Related papers: Formal Analysis of Quantum Systems using Process C…
Determination of the quantum nature of correlations between two spatially separated systems plays a crucial role in quantum information science. Of particular interest is the questions of if and how these correlations enable quantum…
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…
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…
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…
Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a…
This paper develops a model of quantum behavior that is intended to support the abstract yet accurate design and functional verification of quantum communication protocols. The work is motivated by the need for conceptual tools for the…
Quantum machine learning is emerging as a promising application of quantum computing due to its distinct way of encoding and processing data. It is believed that large-scale quantum machine learning demonstrates substantial advantages over…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
We present a quantum computing approach to analyzing Large Language Model (LLM) embeddings, leveraging complex-valued representations and modeling semantic relationships using quantum mechanical principles. By establishing a direct mapping…
We reformulate quantum computation in terms of Lagrangian (sum-over-path) formalism, in contrast to the widely used Hamiltonian (unitary gate) formulation. We exemplify this formalism with some widely-studied models, including the standard…
We consider two-stage hybrid protocols that combine quantum resource and classical resource to generate classical correlations shared by two separated players. Our motivation is twofold. First, in the near future the scale of quantum…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
The realm of this thesis is cryptographic protocol theory in the quantum world. We study the security of quantum and classical protocols against adversaries that are assumed to exploit quantum effects to their advantage. Security in the…
In this abstract we study the resource consumption of quantum programs. Specifically, we focus on the expected runtime of programs and, inspired by recent methods for probabilistic programs, we develop a calculus \`a la weakest precondition…
In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
Over the past 27 years, quantum computing has seen a huge rise in interest from both academia and industry. At the current rate, quantum computers are growing in size rapidly backed up by the increase of research in the field. Significant…
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and…
Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the…