Classical and Quantum CS Theory Seminar: Majorana representation of quantum states and symmetry class of tensors

Speaker: Chi-Kwong Li, College of William & Mary

Title: Majorana representation of quantum states and symmetry class of tensors

Abstract:
By the Majorana representation, for any d > 1 there is a one-one correspondence between a quantum state of dimension d andd − 1 qubits represented as d−1 points in the Bloch (unit) sphere. In this talk, using the theory of symmetry class of tensors, we describe a simple scheme for constructing d − 1 points on the Bloch sphere and the corresponding d − 1 qubits representing a d-dimensional quantum state. Additionally, we demonstrate how the inner product of two d-dimensional quantum states can be expressed as a permanent of a matrix related to their (d−1)-qubit state representations. Extension of the result to mixed states is also discussed. 

A brief bio of Li:

Li is the Ferguson Professor of Mathematics at the College of William & Mary, and is an affiliated member of the Institute for Quantum Computing at the University of Waterloo. His research is on matrix theory, operator theory, combinatorial theory and their applications. He has more than 360 research papers published. He has severed on several editorial boards of journals. (Currently, on “Linear Algebra and its Applications”, “INVOLVE - A Journal of Mathematics”, retired from chief editor positions from “Linear and Multilinear Algebra” and “Operators and Matrices”). He has organized and co-organized many conferences, workshops, symposiums on different topics in matrix and operator theory, served on different positions of the International Linear Algebra Society. He has won a number of awards including the Fulbright Fellowship in 2021 (not able to accept due to the pandemic) and 2011. Very recently, he was selected as a recipient of the 2025 Hans Schneider Prize of the International Linear Algebra Society.

His research has been supported by different grant agencies including the Simons Foundation, NSF, NATO, etc. Besides mathematics, Li likes music and cooking. He plays Chinese flute and cooks Chinese dishes. For more information, one may see:

homepage at http://cklixx.people.wm.edu

CV at http://cklixx.people.wm.edu/vitae.pdf

list of publication at http://cklixx.people.wm.edu/pub.html

Time:  Wednesday, September 25, 12:15pm – 1:15pm

Place:  Exploratory Hall, room 4106