(#017) Y you should ZX: An Introduction to ZX Calculus - Mahathi Vempati
Date & Time: 12-12-2020, 22:15 IST
Abstract
ZX Calculus is a rigorous graphical language for reasoning about linear maps between qubits. Besides being useful in quantum circuit optimization and quantum error correction, it is also quite fun to dabble in!
In this talk, we will briefly define ZX Calculus, and understand diagrammatic reasoning, the principle behind ZX Calculus. We will define the term "process theory" diagrammatically.
We will then define some artefacts that process theories can possess. We will state without proof that linear maps can be expressed as a process theory and learn the correspondence between known operations in linear algebra and the diagrammatic definitions of these operations in the process theory.
We will use this correspondence to prove two simple theorems diagrammatically (so bring a pen and a notebook!)
Finally, we will take a glimpse of what an actual reduction of a quantum-information protocol in ZX Calculus would look like, without attempting to understand it.
Prerequisites
None, to understand most of the talk. Knowledge of linear algebra could make the talk more enjoyable.
Resources
The talk is based on the first few chapters of the book Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning.