Measurement Based Quantum Computation on Fractal Lattices

TL;DR

This paper investigates the potential of fractal lattices as resources for measurement-based quantum computation, analyzing how their topological properties influence their computational capabilities.

Contribution

It extends the analogy between one-way quantum computation and thermodynamics to fractal lattices, identifying topological factors affecting their universality.

Findings

Fractal lattices with dimension > 1 can serve as good quantum computational resources.

Some fractal lattices with dimension > 1 are not suitable for quantum computation.

Topological features like ramification and connectivity determine computational usefulness.

Abstract

In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.