# A staggered gauge-invariant quantum cellular automaton for both the Kogut-Susskind Schwinger model and the Dirac equation

@inproceedings{Sellapillay2021ASG, title={A staggered gauge-invariant quantum cellular automaton for both the Kogut-Susskind Schwinger model and the Dirac equation}, author={Kevissen Sellapillay and Pablo Arrighi and Giuseppe Di Molfetta}, year={2021} }

We build a quantum cellular automaton (QCA) which coincides with 1+1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut-Susskind staggered version of 1+1 QED. We also show…

## One Citation

### 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.

## References

SHOWING 1-10 OF 37 REFERENCES

### Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

- PhysicsNature
- 2016

This work reports the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer and explores the Schwinger mechanism of particle–antiparticle generation by monitoring the mass production and the vacuum persistence amplitude.

### Lattice Schwinger model: Confinement, anomalies, chiral fermions, and all that

- Physics
- 2000

In order to better understand what to expect from numerical CORE computations for two-dimensional massless QED (the Schwinger model) the authors wish to obtain some analytic control over the approach…

### Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks

- PhysicsPhysical Review A
- 2018

Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions,…

### A quantum cellular automaton for one-dimensional QED

- PhysicsQuantum Inf. Process.
- 2020

A discrete spacetime formulation of quantum electrodynamics in one dimension in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates, is proposed, encompassing the notions of continuum limit and renormalization and providing a quantum simulation algorithm for the dynamics.

### Quantum cellular automata and quantum field theory in two spatial dimensions

- Physics
- 2020

Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural…

### 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…

### Scattering and Perturbation Theory for Discrete-Time Dynamics.

- MathematicsPhysical review letters
- 2021

A systematic treatment of scattering processes for quantum systems whose time evolution is discrete, and a rigorous assessment of the comparison for the case of bounded free Hamiltonian, as in a lattice theory with a bounded number of particles.

### A quantum walk with both a continuous-time limit and a continuous-spacetime limit

- PhysicsQuantum Inf. Process.
- 2020

This work provides a first example of a quantum simulation scheme that supports both a continuous-time discrete-space limit, leading to lattice fermions, and aContinuous-spacetime limit,Leading to the Dirac equation.

### Quantum walks and non-Abelian discrete gauge theory

- Physics
- 2016

A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete $\text{U}(N)$ gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists,…

### Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions

- Physics
- 2020

Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one…