From free fermions to parafermions: how to build a universal topological quantum computer from free particles


Contact Dr Jiannis Pachos or Dr Zlatko Papic to discuss this project further informally

Project description

Topology plays a prominent role in describing quantum phenomena such as the quantum Hall effect and topological insulators. This burgeoning field of research, also recognised by the 2016 Nobel physics prize, promises practical applications in terms of new ways of storing and manipulating quantum information [1], which is protected from decoherence (see Figure). A fundamental ingredient of such topological quantum computation is the quasiparticles with non-Abelian exchange statistics, called anyons. In recent years, there has been much effort to experimentally realise the simplest kind of anyon – a Majorana fermion – and use them to build topological qubits. However, the relatively simple physics of Majorana fermions also places limitations on the type of quantum gates that can be simulated. Other types of anyons, like parafermions [2], which occur in more strongly interacting systems, have richer properties and can perform
more powerful (“universal”) quantum computation.

This project will study the fundamental properties of quantum systems that host parafermion quasiparticles. In contrast to Majorana fermions, which are well understood due to the analogies with topological superconductors, there is still little knowledge about parafermions. The main objective of this project is to understand the intrinsically interacting nature of parafermion states by using the new concept of “interaction distance” we recently introduced in [3]. This allows us to approximate quantum states in a new way that generalises traditional methods, e.g., mean-field theory. Applying the interaction distance measure to parafermion states will give us new insights into the microscopic building blocks of parafermion states, which are reflected in their “entanglement spectra” and other properties that can be diagnosed using quantum information tools [4].


[1] Introduction to Topological Quantum Computation, Jiannis K. Pachos, Cambridge University Press, 2012.
[2] Topological phases with parafermions: theory and blueprints, Jason Alicea and Paul Fendley, arXiv:1504.02476.
[3] Optimal free models for many-body interacting theories, Christopher J. Turner, Konstantinos Meichanetzidis, Zlatko
Papic, Jiannis K. Pachos, Nature Communications 8, 14926 (2017); arXiv:1607.02679.
[4] Free-fermion descriptions of parafermion chains and string-net models, K. Meichanetzidis, C. J. Turner, A. Farjami, Z.
Papic, Jiannis K. Pachos, arXiv:1705.09983.
[5] Simulating the exchange of Majorana zero modes with a photonic system, Jin-Shi Xu, Kai Sun, Yong-Jian Han,
Chuan-Feng Li, Jiannis K. Pachos, Guang-Can Guo, Nature Communications 7, 13194 (2016), arXiv:1411.7751.

Entry requirements

Applications are invited from candidates with, or expecting, a minimum of a UK upper second class honours degree (2:1) in a relevant discipline, a Master's degree in a relevant discipline, or both.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section that the PhD you wish to be considered for is 'From free fermions to parafermions' as well as Dr Jiannis Pachos as your proposed supervisor.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

If you require any further information please contact the Graduate School Office

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates.  All scholarships will be awarded on the basis of merit.