Quantum decimation in Hilbert space: Coarse graining without structure
Abstract
We introduce a technique to coarse grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred set of operators (local or otherwise) in an associated algebra. Rather, we use the data corresponding to a given set of states, either specified independently or constructed from a single state evolving in time. Our method is based on principle component analysis (PCA), and the resulting coarse-grained quantum states live in a lower-dimensional Hilbert space whose basis is defined using the underlying (isometric embedding) transformation of the set of fine-grained states we wish to coarse grain. Physically, the transformation can be interpreted to be an “entanglement coarse-graining” scheme that retains most of the global, useful entanglement structure of each state, while needing fewer degrees of freedom for its reconstruction. This scheme could be useful for efficiently describing collections of states whose number is much smaller than the dimension of Hilbert space, or a single state evolving over time.
- Authors:
-
- California Inst. of Technology (CalTech), Pasadena, CA (United States)
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1597497
- Alternate Identifier(s):
- OSTI ID: 1426014
- Grant/Contract Number:
- SC0011632
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 3; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Singh, Ashmeet, and Carroll, Sean M. Quantum decimation in Hilbert space: Coarse graining without structure. United States: N. p., 2018.
Web. doi:10.1103/PhysRevA.97.032111.
Singh, Ashmeet, & Carroll, Sean M. Quantum decimation in Hilbert space: Coarse graining without structure. United States. https://doi.org/10.1103/PhysRevA.97.032111
Singh, Ashmeet, and Carroll, Sean M. Wed .
"Quantum decimation in Hilbert space: Coarse graining without structure". United States. https://doi.org/10.1103/PhysRevA.97.032111. https://www.osti.gov/servlets/purl/1597497.
@article{osti_1597497,
title = {Quantum decimation in Hilbert space: Coarse graining without structure},
author = {Singh, Ashmeet and Carroll, Sean M.},
abstractNote = {We introduce a technique to coarse grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred set of operators (local or otherwise) in an associated algebra. Rather, we use the data corresponding to a given set of states, either specified independently or constructed from a single state evolving in time. Our method is based on principle component analysis (PCA), and the resulting coarse-grained quantum states live in a lower-dimensional Hilbert space whose basis is defined using the underlying (isometric embedding) transformation of the set of fine-grained states we wish to coarse grain. Physically, the transformation can be interpreted to be an “entanglement coarse-graining” scheme that retains most of the global, useful entanglement structure of each state, while needing fewer degrees of freedom for its reconstruction. This scheme could be useful for efficiently describing collections of states whose number is much smaller than the dimension of Hilbert space, or a single state evolving over time.},
doi = {10.1103/PhysRevA.97.032111},
journal = {Physical Review A},
number = 3,
volume = 97,
place = {United States},
year = {Wed Mar 14 00:00:00 EDT 2018},
month = {Wed Mar 14 00:00:00 EDT 2018}
}
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