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

The program information below was valid for the spring 2022 term (May 1, 2022 - August 31, 2022). 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 
  • Minimum grade point average: 78% or its equivalent.
  • It is absolutely essential that the application for admission into the program contain evidence of potential for performing original research. This should be provided by successful completion of a Master’s thesis in a mathematics-related discipline.
  • In some circumstances a student enrolled in the MMath program may transfer to the PhD program without completing their MMath program.
• Application materials 
  • Résumé
  • Supplementary information form
  • Transcript(s)
• References 
  • Number of references:  3
  • Type of references: 

    normally from academic sources.

• English language proficiency (ELP) (if applicable)

Thesis option:

The program of studies of a PhD student is directed by a PhD Advisory Committee consisting of the supervisor(s) and two other faculty members. This committee should be approved (by the graduate officer) within three terms of enrollment. At least one of the two other members should be from (or cross-appointed to) the Department, and one of the members should be from outside the research group of the supervisor(s).

Graduate Academic Integrity Module (Graduate AIM)

Courses 

• Students must complete 4 one-term (0.50 unit) graduate courses after the Master's degree, satisfying a breadth requirement and Quantum Information core course requirement, or 8 one-term (0.50 unit) graduate courses after the Bachelor's degree, satisfying a breadth requirement and Quantum Information core course requirement. Candidates for the PhD degree must maintain a grade point average of at least 70% in their coursework. Besides the breadth and Quantum Information requirements, there are no other constraints on course selection.
• Breadth requirement: to satisfy the breadth requirement, students are required to complete 3 courses from the following lists, with no more than 1 course from each list:
  • ƒApplications:ƒ
    • AMATH 663 Fluid Mechanics
    • AMATH 673 Quantum Theory 2
    • AMATH 674 Quantum Theory 3: Quantum Information and Foundations
    • AMATH 675 Introduction to General Relativity
  • Computation:
    • AMATH 642 Computational Methods for Partial Differential Equations
    • AMATH 740 Numerical Analysis
    • AMATH 741 Numerical Solution of Partial Differential Equations
  • Differential Equations:
    • AMATH 651 Introduction to Dynamical Systemsƒ
    • AMATH 653 Partial Differential Equations 2
    • AMATH 655 Control Theory
    • AMATH 751 Advanced Ordinary Differential Equations
    • AMATH 753 Advanced Partial Differential Equations
  • Techniques:
    • AMATH 656 Calculus of Variations
    • AMATH 677 Stochastic Processes for Applied Mathematics
    • AMATH 731 Applied Functional Analysis
    • AMATH 732 Asymptotic Analysis and Perturbation Theory
    • AMATH 777 Stochastic Processes in the Physical Sciences
• Quantum Information core course requirement: students are required to take the 2 Quantum Information core courses listed below. These interdisciplinary courses provide a strong foundation in quantum information science:
  • QIC 710 Quantum Information Processing
  • QIC 750 Implementation of Quantum Information Processing
• The completion of 2 graduate courses in Quantum Information (other than QIC 710 and QIC 750) is also required.
• Students may not count more than 1 graduate course that is cross-listed with an undergraduate course for credit towards their PhD degree. This restriction applies to all 600-level AMATH courses and any cross-listed courses offered by other departments. Note: students who transfer directly into the PhD program (without completing the Master's degree) may take up to 2 cross-listed courses.
• If a PhD student has taken an equivalent course during a Master's program, this can be counted (upon approval from the Graduate Officer) towards completion of the breadth requirement but does not reduce the number of courses required.
• Courses are selected in consultation with the student's supervisor. Students are encouraged to select courses that will help them develop a broad knowledge of Mathematics and its applications: appropriate courses are often offered by other departments in the Faculties of Mathematics, Science and Engineering.

Link(s) to courses

• Applied Mathematics (AMATH) courses
• Quantum Information (QIC) courses

PhD Comprehensive Examination

• Students are required to meet the University-level PhD Comprehensive Examination minimum requirements outlined in the “Minimum requirements for the PhD degree” section of the Graduate Studies Academic Calendar (GSAC), with certain noted differences that are specific to the Faculty of Mathematics Comprehensive Examination minimum requirements:
  • Comprehensive examination purpose: Consistent with University-level minimum requirements.
  • Timing: Consistent with University-level minimum requirements. 
  • Committee: Consistent with University-level minimum requirements. Note: The Faculty of Mathematics wishes to use the option to have the committee approved by a delegate of the Associate Dean, namely by the Graduate Officer in the home department of the student.
  • Who Chairs an examination: Consistent with University-level minimum requirements.
  • Format / Content: Consistent with University-level minimum requirements.
  • Academic integrity: In the Faculty of Mathematics, when a student needs to submit a written document to their comprehensive examination committee prior to the examination, they are required to sign an acknowledgement form affirming their work does not violate the University policy on Academic Integrity. Students are also encouraged to use a
    plagiarism detection software and include its report with the submission of their written document. Furthermore, the comprehensive examination committee may require the student to use such software and include the report it generated with the submission of their written component.

• In addition to the University-level and Faculty-level PhD Comprehensive Examination minimum requirements, students in the PhD in Applied Mathematics - Quantum Information program are also required to meet the following requirements:
  • During the third term of enrollment, the candidate will give a 30-minute pre-comprehensive seminar on the proposed research area, emphasizing background material. Shortly thereafter the advisory committee shall decide on the background topics that will comprise the candidate's comprehensive exam. The student will be informed of the areas of examination 3-4 months prior to the comprehensive examination.
  • The comprehensive examination is to be completed by the end of the student’s fifth term. The candidate will prepare a written research proposal (approximately 25 pages) that will be submitted to the members of the advisory committee and the examination chair (normally the graduate officer) at least two weeks prior to the comprehensive examination. The proposal should describe the research problem, together with motivation, literature review, an indication of methodology, any progress made to date, and a research plan with timeline.
  • Shortly before the comprehensive examination, the examination chair (through the graduate coordinator) will consult with the advisory committee to determine whether the committee wishes the exam to proceed and, if so, whether the committee wishes to meet to discuss the questions to be asked on background material. Each committee member will provide a typeset list of questions to the graduate coordinator four business days before the exam (about 3-5 questions, which can all be answered at a whiteboard in about 15 minutes). This list of questions will be provided to the candidate one hour prior to the start of the exam. The candidate will use this time to prepare answers, with no access to outside materials.
  • The examination will consist of a 20 minute presentation of the proposed research followed by two rounds of questions: the first on the prepared background questions, the second on the research proposal and the relevant literature. Each examiner shall question the candidate for approximately 15 minutes in each round. If there is more than one supervisor, they will share the allotted 15 minute time-slot. The comprehensive examination should normally be completed in two hours, after which the committee will consider the student’s progress to date, the proposal, and the student’s performance in the exam. Students who have not satisfactorily completed the comprehensive examination by the end of the fifth term will have their progress reviewed by the Departmental Graduate Chair.

PhD Lecturing Requirement

• This requirement is normally met by teaching a one-term undergraduate course, usually at the first or second year level, under the supervision of a faculty member. Students will satisfy this requirement after completing the comprehensive examination and after obtaining experience as a teaching assistant. If the department is unable to provide the student with a suitable undergraduate course to teach, the requirement may be met by giving a series of lectures of an introductory nature concerning the student's field of research.

PhD Quantum Information Seminar

• Students must successfully complete a seminar milestone consisting of one Institute for Quantum Computing (IQC) seminar and one seminar 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 Thesis

• A PhD thesis contains original results that warrant publication in the research literature. Indeed, candidates are encouraged to publish papers based on their research before submitting their theses. Moreover, the Department expects a PhD thesis to be a scholarly work that is broad in scope. As such, it should contain a discussion of the history of the research problem and an analysis of the relevant literature. For University guidelines on coauthored material in PhD theses please visit the Graduate Studies and Postdoctoral Affairs website; additional departmental guidelines apply.
• The thesis must be on a topic in Quantum Information. The supervisor must be an approved Quantum Information thesis supervisor. A list of approved supervisors can be found on the Institute for Quantum Computing website.
• The candidate shall defend the thesis in an oral examination before an Examining Committee, which shall consist of the Advisory Committee, one faculty member from outside the Department, and an external examiner familiar with the student's research field.