Related papers: Colored props for large scale graphical reasoning
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…
The application of diagrammatic reasoning techniques to large-scale quantum processes needs specific tools to describe families of diagrams of arbitrary size. For now, large-scale diagrammatic reasoning tools in ZH-calculus come in two…
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…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
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…
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…
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…
The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor networks that can represent arbitrary linear maps between qubits. Using the ZX-calculus, we can intuitively reason about quantum theory, and optimise…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
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…
Graphical languages offer intuitive and rigorous formalisms for quantum physics. They can be used to simplify expressions, derive equalities, and do computations. Yet in order to replace conventional formalisms, rigour alone is not…
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…
Colors play a crucial role in the design of vector graphic documents by enhancing visual appeal, facilitating communication, improving usability, and ensuring accessibility. In this context, color recommendation involves suggesting…
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…
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…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We propose a colored PROP to model computation in this framework,…
Graph problems are fundamentally challenging for large language models (LLMs). While LLMs excel at processing unstructured text, graph tasks require reasoning over explicit structure, permutation invariance, and computationally complex…
Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The…