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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

In 2008 Coecke and Duncan proposed the graphical ZX-calculus rewrite system which came to formalize reasoning with quantum circuits, measurements and quantum states. The ZX-calculus is sound for qubit quantum mechanics. Hence, equality of…

Quantum Physics · Physics 2023-01-18 J Biamonte , A Nasrallah

We propose a quantum programming language that generalizes the $\lambda$-calculus. The language is non-linear; duplicated variables denote, not cloning of quantum data, but sharing a qubit's state; that is, producing an entangled pair of…

Quantum Physics · Physics 2023-03-31 Nicklas Botö , Fabian Forslund

While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum programming. The current work…

Logic in Computer Science · Computer Science 2016-05-18 Ichiro Hasuo , Naohiko Hoshino

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

Graphical calculi are vital tools for representing and reasoning about quantum circuits and processes. Some are not only graphically intuitive but also logically complete. The best known of these is the ZX-calculus, which is an industry…

Quantum Physics · Physics 2020-03-24 Hector Miller-Bakewell

Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…

Quantum Physics · Physics 2018-06-07 Alwin Zulehner , Robert Wille

Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…

Quantum Physics · Physics 2007-05-23 Philippe Jorrand , Marie Lalire

Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they…

Logic in Computer Science · Computer Science 2011-03-17 Bob Coecke , Aleks Kissinger , Alex Merry , Shibdas Roy

Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the…

Quantum Physics · Physics 2015-05-13 David Collins

Quantum computing (QC) represents the future of computing systems, but the tools for reasoning about the quantum model of computation, in which the laws obeyed are those on the quantum mechanical scale, are still a mix of linear algebra and…

Software Engineering · Computer Science 2021-11-17 Carmelo R. Cartiere

The ZX calculus is a mathematical tool to represent and analyse quantum operations by manipulating diagrams which in effect represent tensor networks. Two families of nodes of these networks are ones which commute with either Z rotations or…

Quantum Physics · Physics 2021-09-07 Niel de Beaudrap

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

Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…

Quantum Physics · Physics 2016-02-24 Ashley Montanaro

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 involve differentiation and integration remain…

Quantum Physics · Physics 2024-10-09 Quanlong Wang , Richie Yeung , Mark Koch

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 a universal graphical language for qubit quantum computation, meaning that every linear map between qubits can be expressed in the ZX-calculus. Furthermore, it is a complete graphical rewrite system: any equation…

Quantum Physics · Physics 2023-08-22 Boldizsár Poór , Quanlong Wang , Razin A. Shaikh , Lia Yeh , Richie Yeung , Bob Coecke

In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…

Quantum Physics · Physics 2016-11-03 Dorit Aharonov

With the potential of quantum algorithms to solve intractable classical problems, quantum computing is rapidly evolving and more algorithms are being developed and optimized. Expressing these quantum algorithms using a high-level language…

Quantum Physics · Physics 2020-05-28 N. Khammassi , I. Ashraf , J. v. Someren , R. Nane , A. M. Krol , M. A. Rol , L. Lao , K. Bertels , C. G. Almudever

Quantum computing exploits quantum phenomena such as superposition and entanglement to realize a form of parallelism that is not available to traditional computing. It offers the potential of significant computational speed-ups in quantum…