Related papers: Mathematical methods for resource-based type theor…
The field of quantum resource theory (QRT) has emerged as an invaluable framework for the examination of small and strongly correlated quantum systems, surpassing the boundaries imposed by traditional statistical treatments. The fundamental…
As new advancements in the field of quantum computing lead to the development of increasingly complex programs, approaches to validate and debug these programs are becoming more important. To this end, methods employed in classical…
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.…
An automated resource analysis technique is introduced, targeting a Call-By-Push-Value abstract machine, with memory prediction as a practical goal. The machine has a polymorphic and linear type system enhanced with a first-order logical…
Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…
In this paper, we study quantitative properties of quantum programs. Properties of interest include (positive) almost-sure termination, expected runtime or expected cost, that is, for example, the expected number of applications of a given…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with a sound type system using the notion of environment classifiers. They are special identifiers, with which code fragments and variable declarations are annotated,…
We present a graded modal type theory, a dependent type theory with grades that can be used to enforce various properties of the code. The theory has $\Pi$-types, weak and strong $\Sigma$-types, natural numbers, an empty type, and a…
Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in…
To formalize calculations in linear algebra for the development of efficient algorithms and a framework suitable for functional programming languages and faster parallelized computations, we adopt an approach that treats elements of linear…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…
Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms.…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
Because of the probabilistic/nondeterministic behavior of quantum programs, it is highly advisable to verify them formally to ensure that they correctly implement their specifications. Formal verification, however, also traditionally…
We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial…
Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…
Session types statically prescribe bidirectional communication protocols for message-passing processes and are in a Curry-Howard correspondence with linear logic propositions. However, simple session types cannot specify properties beyond…
Quantum information processing relies on a variety of resources, including entanglement, coherence, non-Gaussianity, and magic. In realistic settings, protocols run on networks of parties with heterogeneous local resource constraints, so…