Related papers: The Quantum Monadology
Monads provide a simple and concise interface to user-defined computational effects in functional programming languages. This enables equational reasoning about effects, abstraction over monadic interfaces and the development of monad…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
Formalizations of quantum information theory in category theory and type theory, for the design of verifiable quantum programming languages, need to express its two fundamental characteristics: (1) parameterized linearity and (2) metricity.…
As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. In classical computing, formal verification and sound static type systems prevent several classes…
We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is a hybrid classical-quantum computational paradigm. The…
This thesis revolves around an area of computer science called "semantics". We work with operational semantics, equational theories, and denotational semantics. The first contribution of this thesis is a study of the commutativity of…
Monads are a popular tool for the working functional programmer to structure effectful computations. This paper presents polymonads, a generalization of monads. Polymonads give the familiar monadic bind the more general type forall a,b. L a…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in…
Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to…
In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to…
Despite significant advances in quantum computing across various domains, research on applying quantum approaches to language compositionality - such as modeling linguistic structures and interactions - remains limited. This gap extends to…
While the realization of scalable quantum computation will arguably require topological stabilization and, with it, topological-hardware-aware quantum programming and topological-quantum circuit verification, the proper combination of these…
We introduce the abstract notions of "monadic operational semantics", a small-step semantics where computational effects are modularly modeled by a monad, and "type-and-effect system", including "effect types" whose interpretation lifts…
Parameterized stable homotopy theory organizes local systems of spectra over homotopy types, governed by a "yoga" of six functors. To provide semantics for the recently developed Linear Homotopy Type Theory (LHoTT), good model categories of…
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e. the property for an effect to commute…
While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum programming. The current work…
We show that the model of quantum computation based on density matrices and superoperators can be decomposed in a pure classical (functional) part and an effectful part modeling probabilities and measurement. The effectful part can be…