Skip to main content

Topological quantum matter and computation


Key facts

Type of research degree
Application deadline
Friday 17 April 2020
Project start date
Thursday 1 October 2020
Country eligibility
UK and EU
Competition funded
Source of funding
Research council
Dr Joao Goncalves Faria Martins and Professor Jiannis Pachos
Additional supervisors
Dr Zlatko Papic, Professor Paul Martin
School of Mathematics, School of Physics and Astronomy
Research groups/institutes
Pure Mathematics, Theoretical Physics
<h2 class="heading hide-accessible">Summary</h2>

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, which is protected from decoherence. A fundamental ingredient of such topological quantum computation are 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 &ndash; a Majorana fermion &ndash; 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, which occur in more strongly-interacting systems, have richer properties and can perform more powerful (&ldquo;universal&rdquo;) quantum computation.

<h2 class="heading hide-accessible">Full description</h2>

<p>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. Parafermions were initially proposed to describe excitations of certain fractional quantum Hall states [2] and, more recently, have been studied in simple lattice models [3]. The main objective of this project is to understand the intrinsically interacting nature of parafermion states by using the new concept of &ldquo;interaction distance&rdquo; we recently introduced in [4]. Interaction distance quantifies how &ldquo;far&rdquo; a certain quantum state is from a closest non- interacting state. This concept 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 &ldquo;entanglement spectra&rdquo; and other properties that can be diagnosed using quantum information tools. On the other hand, apart from static properties, we will also investigate the dynamics and possible realisations of parafermions out of equilibrium (e.g., due to periodic driving).</p> <h5>First-year project</h5> <p>The initial phase of the project will consist of learning about the basic physics of topological phases of matter and their applications in quantum computation. This will focus on the simple solvable models due to Alexei Kitaev and Paul Fendley, and understanding how the topological features of these systems are reflected in their entanglement properties. The student will also learn a few numerical techniques, such as exact diagonalisation and density-matrix renormalisation group, which are valuable tools in probing topological phases of matter.</p> <h5 class="wrapChildUrls" itemprop="mainContentOfPage" itemscope="" itemtype="">References</h5> <div id="References"> <p>[1] Introduction to topological quantum computation, Jiannis K. Pachos, Cambridge University Press (2012).</p> <p>[2] Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level, N. Read and E. Rezayi, Phys. Rev. B, 59, 8084 (1999).<br /> <br /> [3] Topological phases with parafermions: theory and blueprints , Jason Alicea and Paul Fendley, Annual Review of Condensed Matter Physics 7, 119-139 (2016).<br /> <br /> [4] Optimal free models for many-body interacting theories, Christopher J. Turner, Konstantinos Meichanetzidis, Zlatko Papic, Jiannis K. Pachos, Phys. Rev. B 97, 125104 (2018) .</p> </div>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &ldquo;Topological quantum matter and computation&rdquo; as well as <a href="">Professor Jiannis Pachos</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome 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.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid.

<h2 class="heading">Funding on offer</h2>

<p><strong>UK/EU</strong>&nbsp;&ndash;&nbsp;Engineering &amp; Physical Sciences Research Council Studentship&nbsp;for 3.5 years. A full standard studentship consists of academic fees (&pound;4,600 in Session 2020/21), together with a maintenance grant (&pound;15,285 in Session 2020/21) paid at standard Research Council rates. UK applicants will be eligible for a full award paying tuition fees and maintenance. European Union applicants will be eligible for an award paying tuition fees only, except in exceptional circumstances, or where residency has been established for more than 3 years prior to the start of the course.&nbsp;Funding is awarded on a competitive basis.</p>

<h2 class="heading">Contact details</h2>

<p>For further information please contact Doctoral College Admissions by&nbsp;email:&nbsp;<a href="">m</a><a href=""></a>&nbsp;or by&nbsp;telephone +44 (0)113 343 5057.</p>

<h3 class="heading heading--sm">Linked funding opportunities</h3>
<h3 class="heading heading--sm">Linked research areas</h3>