# Quantum Computer Science: 2018-2019

| |

| Schedule C1 (CS&P) — Computer Science and Philosophy Schedule C1 — Computer Science Schedule C1 — Mathematics and Computer Science |

| Michaelmas Term 2018 (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 (e.g. non-locality, no-cloning principle), and introduces qubits. We give detailed discussions of some key algorithms and protocols such as Grover's search algorithm and Shor's factorisation algorithm, quantum teleportation and quantum key exchange.

At the same time, this course provides a introduction to diagrammatic reasoning. As an entirely diagrammatic presentation of quantum theory and its applications, this course is the first of its kind.

## 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.

## 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

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

Lecture notes will be provided as the course progresses. A textbook is forthcoming:

Picturing Quantum ProcessesA First Course in Quantum Theory and Diagrammatic Reasoning