# Questions tagged [zx-calculus]

The ZX-calculus is a high-level and intuitive graphical language for pure qubit quantum mechanics (QM), based on category theory. (arXiv: 1602.04744)

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### Graphical Calculus for Quantum Circuits

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 ...
4answers
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### Controlled Hadamard gate in ZX-calculus

What is the representation of the CH gate in ZX-calculus? Is there a general recipe for going from a ZX-calculus representation of a gate to the representation of the controlled version?
1answer
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### CNOT gate in ZX-calculus

In ZX-calculus, the CNOT gate is represented by this: Can someone show my why this is true, using just the basic rewriting rules? All books/papers I have seen simply take it without proof, but I can'...
2answers
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### Diagrammatic Quantum Reasoning: Proving the loop equation using yanking equations

I'm trying to study the book: Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning, and would like some help with Exercise 4.12: The relevant equations are as ...
1answer
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### ZX calculus: What do diamond and loop mean?

Recently, I started to study practical application of ZX calculus but I am confused by meaning of "diamond" and "loop". Issue no. 1: There are these rules: B-rule and D-rule But this example seems ...
1answer
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### What are some applications of the ZX calculus?

Recently, I came across ZX calculus. It is an interesting method to describe quantum circuits. However, it seems to me, too complicated for day-to-day use in circuit design (something like to program ...
2answers
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### ZX-Calculus: how to prove this simple equation between two very small circuits

Short version: How could I prove in ZX-calculus that these two diagrams are equal (up to a global phase), using axioms from this paper (Fig. 1) for example? Any intuition is welcome! Long version:...
1answer
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### ZX-calculus : measurement and output probabilities

I'm discovering ZX-Calculus, and it seems to be much easier to do computations on circuit that would take much more time with the usual formalism. However, I can't find a nice way to represent ...