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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Using ZX calculus to postselect the first round of a distance-2 rotated surface code
I'm translating gate model language to ZX calculus diagram using such notation, to describe the first round of measurement of such a distance-2 rotated surface code below.
I wrote this diagram where ...
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$CNOT$ 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 ...
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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 ...
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Global (Ising) Gates and ZX-calculus representation
I could find from this source -- but also from other works on ZX-calculus -- the following extract:
This looks to me as a generalisation of a 2-qubit Ising gate to an $n$-qubit global Ising gate. ...
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Zx graphs in Stim
It is possible to create an ASCII graph in Stimzx for a ZX calculus diagram.
I would like to create something like this
but I cannot seem to recreate the correct ASCII format. When I do something ...
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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 ...
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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, <...
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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 ...
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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 ...
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PyZX optimisation steps for Clifford circuits
Given the following ZX-diagram
It should represent some random Clifford circuit (LC means Local Clifford).
As far as I got, any Clifford circuit can be transformed into a ZX-diagram like the above, i....
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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'...
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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 ...
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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 ...
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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:...
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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 ...
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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 ...
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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?
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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 ...
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