# Non-trivial Lyapunov spectrum from fractal quantum cellular automata

@inproceedings{Berenstein2021NontrivialLS, title={Non-trivial Lyapunov spectrum from fractal quantum cellular automata}, author={David Berenstein and Brian R. Kent}, year={2021} }

A generalized set of Clifford cellular automata, which includes all Clifford cellular automata, result from the quantization of a lattice system where on each site of the lattice one has a 2k-dimensional torus phase space. The dynamics is a linear map in the torus variables and it is also local: the evolution depends only on variables in some region around the original lattice site. Moreover it preserves the symplectic structure. These are classified by 2k× 2k matrices with entries in Laurent… Expand

#### References

SHOWING 1-10 OF 15 REFERENCES

The fractal structure of cellular automata on abelian groups

- Computer Science, Physics
- Automata
- 2010

The class of automata studied in this article is the classical equivalent of the Clifford quantum cellular automata, which have been studied by the quantum community for several reasons, and can be used to generate highly entangled states, which are a primary resource for measurement-based models of quantum computing. Expand

Universal quantum constraints on the butterfly effect

- Physics
- 2015

Lyapunov exponents, a purely classical quantity, play an important role in the evolution of quantum chaotic systems in the semiclassical limit. We conjecture the existence of an upper bound on the… Expand

A review of Quantum Cellular Automata

- Computer Science, Physics
- Quantum
- 2020

This review discusses all of these applications of QCAs, including the matrix product unitary approach and higher dimensional classifications, as well as some other interesting results on the structure of quantum cellular automata. Expand

Time asymptotics and entanglement generation of Clifford quantum cellular automata

- Physics, Mathematics
- 2010

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… Expand

A toy model for time evolving QFT on a lattice with controllable chaos

- Physics
- 2018

A class of models with a dynamics of generalized quantum cat maps on a product of quantum tori is described. These tori are defined by an algebra of clock-shift matrices of dimension $N$. The… Expand

Entanglement entropy converges to classical entropy around periodic orbits

- Physics
- 2015

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic… Expand

Exotic equilibration dynamics on a 1-D quantum CNOT gate lattice

- Physics
- 2021

We consider the dynamics of local entropy and nearest neighbor mutual information of a 1-D lattice of qubits via the repeated application of nearest neighbor CNOT quantum gates. This is a quantum… Expand

Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices

- Mathematics, Physics
- 2018

We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system… Expand

A bound on chaos

- Physics
- 2015

A bstractWe conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation… Expand

Operator Spreading in Random Unitary Circuits

- Physics
- 2017

Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results… Expand