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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How to represent a general 3-qubit state as a symmetric ZX-diagram with 14 parameters?
A general pure 1-qubit state can be written as a ZX-diagram like this:
Correspondingly, for a general pure 2-qubit state:
How can a general pure 3-qubit state be written as a ZX-diagram?
Two things ...
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Deformation rules for ZX "pipe" diagrams
If I consider the 3-dimensional structures from https://arxiv.org/abs/1905.08916, these would form a nice 3-dimensional structure for surface code layouts, except I'm not sure what the equivalence ...
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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. ...
- 1,998
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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....
- 1,998
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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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