# Photonic quantum walks with four-dimensional coins

@article{Lorz2019PhotonicQW, title={Photonic quantum walks with four-dimensional coins}, author={Lennart Lorz and Evan Meyer-Scott and Thomas Nitsche and V{\'a}clav Poto{\vc}ek and Aur'el G'abris and Sonja Barkhofen and Igor Jex and Christine Silberhorn}, journal={Physical Review Research}, year={2019} }

The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators have successfully been used for defining dynamics on complex graphs, higher dimensional coins are necessary to unleash the full potential of discrete-time quantum walks. In this work we present an experimental realisation of a discrete-time quantum walk on a line graph, that instead of a two… Expand

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#### References

SHOWING 1-10 OF 173 REFERENCES

Two-dimensional quantum walk under artificial magnetic field

- Physics
- 2015

We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an… Expand

A 2D Quantum Walk Simulation of Two-Particle Dynamics

- Physics, Medicine
- Science
- 2012

An optical system is demonstrated that can simulate quantum walks over a two-dimensional system, thereby providing the capability of describing much more complex processes and illustrating the potential of quantum walks as a route for simulating and understanding complex quantum systems. Expand

Quantum walks and wavepacket dynamics on a lattice with twisted photons

- Physics, Medicine
- Science Advances
- 2015

This work reports the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons, and introduces a novel versatile photonic platform for quantum simulations. Expand

Localization of two-dimensional quantum walks

- Physics
- 2004

The Grover walk, which is related to Grover's search algorithm on a quantum computer, is one of the typical discrete time quantum walks. However, a localization of the two-dimensional Grover walk… Expand

Quantum Walk in Position Space with Single Optically Trapped Atoms

- Physics, Medicine
- Science
- 2009

In this experiment, a quantum walk on the line with single neutral atoms is implemented by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice and its spatial coherence is demonstrated. Expand

Quantum walk with a four-dimensional coin

- Physics
- 2011

We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our… Expand

Exploring topological phases with quantum walks

- Physics
- 2010

The quantum walk was originally proposed as a quantum-mechanical analog of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that… Expand

Experimental quantum-walk revival with a time-dependent coin.

- Physics, Medicine
- Physical review letters
- 2015

With this technique, an experimental single-photon one-dimensional quantum walk with a linearly ramped time-dependent coin flip operation is realized and two periodic revivals of the walker distribution are demonstrated. Expand

Scattering theory of topological phases in discrete-time quantum walks

- Physics
- 2014

One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach… Expand

Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin.

- Mathematics, Medicine
- Physical review letters
- 2011

A formal proof of this correspondence is presented and the behavior of the coin-position entanglement as well as the x-y spatialEntanglement in the scheme with respect to the Grover one is analyzed. Expand