Related papers: A diagrammatic calculus of fermionic quantum circu…
Diagrammatic techniques for reasoning about monoidal categories provide an intuitive understanding of the symmetries and connections of interacting computational processes. In the context of categorical quantum mechanics, Coecke and…
Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation. Mathematically, it is formalized in the category FHilb, comprising all finite-dimensional Hilbert spaces and linear maps between…
We introduce a graphical calculus, consisting of a set of fermionic tensors with tensor-network equations, which can be used to perform various computations in fermionic many-body physics purely diagrammatically. The indices of our tensors…
We present a new graphical calculus that is sound and complete for a universal family of quantum circuits, which can be seen as the natural string-diagrammatic extension of the approximately (real-valued) universal family of Hadamard+CCZ…
Mapping fermionic systems to qubits on a quantum computer is often the first step for algorithms in quantum chemistry and condensed matter physics. However, it is difficult to reconcile the many different approaches that have been proposed,…
ZW-calculus is a useful graphical language for pure qubit quantum computing. It is via the translation of the completeness of ZW-calculus that the first proof of completeness of ZX-calculus was obtained. A d-level generalisation of qubit…
In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
We introduce fermionic machine learning (FermiML), a machine learning framework based on fermionic quantum computation. FermiML models are expressed in terms of parameterized matchgate circuits, a restricted class of quantum circuits that…
Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this…
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…
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…
Simulating complex systems remains an ongoing challenge for classical computers, while being recognised as a task where a quantum computer has a natural advantage. In both digital and analogue quantum simulations the system description is…
This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantum field theories. We discuss the connection between…
The ZW-calculus is a graphical language capable of representing 2-dimensional quantum systems (qubit) through its diagrams, and manipulating them through its equational theory. We extend the formalism to accommodate finite dimensional…
We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where…
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…
Categorical quantum mechanics and the Wolfram model offer distinct but complementary approaches to studying the relationship between diagrammatic rewriting systems over combinatorial structures and the foundations of physics; the objective…
We introduce diagrammatic differentiation for tensor calculus by generalising the dual number construction from rigs to monoidal categories. Applying this to ZX diagrams, we show how to calculate diagrammatically the gradient of a linear…
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…