# SZX-Calculus: Scalable Graphical Quantum Reasoning

@inproceedings{Carette2019SZXCalculusSG, title={SZX-Calculus: Scalable Graphical Quantum Reasoning}, author={Titouan Carette and Dominic C. Horsman and Simon Perdrix}, booktitle={MFCS}, year={2019} }

We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that captures graphically the fundamental properties of quantum mechanics through its complete set of rewrite rules. The ZX-calculus is, however, a low level language, with each wire representing a single qubit. This limits its ability to handle large and…

## 21 Citations

Quantum Algorithms and Oracles with the Scalable ZX-calculus

- Computer ScienceElectronic Proceedings in Theoretical Computer Science
- 2021

This work considers the standard oracle-based quantum algorithms: Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Grover, and shows they can be described and proved graphically.

ZX-calculus for the working quantum computer scientist

- Computer Science
- 2020

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.

LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits

- Computer ScienceArXiv
- 2022

The LO v -calculus is introduced, a graphical language for reasoning about linear optical quantum circuits with so-called vacuum state auxiliary inputs, and the axiomatics of the language are presented and its soundness and completeness are proved.

Complete ZX-calculi for the stabiliser fragment in odd prime dimensions

- Mathematics
- 2022

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…

Graphical Calculi and their Conjecture Synthesis

- Computer Science
- 2020

This work continues the exploration of graphical calculi, inside and outside of the quantum computing setting, by investigating the algebraic structures with which the authors label diagrams, and introduces two important new calculi here.

The ZX calculus is a language for surface code lattice surgery

- Computer ScienceQuantum
- 2020

The operations of the ZX calculus -- a form of quantum diagrammatic reasoning based on bialgebras -- match exactly the operations of lattice surgery, and ZX diagram re-write rules give lattice operations for these operations that are novel, efficient, and highly configurable.

DisCoPy for the quantum computer scientist

- Computer Science
- 2022

This report gives a short presentation of DisCoPy as a toolbox for the quantum computer scientist and a review of its recent developments.

A Superposition-Based Calculus for Diagrammatic Reasoning

- Mathematics, Computer SciencePPDP
- 2021

A class of rooted graphs which are expressive enough to encode various kinds of classical or quantum circuits are introduced and a new Superposition calculus is proposed to check the unsatisfiability of formulas consisting of equations or disequations over these graphs.

The Structure of Sum-Over-Paths, its Consequences, and Completeness for Clifford

- Computer ScienceFoSSaCS
- 2021

We show that the formalism of “Sum-Over-Path” (SOP), used for symbolically representing linear maps or quantum operators, together with a proper rewrite system, has the structure of a dagger-compact…

An Automated Deductive Verification Framework for Circuit-building Quantum Programs

- Computer ScienceESOP
- 2021

Qbricks is proposed, a formal verification environment for circuit-building quantum programs, featuring both parametric specifications and a high degree of proof automation, and the main tool is developed, PPS, a parametric extension of the recently developed path sum semantics.

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