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arXiv:2312.14807 · International Journal of Geometric Methods in Modern Physics

The geometry of quantum computing

Elisa Ercolessi, R. Fioresi, THOMAS W. WEBER

Published Jan 18, 2024• 2 citations
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Abstract

In this expository paper, we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and [Formula: see text]-calculus, establishing a connection between quantum computing questions and quantum groups, i.e. Hopf algebras.

DOI
10.1142/s0219887824400115

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Quantum computing is closely related to [Formula: see text]-dimensional topological quantum field theory through its approach in topological quantum computation. The following are notes based on lectures given by the author at the Mathematics Department of George Washington University. The idea is to give a brief introduction and survey of a few basic facts of quantum computing to an audience of non-experts interested in taking a quick look at some of the most important concepts of quantum computing. The author is a topologist with strong interest in the general ideas of quantum computing. The notes touch on how quantum topology enters the field but emphasizes the general ideas of quantum computing in the first place.
Quantum information theory seeks to understand the fundamental limits set by quantum mechanics for information processing tasks. The mathematical aspects of quantum information rely on tools from various fields including mathematical optimization, high-dimensional convex geometry, operator algebras and representation theory. The goal of this meeting is to focus on the mathematical aspects connecting geometry, optimization and quantum information theory and develop new tools to solve some of the open problems at the intersection of these fields.