English
Related papers

Related papers: PyZX: Large Scale Automated Diagrammatic Reasoning

200 papers

Optimizing quantum circuits is a key challenge for quantum computing. The PyZX compiler broke new ground by optimizing circuits via the ZX calculus, a powerful graphical alternative to the quantum circuit model. Still, it carries no…

Quantum Physics · Physics 2022-05-20 Adrian Lehmann , Ben Caldwell , Robert Rand

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, measurement-based…

Quantum Physics · Physics 2020-12-29 John van de Wetering

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…

Computational Complexity · Computer Science 2022-06-22 Alex Townsend-Teague , Konstantinos Meichanetzidis

Graphical languages are a convenient shorthand to represent computation, with rewrite rules relating one graph to another. In contrast, proof assistants rely heavily on inductive datatypes, particularly when giving semantics to embedded…

Programming Languages · Computer Science 2026-04-09 Adrian Lehmann , Ben Caldwell , Bhakti Shah , William Spencer , Robert Rand

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…

Quantum Physics · Physics 2020-07-31 Titouan Carette , Dominic Horsman , Simon Perdrix

The ZX-calculus is a graphical language for reasoning about quantum computation using ZX-diagrams, a certain flexible generalisation of quantum circuits that can be used to represent linear maps from $m$ to $n$ qubits for any $m,n \geq 0$.…

Quantum Physics · Physics 2022-09-05 Niel de Beaudrap , Aleks Kissinger , John van de Wetering

The Scalable ZX-calculus is a compact graphical language used to reason about linear maps between quantum states. These diagrams have multiple applications, but they frequently have to be constructed in a case-by-case basis. In this work we…

Quantum Physics · Physics 2023-11-17 Augustin Borgna , Rafael Romero

The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective…

Quantum Physics · Physics 2014-09-22 Miriam Backens

ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machine-based asynchronous model of both pure…

Logic in Computer Science · Computer Science 2022-08-04 Kostia Chardonnet , Benoît Valiron , Renaud Vilmart

ZX-calculus is graphical language for quantum computing which usually focuses on qubits. In this paper, we generalise qubit ZX-calculus to qudit ZX-calculus in any finite dimension by introducing suitable generators, especially a carefully…

Quantum Physics · Physics 2022-09-20 Quanlong Wang

Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…

Quantum Physics · Physics 2023-01-12 Robert Wille , Lukas Burgholzer , Stefan Hillmich , Thomas Grurl , Alexander Ploier , Tom Peham

We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations…

Quantum Physics · Physics 2020-07-01 Ross Duncan , Aleks Kissinger , Simon Perdrix , John van de Wetering

The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics.The language is sound and complete: a stabilizer ZX-diagram can be transformed into another one if and only if these two diagrams represent…

Quantum Physics · Physics 2017-01-04 Miriam Backens , Simon Perdrix , Quanlong Wang

Diagrammatic representations of quantum algorithms and circuits offer novel approaches to their design and analysis. In this work, we describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in…

Quantum Physics · Physics 2023-11-16 Tobias Stollenwerk , Stuart Hadfield

The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum…

Quantum Physics · Physics 2021-09-14 Titouan Carette , Yohann D'Anello , Simon Perdrix

Systematic discovery of optimization paths in quantum circuit simplification remains a challenge. Today, ZX-calculus, a computing model for quantum circuit transformation, is attracting attention for its highly abstract graph-based…

Programming Languages · Computer Science 2025-11-20 Kayo Tei , Haruto Mishina , Naoki Yamamoto , Kazunori Ueda

The ZX-calculus is a graphical language for reasoning about quantum computing and quantum information theory. As a complete graphical language, it incorporates a set of axioms rich enough to derive any equation of the underlying formalism.…

Quantum Physics · Physics 2025-08-21 Boldizsár Poór , Razin A. Shaikh , Quanlong Wang

The ZX-calculus is a powerful framework for reasoning in quantum computing. It provides in particular a compact representation of matrices of interests. A peculiar property of the ZX-calculus is the absence of a formal sum allowing the…

Quantum Physics · Physics 2024-08-07 Emmanuel Jeandel , Simon Perdrix , Margarita Veshchezerova

The ZX-calculus is an intuitive but also mathematically strict graphical language for quantum computing, which is especially powerful for the framework of quantum circuits. Completeness of the ZX-calculus means any equality of matrices with…

Quantum Physics · Physics 2023-05-18 Quanlong Wang

The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics. The language is sound and complete: one can transform a stabilizer ZX-diagram into another one using the graphical rewrite rules if and only…

Quantum Physics · Physics 2023-06-22 Miriam Backens , Simon Perdrix , Quanlong Wang
‹ Prev 1 2 3 10 Next ›