Quantum Error Correction Course Summer 2024
Practical Information—
LECTURES: The lectures will be held on Mondays 12-14 in room 1.4.03 Seminarraum T2 (Arnimallee 14), starting April 15.
EXERCISES: The exercise classes will be held on Tuesdays 16-18 in 1.1.26 Seminarraum E1 (Arnimallee 14), starting on April 23.
Your TA is: Daniel Miller - d.miller@fu-berlin.de .
The first exercise sheet will be distributed on April 23, to be handed in the week after.
Exercise sheets will be handled via Whiteboard (see Assignments tab).
LECTURE NOTES: will be uploaded on Whiteboard (see Resources tab).
COURSE EVALUATION: Instead of a standard written exam, this course will be graded based on individual written homework (approx. 15 pages). You will each be assigned one (or two) quantum error-correcting code(s), and your homework will be to describe the code's construction, the protection it offers, its properties, its uses, and its relation to other codes. You'll also be provided the scientific papers in which these codes are introduced and where the relevant information is to be found in. The assignment of error-correcting codes to students will happen within the first few weeks of the semester and will ensure that each student has a similar and reasonable workload. I'm planning to let you choose your assignments. The course evaluation homework is independent of the weekly exercise sheets. [Update: see information on end-of-semester homework below.]
COURSE EVALUATION HOMEWORK DEADLINE: Please hand in your homework by July 15 at noon by July 22 at noon. Assignments handed past this deadline may take additional time to correct.
ERROR CORRECTION ZOO: Part of the motivation for this examination mode is to enable students to contribute to the Error Correction Zoo, an online collection of error-correcting codes which I'm involved in (https://errorcorrectionzoo.org/). You may propose the contents of your final homework for use in the Error Correction Zoo!
FEEDBACK AND CONTACT: I'm very happy to hear feedback about the course and to answer if you have any questions. Feel free to reach my by email (philippe.faist@fu-berlin.de) or drop by my office (1.3.16, you can email me to check if I'm in).
Course Description—
Current quantum computers are severly limited by noise, preventing them from running quantum algorithms that are large enough to explore the full power of quantum computing. Quantum error correction protects fragile quantum information from noise and is anticipated to enable future quantum computers to run large quantum circuits at low error rates.
With this course, you will assimilate the core concepts in quantum error correction and fault tolerance, familiarize yourself with the current major quantum error correcting codes for various types of quantum hardware, learn how to apply standard techniques to construct new codes with corresponding decoders, and understand how to reliably run a quantum computation on encoded states.
This course builds upon the concepts introduced in the course “Quantum Information Theory” and is targeted to students wishing to deepen their knowledge about modern techniques in quantum computing. This course will both equip you with a strong theoretical background useful to carry out future theoretical research in the field of quantum computing as well as help you develop key skills to join the quantum industry workforce. We will also occasionally have the opportunity to touch upon some connections to broader themes including classical codes, the theory of condensed matter physics, and (if time permits) some models of quantum gravity.
Topics that we will cover include (tentative):
- Fundamental principles of quantum error correction
- Qubit stabilizer codes
- The surface code
- Fault tolerance with the surface code
- Topological codes beyond the surface code
- Quantum Low-Density Partity-Check codes (qLDPC)
- Bosonic codes
- Implementations/realizations on quantum hardware platforms
- Quantum error correction in physical many-body systems and holography
I am happy to further shape the course based on suggestions from registered students, e.g., to include additional topics or to prioritize certain topics.
End-of-semester Homework Information—
The homework is to research a specific quantum error-correcting code and to hand in a written document that reviews its construction, properties, and features.
DISTRIBUTION OF CODES: A list of codes that are available as homework topics is available for sign-up during class and in my office. Codes will be distributed on a first-come, first-serve basis. (You can e-mail me if you are not able to come sign up in person.) While the same code cannot be distributed to multiple students, some codes on the list are related, and you're welcome to work on your research together (though each student will hand in their individual homework). Please feel free to look up corresponding references, and confer with your colleagues as to which codes you'd like to select.
SCOPE: Please review the assigned code's construction, properties, uses, applications, notable features, and relationships with other codes, as appropriate. Include any relevant background definitions and preliminaries. Include figures, tables as appropriate and as necessary. Use your judgment!
TARGET READER: Please ensure that your work is sufficiently self-contained that it introduces any background information, notation conventions, etc., such that a reader who is familiar with the fundamental concepts of quantum error correction (but who might not be closely acquainted to the particular conventions chosen in my course) is able to easily read and understand your work.
FORMAT: No mandatory format requirements, though please remain within reason. The standard LaTeX "\documentclass[11pt]{article}" class is fine.
STRUCTURE: You may (but are not obliged to) follow the structure of the code pages that you can find on the Error Correction Zoo (https://errorcorrectionzoo.org/). In any case, include additional background information as appropriate. (You may add, for instance, a "Preliminaries and Notation" section.)
LENGTH: roughly 15 pages (including figures, references, etc.), as appropriate. You may adjust the level of detail of the text according to this length guideline. If you are assigned a topically narrow code with little existing material about the code (e.g. if the paper in which the code is introduced is very short), more effort on placing the code in the broader landscape of error-correcting codes may be expected.
DEADLINE: Please hand in your homework by July 15 at noon by July 22 at noon. Assignments handed past this deadline may take additional time to correct.
WORKING GROUPS: You are welcome to research and confer with your colleagues, but each student must hand in their own individual assignment.
QUESTIONS: Please feel free to approach Daniel or me if you have questions that arise during your research.
CONTRIBUTION TO THE ERROR CORRECTION ZOO: The homework is independent of contributions to the error correction zoo. After handing in your homework, we'd be happy of course if you'd like to contribute your material to the error correction zoo. Please familiarize yourself with the contribution guidelines there (https://github.com/errorcorrectionzoo/eczoo_data/blob/main/CONTRIBUTING.md) or reach out to Victor or me. We'll likely discuss and/or coordinate contributions with you after your homework is handed in.
Please do let me know if you have any questions.