Chapter 1: Introduction

Karma police, arrest this man. He talks in maths.

- Radiohead, "Karma Police", Oxford, 1997.

Quantum theory: the standard line

• Quantum theory governs the behaviour of the microscopic world
• You've probably heard from credible sources¹ that it is weird, spooky, and defies our natural, classical intuitions.
• True, it has some "bugs" from the p.o.v. of classical physics:
  • irreducible non-determinism
  • non-locality
  • incompatible observations
  • ...
• A century of effort went to answering:

  Why is quantum theory so weird, and can we fix its bugs?

This produced (basically) two answers

Make even weirder ontology		"Shut up and calculate!"
(e.g. Bohmian mechanics, many worlds, ...)		(Mermin, describing the Copenhagen interpretation)

Another, more interesting question

• In the 1980s, a handful of people started to think like software engineers, and ask:

  What if the bugs in quantum theory are actually features?

• Enter:

  quantum teleportation, communication, cryptography		quantum computation

From QT to teleportation

	$\Rightarrow$
1932 - quantum theory		1992 - quantum teleportation

We'll see that teleportation is miraculous...but it's also totally obvious when formulated the right way.

From QT to teleportation

Q: Why did it take so long?

A: It took 60 years to ask the right question.

Q2: Why is this so hard?

A2: QT needs a better language.

Low-level vs. high-level languages

Low-level vs. high-level languages

Quantum picturalism

Quantum picturalism $:=$ the use of diagrams to represent, reason about, and capture essential features and logic of interacting quantum processes.

The Plan

1. Introduce process theories, collections of processes that make sense to compose together as diagrams,
2. Understand the behaviour of quantum theory as a process theory,
3. Apply graphical techniques, namely the ZX-calculus, to solve practical problems in quantum computing.

Warmup: Quantum circuits

:= the "assembly language of quantum computation"

INIT 5 CNOT 1 0 H 2 Z 3 H 0 H 1 CNOT 4 2 ...

↔

Optimising circuits the old-fashioned way

...

A better idea: the ZX calculus

Format

• All material is on the website:

  www.cs.ox.ac.uk/teaching/courses/2024-2025/quantum
  

• 16, 90-min lectures
  • No in-person lectures 23 Oct, 25 Oct, 4 Dec. Videos online.
• Classes in weeks 3-8
• Exam by miniproject
• Combination of exercise-sheet style and more open-ended problems, maybe some coding.

Format

Weeks 1-2	Weeks 3-8
(E-)Book from Library	github.com/zxcalc/book