# The Dirac equation as a quantum walk over the honeycomb and triangular lattices

arXiv: https://arxiv.org/abs/1803.01015 · HTML: https://mlsanity.com/paper/1803.01015/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2018.

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

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

## Abstract (arXiv)

A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in (2+1)--dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice. The former is of interest in the study of graphene-like materials. The latter, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.