Quantum Information

Hyperbolic band theory

Speaker: 
Joseph Maciejko
Date: 
Wed, Jun 9, 2021
Location: 
Zoom
Online
Conference: 
CMS Scientific Session on Quantum Mathematics
Abstract: 

The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit QED, I will present a hyperbolic generalization of Bloch theory, based on ideas from Riemann surface theory and algebraic geometry. The theory is formulated despite the non-Euclidean nature of the problem and concomitant absence of commutative translation symmetries. The general theory will be illustrated by examples of explicit computations of hyperbolic Bloch wavefunctions and bandstructures.

Class: 
Scientific
Subject: 
Mathematics
Physics
Condensed Matter and Statistical Mechanics
Quantum Physics
Quantum Information
Quantum Computing

Random walks and graphs in materials, biology, and quantum information science

Speaker: 
Maria Emelianenko
Date: 
Wed, Apr 14, 2021
Location: 
Zoom
PIMS, University of Saskachewan
Conference: 
quanTA CRG Seminar
Abstract: 

What does mathematics, materials science, biology, and quantum
information science have in common? It turns out, there are many
connections worth exploring. I this talk, I will focus on graphs and random
walks, starting from the classical mathematical constructs and moving on to
quantum descriptions and applications. We will see how the notions of graph
entropy and KL divergence appear in the context of characterizing
polycrystalline material microstructures and predicting their performance
under mechanical deformation, while also allowing to measure adaptation in
cancer networks and entanglement of quantum states. We will discover
unified conditions under which master equations for classical random walks
exhibit nonlocal and non-diffusive behavior and see how quantum walks allow
to realize the coveted exponential speedup in quantum Hamiltonian
simulations. Recent classical and quantum breakthroughs and open questions
will be discussed.

For other events in this series see the quanTA events website.

Class: 
Scientific
Subject: 
Mathematics
Biology
Physics
Condensed Matter and Statistical Mechanics
Materials Science
Quantum Information

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