Title of project: Index for quantum cellular automata

Code: PN2122A

Supervisor: Dr P. Naaijkens

Project description: Quantum cellular automata (QCA) can be seen as discrete time quantum systems with strict locality properties. They are a quantum analogue of classical cellular automata, such as the ‘game of life’. Such systems are local in the sense that the rules to ‘update’ them after a time step are local. That is, they only depend on neighbouring sites. Quantum cellular automata are of interest because of their applications to quantum information theory and quantum computing. They are also relevant as toy models for more complicated physical systems. An interesting problem is to classify all quantum cellular automata. In this project you will look at an invariant, called the index, for 1D QCAs. This index can be used to distinguish different equivalence classes. Possible directions to explore are stability under perturbations of the QCA, or looking at the classification in the presence of additional symmetries. No prior knowledge of quantum mechanics is required for this project.

Project offered as a double module, single module, or both: Double

Prerequisite modules: MA2008 Linear Algebra II MA3005 Functional and Fourier Analysis

Recommended module for concurrent study in year 4: MA4016 Quantum Information

Number of students who could be supervised on this project: 1

Year: 4