Related papers: Quantum Hoare Type Theory: Extended Abstract
Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has…
We present the Quantum Hamiltonian Analysis Toolkit (QHAT), a newly developed application that provides a user-friendly interface for studying Hamiltonians and performing Hamiltonian simulation on fault-tolerant quantum computers. QHAT…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
We propose a 2-categorical formalism for describing classical information, quantum systems, and their interactions, based on the principle that classical information can be encoded as correlations between quantum systems. Applying this in…
We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement…
We explore the possibility of accelerating the formal verification of classical programs with a quantum computer. A common source of security flaws stems from the existence of common programming errors like use after free, null-pointer…
Quantum computing promises to tackle technological and industrial problems insurmountable for classical computers. However, today's quantum computers still have limited demonstrable functionality, and it is expected that scaling up to…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
As we enter the post-Moore era, we experience the rise of various non-von-Neumann-architectures to address the increasing computational demand for modern applications, with quantum computing being among the most prominent and promising…
The framework Pure Type System (PTS) offers a simple and general approach to designing and formalizing type systems. However, in the presence of dependent types, there often exist certain acute problems that make it difficult for PTS to…
Recursive techniques have recently been introduced into quantum programming so that a variety of large quantum circuits and algorithms can be elegantly and economically programmed. In this paper, we present a proof system for formal…
Most machine learning models, especially artificial neural networks, require numerical, not categorical data. We briefly describe the advantages and disadvantages of common encoding schemes. For example, one-hot encoding is commonly used…
Guarded recursion is a powerful modal approach to recursion that can be seen as an abstract form of step-indexing. It is currently used extensively in separation logic to model programming languages with advanced features by solving domain…
Clocked Cubical Type Theory is a new type theory combining the power of guarded recursion with univalence and higher inductive types (HITs). This type theory can be used as a metalanguage for synthetic guarded domain theory in which one can…
Classical program analysis techniques, such as abstract interpretation and symbolic execution, are essential for ensuring software correctness, optimizing performance, and enabling compiler optimizations. However, these techniques face…
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on…
While we expect quantum computers to surpass their classical counterparts in the future, current devices are prone to high error rates and techniques to minimise the impact of these errors are indispensable. There already exists a variety…