On the Algebra of Qubit Quantum States: Part I - String Diagrams, Non-Orthogonal Factorizations, and the Tropical Kernel Algebra of Parent Hamiltonians

Speaker: Jacob Biamonte (Jing Dong Chair Research Professor, BIMSA)

Date:    2023.03.17

Time:   09:30-10:30 am

Venue: Jin Chun Yuan West Building,  the First Meeting Room (近春园西楼第一会议室）

Tencent Meeting ID: 494 8360 9451

Abtract：

We consider the algebraic properties of quantum states represented as polynomials that map binary tuples to complex numbers. Using string diagrams, we review the general factorization results previously established in joint work with Clark, and Jaksch, and explore ongoing developments related to non-orthogonal factorizations based on graded algebra expansions. By imposing a real-valued codomain restriction on these functions, penalty functions are generated that correspond to generalized Ising-type models. We recall the concept of a parent Hamiltonian, a non-negative operator that has a specific state in its zero energy sector, and explain the algebra necessary to control the kernel structure of non-negative pseudo-Boolean functions that represent parent Hamiltonians of quantum states. Our results contribute to the ongoing development of mathematical tools for analyzing and manipulating quantum states, with applications in quantum information science. 

Biography:

Dr. Biamonte's research career has been dedicated to studying the theoretical aspects of quantum information processing, specifically at the interface between quantum applications and physical hardware constraints.

He has held positions as a quantum applications developer at D-Wave Systems Inc. in Vancouver, Canada, and as a Fellow at Harvard University in the Aspuru-Guzik Group. In 2010, Dr. Biamonte obtained his PhD from the University of Oxford. He then worked as a postdoctoral researcher with John Carlos Baez as part of a joint Oxford/Singapore program and as a Lecturer at St Peter's College Oxford before joining the Institute for Scientific Interchange (ISI Foundation) in Torino, Italy as their Quantum Science Group Leader from 2012-2017.

In 2017, Dr. Biamonte joined the Skolkovo Institute of Science and Technology as a Tenure Track Associate Professor. He was subsequently promoted to Head of the Laboratory for Quantum Information Processing and then to tenured Full Professor. Dr. Biamonte was the first American-born scientist to have successfully defended a higher Doctorate at the Moscow Institute of Physics and Technology. Unfortunately, his time in Moscow was cut short due to the war against Ukraine. Dr. Biamonte currently holds the Jingdong Foundation Chair at the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications.

Dr. Biamonte's research vision is to develop a data-driven approach to quantify emergent and collective effects in quantum information processing. He is also a dedicated educator, teaching applied and engineering mathematics, quantum information theory, and quantum computation.

[YMSC-BIMSA Quantum Information Seminar]