Doctor of Philosophy (PhD) in Pure Mathematics - Quantum Information

The program information below was valid for the fall 2020 term (September 1, 2020 - December 31, 2020). This is the archived version; the most up-to-date program information is available through the current Graduate Studies Academic Calendar.

The Graduate Studies Academic Calendar is updated 3 times per year, at the start of each academic term (January 1, May 1, September 1). Graduate Studies Academic Calendars from previous terms can be found in the archives.

• Admit term(s) 
  • Fall
  • Winter
  • Spring
• Delivery mode 
  • On-campus
• Program type 
  • Collaborative
  • Doctoral
  • Research
• Registration option(s) 
  • Full-time
  • Part-time
• Study option(s) 
  • Thesis

• Minimum requirements 
  • A Master's degree (or equivalent) in Mathematics with at least a 78% standing. Exceptions may be made for students with an Honours Bachelor degree who demonstrate a very high level of background preparation and research potential.
  • A one-page personal statement.
• Application materials 
  • Supplementary information form
  • Transcript(s)
• References 
  • Number of references:  3
  • Type of references: 

    at least 2 academic

• English language proficiency (ELP) (if applicable)

Thesis option:

Graduate Academic Integrity Module (Graduate AIM)

Courses 

• The program requires a minimum of 4 graduate courses, including the 2 Quantum Information core courses, with an average of at least 70% (with unit weights equal to 0.50) for those entering the PhD program with a Master's degree. At least 3 of the 4 required courses must be PMATH graduate courses numbered in the 800's and 900's, and at least 1 of the 4 required courses must be a QIC graduate course (note that cross-listed courses, such as PMATH 871/QIC 710, are regarded as both PMATH and QIC courses). If the 4th course is not a PMATH or QIC course it must be approved by the Pure Mathematics Graduate Committee. None of the 4 required courses can be graduate courses numbered in the 600s or reading courses. Up to 3 course credits may be granted by the Graduate Committee for work completed towards the PhD degree at another institution provided that the relevance of the previous work to the student's proposed program is clearly established.
• Quantum Information core courses:
  • QIC 710 Quantum Information Processing (equivalent to PMATH 871 Quantum Information Processing)
  • QIC 750 Implementation of Quantum Information Processing
• If students have credit for a course deemed equivalent to a particular core QIC course by the IQC Curriculum Committee, then that part of the core requirement may be waived, but the minimum number of required courses will remain 4.
• Students entering the program with a Bachelor's degree normally must also satisfy the course requirements of a Master of Mathematics (MMath) dgree in addition to those of the PhD program. The number and nature of such courses shall be specified at the time of admission, or early on in the program.

Link(s) to courses

• Pure Mathematics (PMATH) courses
• Quantum Information (QIC) courses

PhD Lecturing Requirement

• Regular participation in at least 1 departmental seminar is expected and the student must present at least 2 talks in a department seminar.

PhD Quantum Information Seminar

• Students must successfully complete a seminar milestone consisting of presenting 1 talk in an Institute for Quantum Computing (IQC) seminar, and presenting 1 seminar talk on a Quantum Information (QI) topic. If appropriate, lectures given as part of the PhD Lecturing Requirement may also be used to satisfy the seminar requirement.

PhD Comprehensive Examination

• Students in the PhD in Pure Mathematics program are required to meet the following requirements:
• Satisfactory performance in 2 written Comprehensive Examinations:
  • 1 in algebra
  • 1 in analysis and topology
• Each exam is set and assessed by two examiners, with oversight from the Graduate Committee. Members of the Graduate Committee are allowed to serve as examiners. The outcome of each exam is determined by the Graduate Committee.
• The syllabus is based on the material covered in the University of Waterloo's third and fourth year undergraduate courses. The Graduate Committee offers these written exams annually.
• Students must attempt both exams within one year of their registration in the PhD program, and both exams must be successfully completed within seven terms.

PhD Thesis

• Students must complete a thesis embodying the results of original research. This is the most important requirement! The thesis should be on a topic related to quantum information. The thesis must be of a standard that warrants publication in the research literature of the field. The thesis must be acceptable to a committee approved by the Graduate Committee consisting of the student's supervisor and four other professors; one of whom must be from another department, and one must be an independent external examiner familiar with the student's research field. The student is required to defend the thesis at an oral examination.