Quantum Processes and Computation: 2024-2025
Lecturer | |
Degrees | Schedule C1 (CS&P) — Computer Science and Philosophy Schedule C1 — Computer Science Schedule C1 — Mathematics and Computer Science |
Term | Michaelmas Term 2024 (24 lectures) |
Overview
Both physics and computer science have been very dominant scientific and technological disciplines in the previous century. Quantum Computer Science aims at combining both and may come to play a similarly important role in this century. Combining the existing expertise in both fields proves to be a non-trivial but very exciting interdisciplinary journey. Besides the actual issue of building a quantum computer or realising quantum protocols it involves a fascinating encounter of concepts and formal tools which arose in distinct disciplines. 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 introduces 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.
- Lecture dates/times TBC. Recordings will appear online after each 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:
- ...
- 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 is subject to change.
Handwritten lecture notes (part 1, part 2) cover the material in each lecture. Note these are from a previous year, so they might not line up with lecture numbers precisely.
- Lecture 1: Introduction to diagrammatic reasoning (slides)
- Lecture 2: Circuit diagrams and special processes
- Lecture 3: (Non-)separability and string diagrams
- Lecture 4: Transpose, adjoint, and conjugate processes
- Lecture 5: Quantum-like features from string diagrams
- Lecture 6: Bases, sums, and Hilbert spaces
- Lecture 7: Quantum theory is SCUM: states
- Lecture 8: Quantum theory is SCUM: compound systems
- Lecture 9: Quantum theory is SCUM: unitaries and measurements
- Lecture 10: Quantum circuits and algorithms
- Lecture 11: Quantum algorithms cont'd
- Lecture 12: The ZX-calculus
- Lecture 13: Phase-free ZX and CNOT circuits
- Lecture 14: Normal forms and circuit extraction for phase-free diagrams
- Lecture 15: Clifford circuits and graph states
- Lecture 16: Simplifying Clifford ZX diagrams
- Lecture 17: Strong classical simulation of Clifford circuits
- Lecture 18: Stabiliser theory
- Lecture 19: Phase gadgets and Clifford+phase circuit optimisation
- Lecture 20: Pauli gadgets and Hamiltonian simulation
- Lecture 21: Quantum error correction
- Lecture 22: CSS codes in the ZX calculus
- Lecture 23: The surface code
- Lecture 24: Basics of 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, knowledge of important algorithms such as Grover's and Shor's algorithm and important protocols such as quantum teleportation.At the same time, the student will understand diagrammatic reasoning as an alternative form of mathematics.
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. The course notes and the slides contain an overview of this material, so we advise students with a limited background in linear algebra to consult the course notes before the course starts.
To do the practicals, 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
[from CUP book page] The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to Ph.D. level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying processes and interaction.
Syllabus
Summary / keywords: diagram, parallel and sequential composition of diagrams, string diagram, transpose, adjoints and conjugate, umitarity and inner-product, Bell state, teleportation, no universal separability, no universal cloning, matrix calcu;us, Hilbert space, completeness for string diagrams, logic gate, Bell-basis, doubling, eliminating global phases, discarding, causality, Stinespirng dilation, no-signalling, Krauss decomposition and mixing, ONB measurements, entaglement swapping, gate-teleportation, Naimark dilation, von Neumann measurements, POVM measurements, tomography, classical wires, dense coding, classical-quantum map, copy, delete, measure, encode, classical, quantum and bastard spiders, phase spiders, phase group, complementarity, QKD, strong complementarity, classical subgroup, ZX-calculus, its universality and completeness for stabiliser QM, quantum non-locality, Spekkens' toy theory, circuit model of quantum computing, quantum algorithms (DJ, search, HS), MBQC, resource theories, purity theory, LOCC- and SLOCC-entanglement
Reading list
The textbook for this course is Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning.
It 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:
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 Core to view the book on CUP's website.
Related research
Themes |
Taking our courses
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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.