Quantum Processes and Computation: 2025-2026
Lecturer | |
Degrees | Schedule C1 (CS&P) — Computer Science and Philosophy Schedule C1 — Computer Science Schedule C1 — Mathematics and Computer Science |
Term | Hilary Term 2026 (24 lectures) |
Overview
Quantum computing is an exciting new computational paradigm that combines computer science and quantum physics to solve problems that are far beyond the reach of traditional computers. This course provides an interdisciplinary introduction to the emerging field of quantum computer science, explaining basic quantum mechanics (including finite dimensional Hilbert spaces and their tensor products), quantum entanglement, its structure and its physical consequences, and introducing qubits. We introduce the basics of quantum algorithms and delve into the how to represent and reason about quantum computations using a powerful graphical tool called the ZX calculus. We will apply this tool to discuss optimisation and classical simulation of quantum computation, as well as quantum error correction and fault-tolerant quantum computing, which are key ingredients in emerging quantum technologies.
- Lectures will be the Computer Science Department, Lecture Theatre A, Mondays and Wednesdays 16:00-17:30. Lectures will be in-person except for 28 January, which will be pre-recorded and made available online. Recordings of all other lectures will appear on Panopto after the lecture.
- Class info, including weekly deadlines is on Minerva
- Everything else (problem sheets, schedule of material, etc) is here on the course website
The course consists of:
- 24 lectures (see Lectures below)
- 6 classes (weeks 3, 4, 5, 6, 7, 8). Here are the problem sheets: They will be made available a week before the deadline. Click here to see which class you are in and how to submit your work.
- The miniproject. This will have a similar format to the problem sheets, but questions will be much more in-depth and/or open-ended.
Lectures
The following is a provisional list of topics / sections covered in the lectures. This schedule and the handwritten lecture notes are subject to change during the term.
Handwritten lecture notes ( part 1, part 2, part 3, part 4, part 5 ) cover the material in each lecture.
- Lecture 1: Introduction to diagrammatic reasoning (slides)
- Lecture 2: States and effects, string diagrams, and (non-)separability
- Lecture 3: Quantum-like features from string diagrams
- Lecture 4: Bases, sums, and Hilbert spaces (watch video with SSO)
- Lecture 5: Quantum theory is SCUM: states, compound systems, and unitaries
- Lecture 6: Measurements, the quantum circuit model, and quantum algorithms
- Lecture 7: Quantum algorithms and circuit problems
- Lecture 8: The ZX-calculus
- Lecture 9: Phase-free ZX and CNOT circuits
- Lecture 10: Clifford circuits and diagrams
- Lecture 11: Simplifying Clifford circuits and applications
- Lecture 12: Phase gadgets and optimisation
- Lecture 13: Pauli exponentials and quantum simulation
- Lecture 14: Stabiliser theory and quantum error correction
- Lecture 15: Interlude: quantum algorithms and complexity (guest lecturer Matty Hoban)
- Lecture 16: CSS codes and fault-tolerant quantum computation
Learning outcomes
The student will know by the end of the course what quantum computing and quantum protocols are about, why they matter, and what the scientific prospects of the field are. This includes a structural understanding of some basic quantum mechanics, understanding of the high-level structure of most well-known quantum algorithms in the circuit model as well as important protocols such as quantum teleportation, and some basic understanding of state-of-the-art techniques for quantum compilation and classical simulation of quantum computing.Prerequisites
We do not assume any prior knowledge of quantum mechanics. However, a solid understanding of basic linear algebra (finite-dimensional vector spaces, matrices, eigenvectors and eigenvalues, linear maps etc.) is required as a pre-requisite.
Some of the problem sheets are in the form of Jupyter notebooks. To complete these, you will need to have a basic working knowledge of the Python programming language. If you've never used Python before, I suggest working through the first 4 sections of: https://docs.python.org/3/tutorial/.
Synopsis
Quantum computing is an exciting new computational paradigm that combines computer science and quantum physics to solve problems that are far beyond the reach of traditional computers. This course provides an interdisciplinary introduction to the emerging field of quantum computer science, explaining basic quantum mechanics (including finite dimensional Hilbert spaces and their tensor products), quantum entanglement, its structure and its physical consequences, and introducing qubits. We introduce the basics of quantum algorithms and delve into the how to represent and reason about quantum computations using a powerful graphical tool called the ZX calculus. We will apply this tool to discuss optimisation and classical simulation of quantum computation, as well as quantum error correction and fault-tolerant quantum computing, which are key ingredients in emerging quantum technologies.
Syllabus
Matrices, string diagrams, and tensor contraction. Generalised states and effects, (non-)separability of diagrams. Basic introduction to quantum theory: states, composition, unitary evolution, measurement. The quantum circuit model and the anatomy of a quantum algorithm. Simulation, equality, and optimisation of quantum circuits. The ZX-calculus. Clifford circuits: simulation, synthesis, optimisation. Advanced circuit techniques (phase gadgets and Pauli exponentials). Quantum simulation. Quantum error correction and fault-tolerance.
Reading list
The first two weeks of the course are based roughly on the textbook Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. The remainder of the course is based on Picturing Quantum Software: An Introduction to the ZX-Calculus and Quantum Compilation.
Picturing Quantum Software is available for free online: https://github.com/zxcalc/book
Picturing Quantum Processes should be available in many libraries throughout the university and most online bookstores. The ebook PDF is also available for free to all members of Oxford University through a deal between the Bodleian Library and Cambridge University Press:
https://solo.bodleian.ox.ac.uk/permalink/44OXF_INST/35n82s/alma991025406270107026
If the link above doesn't work, go to http://solo.bodleian.ox.ac.uk, search for the book title, and click on the "Online Access" version. Under the section "View Online", click the link to Cambridge ebooks.
Related research
Themes |
Taking our courses
This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses
Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.