Related papers: Categorical Quantum Circuits
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems…
This is the second part of a three-part overview, in which we derive the category-theoretic backbone of quantum theory from a process ontology, treating quantum theory as a theory of systems, processes and their interactions. In this part…
We introduce the category $\mathsf{NCP}$, whose objects are pairs of W$^\ast$-algebras and normal states and whose morphisms are state-preserving unital completely positive (CPU) maps, as a common stage for classical and quantum information…
Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by…
Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
The classification of quantum states into distinct classes poses a significant challenge. In this study, we address this problem using quantum neural networks in combination with a problem-inspired circuit and customised as well as…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the…
Scattering processes in high-energy physics are inherently quantum mechanical, yet are typically analyzed at the level of final states, where entanglement appears as a property of the outcome rather than a consequence of the underlying…
Quantum computing is poised to dramatically change the computational landscape, worldwide. Quantum computers can solve complex problems that are, at least in some cases, beyond the ability of even advanced future classical-style computers.…
We introduce the CP*-construction on a dagger compact closed category as a generalisation of Selinger's CPM-construction. While the latter takes a dagger compact closed category and forms its category of "abstract matrix algebras" and…
Near-term quantum computers can hold only a small number of qubits. One way to facilitate large-scale quantum computations is through a distributed network of quantum computers. In this work, we consider the problem of distributing quantum…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
This report introduces a novel class of reasoning architectures, termed Quantum Circuit Reasoning Models (QCRM), which extend the concept of Variational Quantum Circuits (VQC) from energy minimization and classification tasks to structured…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
Image-based data is a popular arena for testing quantum machine learning algorithms. A crucial factor in realizing quantum advantage for these applications is the ability to efficiently represent images as quantum states. Here we present a…
The advent of noisy-intermediate scale quantum computers has introduced the exciting possibility of achieving quantum speedups in machine learning tasks. These devices, however, are composed of a small number of qubits, and can faithfully…
A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ``quantum dot'') and through the interface between a normal…