Related papers: Quantum Picturalism
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
Quantum theory is often regarded as challenging to learn and teach, with advanced mathematical prerequisites ranging from complex numbers and probability theory to matrix multiplication, vector space algebra and symbolic manipulation within…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
Recently there has been much interest in deriving the quantum formalism and the set of quantum correlations from simple axioms. In this paper, we provide a step-by-step derivation of the quantum formalism that tackles both these problems…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
The cognitive state of mind concerning a range of choices to be made can effectively be modelled in terms of an element of a high-dimensional Hilbert space. The dynamics of the state of mind resulting form information acquisition is…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
Quantum physics education at the upper-secondary level traditionally follows a historical approach, rarely extending beyond early 20th-century ideas, leaving students unprepared for comprehending modern quantum technologies central to…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…
The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of…
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
Quantum computing is captured in the formalism of the monoidal subcategory of $\textbf{Vect}_{\mathbb C}$ generated by $\mathbb C^2$ -- in particular, quantum circuits are diagrams in $\textbf{Vect}_{\mathbb C}$ -- while topological quantum…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…
The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition…
The quantum-classical isomorphism for self-consistent field theory, which allows quantum particles in space-time to be represented as classical one-dimensional threads embedded in a five dimensional thermal-space-time, is summarized and…
We are at the dawn of the second quantum revolution, where our ability to create and control individual quantum systems is poised to drive transformative advancements in basic science, computation, and everyday life. However, quantum theory…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
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…