# The Dirac equation as a quantum walk: higher dimensions, observational convergence

@article{Arrighi2014TheDE, title={The Dirac equation as a quantum walk: higher dimensions, observational convergence}, author={Pablo Arrighi and M. Forets and Vincent Nesme}, journal={Journal of Physics A}, year={2014}, volume={47}, pages={465302} }

The Dirac equation can be modelled as a quantum walk (QW), whose main features are being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a lattice); homogeneous (i.e. translation-invariant and time-independent) and causal (i.e. information propagates at a bounded speed, in a strict sense). This link, which was proposed already by Succi and Benzi, Bialynicki-Birula and Meyer, is shown to hold for Bargmann–Wigner equations and symmetric hyperbolic…

## 66 Citations

Quantum field as a quantum cellular automaton: The Dirac free evolution in one dimension

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Quantum walking in curved spacetime: discrete metric

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- 2017

A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some…

Quantum walking in curved spacetime

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- 2016

The continuum limit of a wide class of QWs is studied and it is shown that it leads to an entire class of PDEs, encompassing the Hamiltonian form of the massive Dirac equation in ($$1+1$$1-1) curved spacetime.

Weyl, Dirac and Maxwell Quantum Cellular Automata

- Physics
- 2015

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the…

Quantum walks, limits and transport equations

- MathematicsArXiv
- 2021

Plastic QWs are those ones admitting both continuous time-discrete space and continuous spacetime time limit, and it is shown that such QW-based quantum simulators can be used to quantum simulate a large class of physical phenomena described by transport equations.

Quantum Walks, Weyl Equation and the Lorentz Group

- Mathematics, Physics
- 2017

Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the…

Discrete spacetime, quantum walks, and relativistic wave equations

- Physics
- 2018

It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper we define the 3D walk as a product of…

Discrete-time quantum walks as fermions of lattice gauge theory

- PhysicsPhysical Review A
- 2019

It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus…

Path-sum solution of the Weyl quantum walk in 3 + 1 dimensions

- MathematicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group , which in an…

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