• Corpus ID: 249921415

Simplification Strategies for the Qutrit ZX-Calculus

@inproceedings{TownsendTeague2021SimplificationSF,
  title={Simplification Strategies for the Qutrit ZX-Calculus},
  author={Alex Townsend-Teague and Konstantinos Meichanetzidis},
  year={2021}
}
The ZX-calculus is a graphical language for suitably represented tensor networks, called ZX-diagrams. Calculations are performed by transforming ZX-diagrams with rewrite rules. The ZX-calculus has found applications in reasoning about quantum circuits, condensed matter systems, quantum algo-rithms, quantum error correcting codes, and counting problems. A key notion is the stabiliser fragment of the ZX-calculus, a subfamily of ZX-diagrams for which rewriting can be done efficiently in terms of… 

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References

SHOWING 1-10 OF 33 REFERENCES
ZX-calculus for the working quantum computer scientist
TLDR
This review discusses Clifford computation and graphically prove the Gottesman-Knill theorem, a recently introduced extension of the ZX-calculus that allows for convenient reasoning about Toffoli gates, and the recent completeness theorems that show that, in principle, all reasoning about quantum computation can be done using Zx-diagrams.
Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
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.
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
ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
TLDR
A new graphical calculus is presented that is sound and complete for universal quantum computation by demonstrating the reduction of any diagram to an easily describable normal form, which suggests that this calculus will be significantly more convenient for reasoning about the interplay between classical non-linear behaviour and purely quantum operations.
Interacting Quantum Observables: Categorical Algebra and Diagrammatics
TLDR
The ZX-calculus is introduced, an intuitive and universal graphical calculus for multi-qubit systems, which greatly simplifies derivations in the area of quantum computation and information and axiomatize phase shifts within this framework.
Phase gadget compilation for diagonal qutrit gates
Phase gadgets have proved to be an indispensable tool for reasoning about ZX-diagrams, being used in optimisation and simulation of quantum circuits and the theory of measurement-based quantum
Qutrit ZX-calculus is Complete for Stabilizer Quantum Mechanics
In this paper, we show that a qutrit version of ZX-calculus, with rules significantly different from that of the qubit version, is complete for pure qutrit stabilizer quantum mechanics, where state
There and back again: A circuit extraction tale
TLDR
This work gives the first circuit-extraction algorithm to work for one-way computations containing measurements in all three planes and having gflow, and brings together several known rewrite rules for measurement patterns and formalise them in a unified notation using the ZX-calculus.
Tensor Network Rewriting Strategies for Satisfiability and Counting
TLDR
It is found that for classes known to be in P, such as $2$SAT and \#XORSAT, the existence of appropriate rewrite rules allows for efficient simplification of the diagram, producing the solution in polynomial time.
On completeness of algebraic ZX-calculus over arbitrary commutative rings and semirings
TLDR
It is proved that the proposed ZX-calculus over an arbitrary commutative ring is complete for matrices over the same ring, via a normal form inspired from matrix elementary operations such as row addition and row multiplication, paving the way for doing elementary number theory in string diagrams.
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