English
Related papers

Related papers: Encoding High-level Quantum Programs as SZX-diagra…

200 papers

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

Circuit description languages are a class of quantum programming languages in which programs are classical and produce a description of a quantum computation, in the form of a quantum circuit. Since these programs can leverage all the…

Programming Languages · Computer Science 2023-11-01 Andrea Colledan , Ugo Dal Lago

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

Graphical calculi such as the ZH-calculus are powerful tools in the study and analysis of quantum processes, with links to other models of quantum computation such as quantum circuits, measurement-based computing, etc. A somewhat compact…

Quantum Physics · Physics 2021-07-05 Renaud Vilmart

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

Graphical languages, like quantum circuits or ZX-calculus, have been successfully designed to represent (memoryless) quantum computations acting on a finite number of qubits. Meanwhile, delayed traces have been used as a graphical way to…

Quantum Physics · Physics 2021-04-29 Titouan Carette , Marc de Visme , Simon Perdrix

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

In this paper, we introduce a technique for contracting (i.e. numerically evaluating) ZX-diagrams whose complexity scales with their rank-width, a graph parameter that behaves nicely under ZX rewrite rules. Given a rank-decomposition of…

Quantum Physics · Physics 2026-03-10 Fedor Kuyanov , Aleks Kissinger

Quipper is a domain-specific programming language for the description of quantum circuits. Because it is implemented as an embedded language in Haskell, Quipper is a very practical functional language. However, for the same reason, it lacks…

Programming Languages · Computer Science 2021-05-11 Andrea Colledan

Quipper is a recently developed programming language for expressing quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate…

Programming Languages · Computer Science 2013-07-08 Alexander S. Green , Peter LeFanu Lumsdaine , Neil J. Ross , Peter Selinger , Benoît Valiron

We develop a linear logical framework within the Hybrid system and use it to reason about the type system of a quantum lambda calculus. In particular, we consider a practical version of the calculus called Proto-Quipper, which contains the…

Logic in Computer Science · Computer Science 2018-12-11 Mohamed Yousri Mahmoud , Amy P. Felty

Classical program analysis techniques, such as abstract interpretation and symbolic execution, are essential for ensuring software correctness, optimizing performance, and enabling compiler optimizations. However, these techniques face…

Quantum Physics · Physics 2025-10-14 Yicheng Guang , Pietro Zanotta , Kai Zhou , Yueqi Chen , Ramin Ayanzadeh

This note describes how the the scalable ZXH calculus can be used to represent in a compact way the quantum gates that are diagonal in the computational basis. This includes controlled and multi-controlled Z gates, their generalizations,…

Quantum Physics · Physics 2020-12-18 Titouan Carette

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

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 quantum processes with built-in rewrite rules. The rewrite rules allow equalities to be derived entirely graphically, leading to the question of completeness: can any equality that is derivable…

Quantum Physics · Physics 2015-11-06 Miriam Backens

Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed…

Logic in Computer Science · Computer Science 2020-08-11 Titouan Carette , Emmanuel Jeandel

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

Quipper is a functional programming language for quantum computing. Proto-Quipper is a family of languages aiming to provide a formal foundation for Quipper. In this paper, we extend Proto-Quipper-M with a construct called dynamic lifting,…

Programming Languages · Computer Science 2022-11-10 Peng Fu , Kohei Kishida , Neil J. Ross , Peter Selinger

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