuits.

A specific problem in finite temperature classical spin systems is Merlin-Arthur complete.

Abstract

We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error free manner when working at non-zero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.