# Dynamical Triangulation Induced by Quantum Walk

arXiv: https://arxiv.org/abs/1907.10717 · HTML: https://mlsanity.com/paper/1907.10717/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Geodesic Quantum Walks](https://mlsanity.com/paper/2202.10235/) (2022)

## Abstract (arXiv)

We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated 2-manifold. The triangulation is changed through Pachner moves, induced by the walker density itself, allowing the surface to transform into any topologically equivalent one. This model extends the quantum walk over triangular grid, introduced in a previous work, by one of the authors, whose space-time limit recovers the Dirac equation in (2+1)-dimensions. Numerical simulations show that the number of triangles and the local curvature grow as tα e-β t2, where α and β parametrize the way geometry changes upon the local density of the walker, and that, in the long run, flatness emerges. Finally, we also prove that the global behavior of the walker, remains the same under spacetime random fluctuations.