Quantum Vertex Model for Reversible Classical Computing

TL;DR

This paper introduces a planar vertex model that encodes reversible classical computation without thermodynamic phase transitions, enabling new approaches to solving computational problems via thermal annealing and quantum annealing.

Contribution

It presents a novel mapping of reversible classical computation onto a vertex model that avoids phase transitions, facilitating more efficient problem-solving methods.

Findings

The vertex model encodes computation in its ground state.

Thermal annealing can solve problems encoded in the model.

Mapping to D-Wave's architecture enables quantum annealing approaches.

Abstract

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without 'learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.