Related papers: Refinement calculus of quantum programs with proje…
We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation and termination analysis for quantum…
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…
The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing…
We propose quaternion-based strategies for quantum error correction by extending quantum mechanics into quaternionic Hilbert spaces. Building on the properties of quaternionic quantum states, we define quaternionic analogues of Pauli…
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…
A syntax-directed formal system for the development of totally correct programs with respect to an unfair shared-state parallel while-language is proposed. The system can be understood as a compositional reformulation of the Owicki/Gries…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
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…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…
Different platforms for quantum computation are currently being developed with a steadily increasing number of physical qubits. To make today's devices practical for quantum software engineers, novel programming tools with maximal…
As we enter a new era of quantum technology, it is increasingly important to develop methods to aid in the accurate preparation of quantum states for a variety of materials, matter, and devices. Computational techniques can be used to…
Guided by grammatical structure, words compose to form sentences, and guided by discourse structure, sentences compose to form dialogues and documents. The compositional aspect of sentence and discourse units is often overlooked by machine…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
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…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so…
While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of…