So far I have read a little bit about zx-calculus & y-calculus.
From Reversible Computation:
The zx-calculus is a graphical language for describing quantum systems.
The zx-calculus is an equational theory, based on rewriting the diagrams which comprise its syntax. Re-writing can be automated by means of the quantomatic software.
This method seems very interesting, however I am not able to find much introductory information on the subject. Any insight into the subject or additional resources would be greatly appreciated.
- ZX-calculus for the working quantum computer scientist
- A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics
- ZX-Rules for 2-qubit Clifford+T Quantum Circuits
- Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus
- Tutorial: Graphical Calculus for Quantum Circuits
- ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
- Tensor networks and graphical calculus for open quantum system
- Papers from Quantomatic
- A survery of graphical languages for monoidal categories (PDF)