Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)

02/22/2021
by   Bob Coecke, et al.
0

This paper is a `spiritual child' of the 2005 lecture notes Kindergarten Quantum Mechanics, which showed how a simple, pictorial extension of Dirac notation allowed several quantum features to be easily expressed and derived, using language even a kindergartner can understand. Central to that approach was the use of pictures and pictorial transformation rules to understand and derive features of quantum theory and computation. However, this approach left many wondering `where's the beef?' In other words, was this new approach capable of producing new results, or was it simply an aesthetically pleasing way to restate stuff we already know? The aim of this sequel paper is to say `here's the beef!', and highlight some of the major results of the approach advocated in Kindergarten Quantum Mechanics, and how they are being applied to tackle practical problems on real quantum computers. We will focus mainly on what has become the Swiss army knife of the pictorial formalism: the ZX-calculus. First we look at some of the ideas behind the ZX-calculus, comparing and contrasting it with the usual quantum circuit formalism. We then survey results from the past 2 years falling into three categories: (1) completeness of the rules of the ZX-calculus, (2) state-of-the-art quantum circuit optimisation results in commercial and open-source quantum compilers relying on ZX, and (3) the use of ZX in translating real-world stuff like natural language into quantum circuits that can be run on today's (very limited) quantum hardware. We also take the title literally, and outline an ongoing experiment aiming to show that ZX-calculus enables children to do cutting-edge quantum computing stuff. If anything, this would truly confirm that `kindergarten quantum mechanics' wasn't just a joke.

READ FULL TEXT

page 6

page 7

research
02/08/2019

Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus

We present a new circuit-to-circuit optimisation routine based on an equ...
research
05/05/2022

Completeness of Sum-Over-Paths for Toffoli-Hadamard and the Clifford Hierarchy

The "Sum-Over-Paths" formalism is a way to symbolically manipulate linea...
research
07/26/2023

Rewriting and Completeness of Sum-Over-Paths in Dyadic Fragments of Quantum Computing

The "Sum-Over-Paths" formalism is a way to symbolically manipulate linea...
research
10/27/2022

Programming with Quantum Mechanics

Quantum computing is an emerging paradigm that opens a new era for expon...
research
09/26/2017

Towards a Minimal Stabilizer ZX-calculus

The stabilizer ZX-calculus is a rigorous graphical language for reasonin...
research
03/06/2023

Basic ZX-calculus for students and professionals

These are the lecture notes of guest lectures for Artur Ekert's course I...
research
07/19/2021

On the Quantum-like Contextuality of Ambiguous Phrases

Language is contextual as meanings of words are dependent on their conte...

Please sign up or login with your details

Forgot password? Click here to reset