Classical and quantum computers are vying for superiority

Adrian Lehmann, Ben Caldwell, Bhakti Shah +2 more

Graphical languages are a convenient shorthand to represent computation, with rewrite rules relating one graph to another. In contrast, proof assistants rely heavily on inductive datatypes, particularly when giving semantics to embedded languages. This creates obstacles to formally reasoning about graphical languages, since imposing an inductive structure obfuscates the diagrammatic nature of graphical languages, along with their corresponding equational theories. To address this gap, we present Vy ZX, a verified library for reasoning about inductively defined graphical languages. These inductive constructs arise naturally from category-theoretic definitions. We developed Vy ZX to V erify the ZX -calculus, a graphical language for reasoning about quantum computation. The ZX-calculus comes with a collection of diagrammatic rewrite rules that preserve the graph’s semantic interpretation. We show how inductive graphs in Vy ZX are used to prove the soundness of the ZX-calculus rewrite rules and apply them in practice using standard proof assistant techniques. We also provide an IDE-integrated visualizer for proof engineers to directly reason about diagrams in graphical form.

John Horgan

Jeff Kabachinski

Cheng, Zheng-Wei, You-Kai Wang, Wan Xia

We develop a path integral approach to quantum field theory that is defined over the paths of the Le'vy flights possessing a fractal dimension $1

Steve R. Cloutier

Quantum mechanics has been around since the early 1900s and computers made their first appearance in the late 1930s. In the decades after that, the two came together to bring about quantum computing. A sub field of quantum computing is quantum communications, the ability to transmit a quantum state from one place to another. This communication takes place between two entities. Communication over a classic network involves many entities each vying for network time. This is done through various network protocols, one of them being Medium Access Control (MAC). Although quantum computing is currently a one-to-one medium, it's properties can be used to assist the MAC protocol to enhance it's current abilities. In this thesis, we propose two different quantum communication assisted MAC protocols to achieve shared communication over a classic network. These protocols are based on quantum entanglement principles and contention-free collision avoidance algorithms.