# A non-anyonic qudit ZW-calculus

@inproceedings{Wang2021ANQ, title={A non-anyonic qudit ZW-calculus}, author={Quanlong Wang}, year={2021} }

ZW-calculus is a useful graphical language for pure qubit quantum computing. It is via the translation of the completeness of ZW-calculus that the ﬁrst proof of completeness of ZX-calculus was obtained. A d-level generalisation of qubit ZW-calculus (anyonic qudit ZW-calculus) has been given in [7] which is universal for pure qudit quantum computing. However, the interpretation of the W spider in this type of ZW-calculus has so-called q-binomial coe ﬃ cients involved, thus makes computation…

## 4 Citations

### Qufinite ZX-calculus: a unified framework of qudit ZX-calculi

- Mathematics, Computer Science
- 2021

This paper generalises qubit ZX-calculus to qudit ZX -calculus in any ﬁnite dimension by introducing suitable generators, especially a carefully chosen triangle node, and obtains a set of rewriting rules which can be seen as a direct generalisation of qubit rules, and a normal form for any qudit vectors.

### Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions

- Computer ScienceMFCS
- 2022

A family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions are introduced, and it is proved that these calculi are complete, i.e. provide a set of rewrite rules which can be used to prove any equality of stabiliser quantum operations.

### Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning

- Computer Science
- 2022

The new analytic framework of ZX-calculus is illustrated by applying it in context of quantum machine learning for the analysis of barren plateaus by elevating ZX to an analytical perspective.

### Differentiating and Integrating ZX Diagrams

- MathematicsArXiv
- 2022

ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that…

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This paper generalises qubit ZX-calculus to qudit ZX -calculus in any ﬁnite dimension by introducing suitable generators, especially a carefully chosen triangle node, and obtains a set of rewriting rules which can be seen as a direct generalisation of qubit rules, and a normal form for any qudit vectors.

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Extended versions of ZW and ZX calculus are presented, and their completeness for pure-state qubit theory is proved by a strategy that rewrites all diagrams into a normal form, thus solving two major open problems in categorical quantum mechanics.

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This paper presents a full graphical axiomatisation of the relations between GHZ and W: the ZW calculus, which refines a version of the preexisting ZX calculus, while keeping its most desirable characteristics: undirected ness, a large degree of symmetry, and an algebraic underpinning.

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In this paper we give a complete axiomatisation of qubit ZX-calculus via elementary transformations which are basic operations in linear algebra. This formalism has two main advantages. First, all…

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