English
Related papers

Related papers: The ZX&-calculus: A complete graphical calculus fo…

200 papers

Loop quantum gravity (LQG) attempts to unify general relativity with quantum physics to offer a complete description of the universe by quantising spacetime geometry, but the numerical calculations we encounter are extraordinarily…

General Relativity and Quantum Cosmology · Physics 2025-11-21 Ben Priestley

Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more…

Quantum Physics · Physics 2023-02-28 Anastasiia S. Nikolaeva , Evgeniy O. Kiktenko , Aleksey K. Fedorov

Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the \textit{directed acyclic graph} (DAG) configurations of undirected graphs in graph…

Quantum Physics · Physics 2025-07-25 Selomit Ramírez-Uribe , Andrés E. Rentería-Olivo , Germán Rodrigo

Quantum circuit cutting refers to a series of techniques that allow one to partition a quantum computation on a large quantum computer into several quantum computations on smaller devices. This usually comes at the price of a sampling…

Quantum Physics · Physics 2025-12-09 Marco Schumann , Tobias Stollenwerk , Alessandro Ciani

The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less…

Quantum Physics · Physics 2024-05-28 Akash Sinha , Pramod Padmanabhan , Vladimir Korepin

Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of…

Quantum Physics · Physics 2016-04-20 Bobby Antonio

The discard ZX-calculus is known to be complete and universal for mixed-state quantum mechanics, allowing for both quantum and classical processes. However, if the quantum aspects of ZX-calculus have been explored in depth, little work has…

Quantum Physics · Physics 2025-08-07 Titouan Carette , Daniela Cojocaru , Renaud Vilmart

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

We present a complete optimization procedure for hybrid quantum-classical circuits with classical parity logic. While common optimization techniques for quantum algorithms focus on rewriting solely the pure quantum segments, there is…

Quantum Physics · Physics 2022-06-22 Agustín Borgna , Simon Perdrix , Benoît Valiron

We introduce the Spin-ZX calculus as an elevation of Penrose's diagrams and associated binor calculus to the level of a formal diagrammatic language. The power of doing so is illustrated by the variety of scientific areas we apply it to:…

Quantum Physics · Physics 2025-11-11 Quanlong Wang , Richard D. P. East , Razin A. Shaikh , Lia Yeh , Boldizsár Poór , Bob Coecke

Multiplication over binary fields is a crucial operation in quantum algorithms designed to solve the discrete logarithm problem for elliptic curve defined over $GF(2^n)$. In this paper, we present an algorithm for constructing quantum…

Quantum Physics · Physics 2025-01-28 Vivien Vandaele

We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by…

High Energy Physics - Theory · Physics 2020-12-02 Songyuan Li , Jan Troost

We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic…

We introduce the first complete and approximatively universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum…

Quantum Physics · Physics 2018-02-26 Emmanuel Jeandel , Simon Perdrix , Renaud Vilmart

The ZX calculus and ZH calculus use diagrams to denote and compute properties of quantum operations, using `rewrite rules' to transform between diagrams which denote the same operator through a functorial semantic map. Different semantic…

Quantum Physics · Physics 2024-08-26 Niel de Beaudrap , Richard D. P. East

We describe a generalization of Gabriel and Zisman's Calculus of Fractions to quasicategories, showing that the two essentially coincide for the nerve of a category. We then prove that the marked Ex-functor can be used to compute the…

Algebraic Topology · Mathematics 2025-08-19 Daniel Carranza , Chris Kapulkin , Zachery Lindsey

Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…

Quantum Physics · Physics 2007-05-23 A. Kawaguchi , K. Shimizu , Y. Tokura , N. Imoto

We propose a universal set of single- and two-qubit quantum gates acting on a hybrid qubit formed by coupling a quantum dot spin qubit to a $\mathbb{Z}_{2m}$ parafermion qubit with arbitrary integer $m$. The special case $m=1$ reproduces…

Mesoscale and Nanoscale Physics · Physics 2024-06-03 Denis V. Kurlov , Melina Luethi , Anatoliy I. Lotkov , Katharina Laubscher , Jelena Klinovaja , Daniel Loss

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

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…