相关论文: Beyond Penrose tensor diagrams with the ZX calculu…
The ZX-Calculus is a graphical language for quantum mechanics. An axiomatisation has recently been proven to be complete for an approximatively universal fragment of quantum mechanics, the so-called Clifford+T fragment. We focus here on the…
The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum mechanics and quantum information theory. It comes equipped with an equational presentation. We focus here on a very important property of the language:…
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…
Tensor networks provide a natural language for non-invertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a non-invertible operator implementing…
ZX-calculus is a graphical language for quantum computing which is complete in the sense that calculation in matrices can be done in a purely diagrammatic way. However, all previous universally complete axiomatisations of ZX-calculus have…
String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…
From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalysed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation,…
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…
This article presents a novel algorithmic methodology for performing automated diagrammatic deductions over combinatorial structures, using a combination of modified equational theorem-proving techniques and the extended Wolfram model…
The ZX-calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. We prove that its \pi/4-fragment is not complete, in other words the ZX-calculus is not complete for the so called "Clifford+T…
While the ZX and ZW calculi have been effective as graphical reasoning tools for finite-dimensional quantum computation, the possibilities for continuous-variable quantum computation (CVQC) in infinite-dimensional Hilbert space are only…
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…
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…
The "Spinors" software is a "Mathematica" package which implements 2-component spinor calculus as devised by Penrose for General Relativity in dimension 3+1. The "Spinors" software is part of the "xAct" system, which is a collection of…
Quantum computations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantum computing, where the graphical syntax…
Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a…
ZX-calculus is a strict mathematical formalism for graphical quantum computing which is based on the field of complex numbers. In this paper, we extend its power by generalising ZX-calculus to such an extent that it is universal both in an…
Quantum computers allow a near-exponential speed-up for specific applications when compared to classical computers. Despite recent advances in the hardware of quantum computers, their practical usage is still severely limited due to a…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…
Categorical Quantum Mechanics, and graphical calculi in particular, has proven to be an intuitive and powerful way to reason about quantum computing. This work continues the exploration of graphical calculi, inside and outside of the…