Doctor of Philosophy (PhD) in Combinatorics and Optimization - Quantum Information - Internship

The program information below was valid for the fall 2023 term (September 1, 2023 - December 31, 2023). 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
• Length of program 
  • Students are required to complete the program in accordance with the University program time limits.
• Program type 
  • Collaborative
  • Doctoral
  • Research
• Registration option(s) 
  • Full-time
  • Part-time
• Study option(s) 
  • Thesis

• Minimum requirements 
  • Students in the Doctor of Philosophy (PhD) in Combinatorics and Optimization - Quantum Information program can apply to transfer into the Doctor of Philosophy (PhD) in Combinatorics and Optimization - Quantum Information - Internship program option after completing at least one academic term. Admittance will be decided based on the student’s progress to date, and is subject to approval by the student’s supervisor(s) and the Associate Chair, Graduate Studies in the Department of Combinatorics and Optimization.
• References 

Thesis option:

Graduate Academic Integrity Module (Graduate AIM)

Courses 

• Students must complete 8 courses, including the 2 Quantum Information core courses, and 3 other CO core courses. At least 5 of the courses taken should be CO courses and at least 4 should be QI courses (note that jointly offered or cross-listed courses, like CO681/QIC710, are regarded as both CO and QIC courses). The remaining course (if any) must be a graduate course in the Faculty of Mathematics, or a course approved by the CO Graduate Committee.
• At least 6 courses should normally be completed within the first 6 terms.
• Combinatorics and Optimization core courses:
  • CO 630 Algebraic Enumeration
  • CO 642 Graph Theory
  • CO 650 Combinatorial Optimization
  • CO 663 Convex Optimization and Analysis
  • CO 681 Quantum Information Processing
  • CO 685 The Mathematics of Public-Key Cryptography
• Quantum Information core courses:
  • QIC 710 Quantum Information Processing (equivalent to CO 681 Quantum Information Processing)
  • QIC 750 Quantum Information Processing Devices
• If students have credit for a course deemed equivalent to a particular core course by the Department Graduate Committee, then that part of the core requirement may be waived.
• The Department may require additional coursework in cases where this is judged to be necessary; for instance, when a student is admitted to the PhD program without having been granted credit for a Master's degree.

Link(s) to courses

• Combinatorics and Optimization (CO) courses
• Quantum Information (QIC) courses

PhD Internship

• Students are required to complete one or more 3-4 month internships working on a topic related to their program. The internships will normally be arranged by the student, possibly with assistance from the supervisor. The internship must be approved by the supervisor and the Associate Chair, Graduate Studies in the Department of Combinatorics and Optimization. At most two consecutive terms can be taken for an internship. An internship may not be taken in the student's final term.

Graduate Studies Research Skills Seminar

• Required for PhD students unless the student satisfied this requirement as a MMath student at the Department of Combinatorics and Optimization.

PhD Quantum Information Seminar

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

PhD Lecturing Requirement

• Every PhD student will be required to lecture under supervision during the program of studies. If a PhD student gives a scheduled course on a regular basis, the same two faculty members will attend three of the lectures and make a confidential, constructive critique of the student's performance to the student.
• The PhD Lecturing Requirement should normally be completed within the first eight terms of the student’s PhD program. Students may not put their thesis on display until at least the term following that in which the Lecturing Requirement was successfully completed.

PhD Comprehensive Examination

• This requirement consists of 2 written examinations covering the fundamentals of combinatorics and optimization. These are usually offered once a year, in the Spring term. The student must write one exam from two of the following three categories:
  • Combinatorial Enumeration, Graph Theory
  • Continuous Optimization, Discrete Optimization
  • Cryptography, Quantum Computing
• The choice of exams is made by the student, in consultation with their supervisor. The exams must be taken within the first four terms of the student’s PhD program.
• The PhD Comprehensive Examination requirement is satisfied by passing both examinations.

PhD Thesis Proposal

• The PhD Thesis Proposal is an oral exam at which the student is expected to give a brief description of the questions they propose to work on for the PhD and a summary of the main results in this area. This exam should normally be taken within the first six terms of the student’s PhD program. The student should provide a short written version of their thesis proposal to their committee one week before the oral presentation. The PhD Thesis Proposal requirement is satisfied by successful completion of this exam.
• Advisory Committee: each student has an Advisory Committee, which normally consists of the student's supervisor and two other department members with expertise in the area of the student's research interests. The Advisory Committee acts as the examining committee at the student's PhD Thesis Proposal, and is usually formed at this time. The members of the advisory committee will also usually act as examiners at the student's PhD defence. The Advisory Committee is selected by the Graduate Officer, who will consult the student and their supervisor.

PhD Thesis

• Students must prepare a thesis in Quantum Information, embodying the results of original research, of a standard that would warrant publication in a research journal of the field. The thesis must be acceptable to the student's supervisor, to two professors in the Department and one professor outside the Department, and to an external examiner familiar with the student's research field. The student is required to defend the thesis at an oral examination. This requirement is met when the thesis has been successfully defended and accepted.