# The Grover search as a naturally occurring phenomenon

arXiv: https://arxiv.org/abs/1908.11213 · HTML: https://mlsanity.com/paper/1908.11213/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2019.

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

- [Quantum Perceptron Revisited: Computational-Statistical Tradeoffs](https://mlsanity.com/paper/2106.02496/) (2021)

## Abstract (arXiv)

We provide first evidence that under certain conditions, 1/2-spin fermions may naturally behave like a Grover search, looking for topological defects in a material. The theoretical framework is that of discrete-time quantum walks (QW), i.e. local unitary matrices that drive the evolution of a single particle on the lattice. Some QW are well-known to recover the (2+1)--dimensional Dirac equation in continuum limit, i.e. the free propagation of the 1/2-spin fermion. We study two such Dirac QW, one on the square grid and the other on a triangular grid reminiscent of graphene-like materials. The numerical simulations show that the walker localises around the defects in O(√N) steps with probability O(1/logN), in line with previous QW search on the grid. The main advantage brought by those of this paper is that they could be implemented as `naturally occurring' freely propagating particles over a surface featuring topological---without the need for a specific oracle step. From a quantum computing perspective, however, this hints at novel applications of QW search : instead of using them to look for `good' solutions within the configuration space of a problem, we could use them to look for topological properties of the entire configuration space.