CONFERENCE PROCEEDINGS
Advanced Search
Home > Proceedings > Volume 11391 > Article
Presentation
24 April 2020 Entanglement and the topology of tensor nets (Conference Presentation)
Louis H. Kauffman
Author Affiliations +
Proceedings Volume 11391, Quantum Information Science, Sensing, and Computation XII; 113910H (2020) https://doi.org/10.1117/12.2557860
Event: SPIE Defense + Commercial Sensing, 2020, Online Only
Abstract
This talk will explain the structure of Khovanov homology for knots and links and will present a quantum algorithm for its computation that is based on the use of combinatorial Hodge theory. By using combinatorial Hodge theory we can formulate the problem of computing the homology in terms of the determination of the dimension of the eigenvalue one subspace of a unitary operator that is associated with the boundary and coboundary operators of the Khovanov complex. We then use the quantum phase estimation algorithm to find the dimension of this subspace. This is a first foray into the problems of producing a quantum algorithm for the significant knot and link invariant Khovanov homology. There are other deeper problems related to the structure of the chain complex and we shall discuss these difficulties. This paper represents joint work with Sam Lomonaco and Nadya Shirakova.
Conference Presentation
© (2020) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Citation Download Citation
Louis H. Kauffman "Entanglement and the topology of tensor nets (Conference Presentation)", Proc. SPIE 11391, Quantum Information Science, Sensing, and Computation XII, 113910H (24 April 2020); https://doi.org/10.1117/12.2557860
ACCESS THE FULL ARTICLE
ORGANIZATIONAL
Sign in with credentials provided by your organization.
INSTITUTIONAL
Select your institution to access the SPIE Digital Library.
SELECT YOUR INSTITUTION
PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.
PERSONAL SIGN IN
No SPIE Account? Create one
PURCHASE THIS CONTENT
SUBSCRIBE TO DIGITAL LIBRARY
50 downloads per 1-year subscription
Members: $195
Non-members: $335 ADD TO CART
25 downloads per 1 - year subscription
Members: $145
Non-members: $250 ADD TO CART
PURCHASE SINGLE ARTICLE
Includes PDF, HTML & Video, when available
Members: $17.00
Non-members: $21.00 ADD TO CART
PROCEEDINGS
 PRESENTATION
WATCH
PRESENTATION SAVE TO MY LIBRARY
GET CITATION
Advertisement
Advertisement
KEYWORDS
Quantum computing
Algorithms
Quantum physics
RELATED CONTENT
Subscribe to Digital Library
Receive Erratum Email Alert
Back to Top