The ZX-calculus is a high-level and intuitive graphical language for pure qubit quantum mechanics (QM), based on category theory. (arXiv: 1602.04744)
A Simplified Stabilizer ZX-calculus
arXiv:1602.04744 [quant-ph]
Questions tagged [zx-calculus]
23 questions
7
votes
2 answers
ZX-calculus: pi-copy rule not required for completeness?
In ZX-calculus, the $\pi$-copy rule is quite famous, and is used for instance here:
However, this paper never introduces this rule, and says that this set is enough to prove the Clifford completeness of the ZX calculus:
Is it just that they forgot…
Léo Colisson
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5
votes
1 answer
ZX-Calculus: understand clifford+T/general ZX rules
This paper that proves the completeness of the ZX-Calculus introduces different gates:
and
However, they seem very cryptic to me (except maybe the rule E). What is the intuition (what they mean, and how they where obtained) behind these rules? I…
Léo Colisson
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4
votes
1 answer
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 to use the rules wrongly:
In the middle of a…
Martin Vesely
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4
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3 answers
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 an application in assembler instead of in higher…
Martin Vesely
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4
votes
1 answer
Is it possible to implement the ZX-calculus bialgebra rule without adaptivity or post-selection?
In the ZX-calculus, one of the fundamental rules of the diagrammatic reasoning is known as the bialgebra rule and it is described by the given diagrammatic equation:
Question: Can we implement this diagram without using post-selection or…
R.W
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2
votes
2 answers
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:
I'm starting to learn about ZX-Calculus, and I…
Léo Colisson
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1
vote
1 answer
ZX-calculus: meaning of no horizontal edge
Consider the following ZX-diagram:
As you can notice, there are some nodes, belonging the same qubit, which are not connected by any edge (neither blue or black).
What is the meaning of that (during circuit extraction)? Can I assume a black edge?
Daniele Cuomo
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1
vote
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ZX Calculus -- proving the most basic of identities
I'm trying to show the following equivalence in the ZX calculus:
This is equivalent to showing that $$|0\rangle - i|1\rangle = |+\rangle + i|-\rangle.$$
I want to do this using the rules listed on Wikipedia, but am struggling. I tried applying the…
T.H
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0
votes
1 answer
Rewriting a contradictory ZX loop into an independent pi node
Consider the following ZX graph:
If you perform tensor contraction on this graph, you get the zero tensor. Therefore it should be equivalent to this graph:
How do you rewrite the graph, axiom by axiom, to get from the attached loop to the…
Craig Gidney
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