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]
28 questions
16
votes
2 answers
Graphical Calculus for Quantum Circuits
So far I have read a little bit about zx-calculus & y-calculus.
From the first chapter of Reversible Computation:
The zx-calculus is a graphical language for describing quantum systems.
The zx-calculus is an equational theory, based on rewriting…
user820789
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9
votes
4 answers
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?
Daniel Mahler
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9
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1 answer
Explain the representation of the CNOT gate in ZX-calculus
In ZX-calculus, the CNOT gate is represented by this:
Can someone show me why this is true, using just the basic rewriting rules? All books/papers I have seen simply take it without proof, but I can't see why it is true.
NNN
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7
votes
2 answers
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 follows:
As an aside, I would really appreciate it…
Mahathi Vempati
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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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6
votes
1 answer
Getting intuition on the state-injection relations for the generalized $\exp(-iP \pi/8)$ $T$-gates (ideally using ZX calculus)
In Litinsky's paper, there are many circuits relations, like the one below.
The left handside represents the "rotation" $\exp(-i P \phi)$ with $\phi=\pi/8$ with similar definitions for the orange ($\phi=\pi/4$) and gray box ($\phi=\pi/2$) on the…
Marco Fellous-Asiani
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5
votes
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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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
votes
2 answers
Does the ZX calculus allow for Y-axis rotations?
I'm trying to understand how Y-axis rotations are represented in ZX Calculus. In the paper, wikipedia, everywhere I look, it's as if there is no such thing as Y-axis rotations, only X and Z.
I understand that I can translate a Y-axis rotation to X…
RustyToms
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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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3
votes
2 answers
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 measurements (instead of post-selection) and compute the…
Léo Colisson
- 696
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3
votes
1 answer
$CNOT$ teleportation in ZX-calculus: how to simplify my circuit further?
I am stuck in simplyfing the following cNOT teleportation in ZX-calculus. I don't know how to proceed further. The circuit I start from is taken from this thesis (Fig 2.14, page 22).
Which property can I use to simplify the circuit further? Am I…
Marco Fellous-Asiani
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3
votes
1 answer
How do I get correct measurement probabilities in ZX calculus?
I'm learning ZX-calculus, but I'm getting confused when trying to obtain some simple results to compute probabilities for different outcomes.
Here's a simple example where I'm getting lost. Here, a is a Boolean / binary variable.
Given the circuit…
jjgoings
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3
votes
1 answer
Can H-boxes have a copy-like rule in the ZH-calculus with respect to $\pi$ gates?
In the ZX-calculus we have the following rule, which I think it is known as the copy-rule (grey/white colours may be interchanged; with respect to the usual red/green notation the translation is white equivalent to green and grey equivalent to…
R.W
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