Phys 523B: Fault-tolerant quantum computation

Decoherence is an ubiquitous effect observed in quantum mechanics, driving quantum systems towards the classical regime. It is detrimental to quantum computers, and for a long time was thought to be a fundamental obstacle to the physical realization of quantum computation. However, it turns out that decoherence is NOT a fundamental obstacle, rather it can be overcome by the techniques of quantum error-correction and fault-tolerant quantum computation.

This course teaches those techniques and how to apply them. The capstone result presented is the so-called Threshold Theorem of Fault-tolerant Quantum Computation (TT). It says that arbitrarily long quantum algorithms can be run efficiently on imperfect quantum computer hardware, as long this hardware matches a certain accuracy threshold. Slightly simplified, if the logical error introduced by decoherence per quantum gate is below a critical threshold, then the faulty gates are pretty much as good as prefect gates.

After presenting the TT, the course addresses questions regarding the value of the threshold, the scaling of the overhead for error correction, and fault-tolerance in the presence of architectural constraints (short range entangling gates, magic state factories, etc.)

Schedule and practical information


Audience: The course is intended for graduate and senior undergraduate students of Physics, Computer Science, Engineering and Mathematics.

Time and location: Term 2 (Jan 11, 2021 to Apr 14, 2021). The class takes place Monday + Wednesday 2pm-3:30pm, location: Zoom.

Credits: 3.

Grading: 1/3 homework assignments, 1/3 written exam, 1/3 essay/ oral presentation.

Office hour: My office hour takes place Friday 6-7 PM (Zoom).

Lecture notes

The Lecture Notes (under construction) can be found here.

Homework assignments

Office hour recordings


Course outline

In this course we address the questions of which physical systems, from the current perspective, are suitable for building a quantum computer; and how to counteract the effects of decoherence. The course outline is as follows:

  1. Elements of quantum computation

  2. Quantum codes

  3. Fundamental techniques for fault-tolerant quantum computation

  4. Fault-tolerance and quantum computer architecture

  5. Error mitigation in the NISQ era

  6. Student Presentations: Monday April 12 and Wednesday April 14, in class (plan for 2hrs). Schedule TBA.


Instructor: Robert Raussendorf, Department of Physics and Astronomy, raussen[at]

Teaching Assistant: Xiruo Yan, Department of Physics and Astronomy, xyan[at]