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Algebraic, geometric and physical underpinnings of topological quantum computation

PGR-P-596

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Project start date
Friday 1 October 2021
Country eligibility
International (open to all nationalities, including the UK)
Funding
Non-funded
Supervisors
Dr Joao Goncalves Faria Martins and Professor Paul Martin
Schools
School of Mathematics
Research groups/institutes
Pure Mathematics
<h2 class="heading hide-accessible">Summary</h2>

The motivating aim is to build a `quantum computer&#039;. Feynman&#039;s idea is, broadly, to use the quantum nature of physical systems to build a massively parallel computer. There are several major technical obstructions to puting this into practice. One is that this device breaks the discreteness of binary computation (a barrier to errors in the classical case), so problems have to be recoded to make computation computational-fault-tolerant.<br /> <br /> One kind of discreteness that can be set up (in principle) to survive the quantum setting, is topological discreteness. (Very roughly speaking, while the precise trajectories of a collection of particles in a plane from one time to another are obscured from us by system noise, the braiding of suitably prepared particle time-lines is a relatively robust datum.) This leads us to study certain realisations/representations of braid groups, such as those provided by the Temperley-Lieb algebra, and several beautiful generalisations of this type of problem.

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

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="http://www.leeds.ac.uk/rsa/prospective_students/apply/I_want_to_apply.html">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 &lsquo;Algebraic, geometric and physical underpinnings of topological quantum computation&rsquo; as well as&nbsp;<a href="mailto:https://eps.leeds.ac.uk/maths/staff/4061/professor-paul-martin">Professor Paul Martin</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. Some schools and faculties have a higher requirement.

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

<p><strong>Self-funded students are welcome to apply.</strong></p> <p><strong>UK&nbsp;students</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarships-2021-january-deadline">Leeds Doctoral Scholarship (January deadline)</a>&nbsp;and the&nbsp;<a href="https://phd.leeds.ac.uk/funding/142-william-wright-smith-scholarship-2021">William Wright Smith Scholarship&nbsp;</a>are available to UK applicants. &nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK students</strong>&nbsp;&ndash; The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens.&nbsp; <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p>

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

<p>For further information regarding your application,&nbsp;please contact Doctoral College Admissions by email:&nbsp;&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>&nbsp;or by telephone:&nbsp; + 44 (0) 113 343 5057.</p> <p>For further information regarding the project, please contact Professor Paul Martin: <a href="mailto:EMAIL@leeds.ac.uk">p.p.martin@leeds.ac.uk</a>&nbsp;or&nbsp;telephone: + 44 (0) 113 343 7787.</p>


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