Johannes Gütschow

Publications

[Gut10]  J. Gütschow

Entanglement generation of Clifford quantum cellular automata.
Applied Physics B 98(2010) 623-633 [arXiv:1001.1062] [DOI] [Springerlink]

Clifford quantum cellular automata (CQCAs) are a special kind of quantum cellular automata (QCAs) that incorporate Clifford group operations for the time evolution. Despite being classically simulable, they can be used as basic building blocks for universal quantum computation. This is due to the connection to translation-invariant stabilizer states and their entanglement properties. We will give a self-contained introduction to CQCAs and investigate the generation of entanglement under CQCA action. Furthermore, we will discuss finite configurations and applications of CQCAs.

[GUWZ09]  J. Gütschow, S. Uphoff, R. F. Werner, and  Z. Zimborás

Time asymptotics and entanglement generation of Clifford quantum celluar automata.
Journal of Mathematical Physics 51(2010) Selected as JMP research highlight in Feb. 2010. Selected for the Virtual Journal of Quantum Information Volume 10, Issue 2 (Feb 2010). [arXiv:0906.3195] [DOI] [scitation.aip.org]

We consider Clifford Quantum Cellular Automata (CQCAs) and their time evolution. CQCAs are an especially simple type of Quantum Cellular Automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum computation. In this work we study the time evolution of different classes of CQCAs. We distinguish between periodic CQCAs, fractal CQCAs and CQCAs with gliders. We then identify invariant states and study convergence properties of classes of states, like quasifree and stabilizer states. Finally we consider the generation of entanglement analytically and numerically for stabilizer and quasifree states.

[GNW10]  J. Gütschow, V. Nesme, and  R. F. Werner

The fractal structure of cellular automata on abelian groups.
[arXiv:1011.0313]

It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structure of the spacetime diagrams of cellular automata is a much explored topic, but virtually all of the results revolve around a special class of automata, whose typical features include irreversibility, an alphabet with a ring structure, a global evolution that is a ring homomorphism, and a property known as (weakly) p-Fermat. The class of automata that we study in this article has none of these properties. Their cell structure is weaker, as it does not come with a multiplication, and they are far from being p-Fermat, even weakly. However, they do produce fractal spacetime diagrams, and we explain why and how.

Diploma Thesis