• Corpus ID: 229680014

ZX-calculus for the working quantum computer scientist

@inproceedings{Wetering2020ZXcalculusFT,
  title={ZX-calculus for the working quantum computer scientist},
  author={John van de Wetering},
  year={2020}
}
The ZX-calculus is a graphical language for reasoning about quantum computation that has recently seen an increased usage in a variety of areas such as quantum circuit optimisation, surface codes and lattice surgery, measurementbased quantum computation, and quantum foundations. The first half of this review gives a gentle introduction to the ZX-calculus suitable for those familiar with the basics of quantum computing. The aim here is to make the reader comfortable enough with the ZX-calculus… 
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32 Citations
Highly Influential Citations
5
Background Citations
14
Methods Citations
8

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32 Citations

Circuit Extraction for ZX-diagrams can be #P-hard
TLDR
This paper proves that any oracle that takes as input a ZX-diagram description of a unitary and produces samples of the output of the associated quantum computation enables efficient probabilistic solutions to NP-complete problems.
Complete ZX-calculi for the stabiliser fragment in odd prime dimensions
We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions. These calculi recover many of the nice features of the qubit ZX-calculus which…
Spin-networks in the ZX-calculus
TLDR
This paper writes the spin-networks of loop quantum gravity in the ZX-diagrammatic language of quantum computation by writing the Yutsis diagrams, a standard graphical calculus used in quantum chemistry and quantum gravity, which captures the main features of SU(2) representation theory.
Diagrammatic Analysis for Parameterized Quantum Circuits
TLDR
Extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in particular for computing observable expectation values as functions of or for parameters, which are important algorithmic quantities in a variety of applications ranging from combinatorial optimization to quantum chemistry are described.
Simplification Strategies for the Qutrit ZX-Calculus
TLDR
The main contribution of this work is the derivation of efficient rewrite strategies for the stabiliser fragment of the qutrit ZX-calculus, which constitutes a first non-trivial step towards the simplification ofqutrit quantum circuits.
VyZX : A Vision for Verifying the ZX Calculus
TLDR
Vy ZX is developed, a verified ZX-calculus in the Coq proof assistant that provides two distinct representations of ZX diagrams for ease of programming and proof.
Addition and Differentiation of ZX-Diagrams
TLDR
This work introduces a general, inductive definition of the addition of ZX-diagrams, relying on the construction of controlled diagrams, and provides an inductive differentiation of Zx-displays, based on the isolation of variables.
Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions
We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the ‘sum-of-stabilisers’ method with an automated simplification strategy based on the…
Classifying Complexity with the ZX-Calculus: Jones Polynomials and Potts Partition Functions
TLDR
This work presents simplifying rewrites for the case of qutrits, which are of independent interest in the field of quantum circuit optimisation and further champions the ZX-calculus as a suitable and unifying language for studying the complexity of classical and quantum problems.
AKLT-States as ZX-Diagrams: Diagrammatic Reasoning for Quantum States
TLDR
The results show that the ZXH-calculus is a powerful language for representing and computing with physical states entirely graphically, paving the way to develop more efficient many-body algorithms.
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References

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TLDR
A simplification strategy for ZX-diagrams is given based on the two graph transformations of local complementation and pivoting and it is shown that the resulting reduced diagram can be transformed back into a quantum circuit.
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The ZX-calculus is a convenient formalism for expressing and reasoning about quantum circuits at a low level, whereas the recently-proposed ZH-calculus yields convenient expressions of mid-level…
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TLDR
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TLDR
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TLDR
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