Related papers: A diagrammatic calculus for categorical quantum pr…
This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al) to braided systems. In our view a uniform description of quantum information for braided systems has not yet…
In this paper, we extend past work done on the application of the mathematics of category theory to quantum information science. Specifically, we present a realization of a dagger-compact category that can model finite-dimensional quantum…
In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this…
Categorical quantum mechanics exploits the dagger compact closed structure of finite dimensional Hilbert spaces, and uses the graphical calculus of string diagrams to facilitate reasoning about finite dimensional processes. A significant…
We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann, at a more abstract level, of compact closed categories…
Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and…
We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
We reconstruct finite-dimensional quantum theory from categorical principles. That is, we provide properties ensuring that a given physical theory described by a dagger compact category in which one may `discard' objects is equivalent to a…
Toy models have been used to separate important features of quantum computation from the rich background of the standard Hilbert space model. Category theory, on the other hand, is a general tool to separate components of mathematical…
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…
This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus…
Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of…
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…
We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. The key idea is to define two systems, one modelling…
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…
Formal methods have been a successful approach for modelling and verifying the correctness of complex technologies like microprocessor chip design, biological systems and others. This is the main motivation of developing quantum formal…
Despite the rapid development of quantum computing these years, state-of-the-art quantum devices still contain only a very limited number of qubits. One possible way to execute more realistic algorithms in near-term quantum devices is to…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…