Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published March 2018 | Published + Submitted
Journal Article Open

Quantum decimation in Hilbert space: Coarse graining without structure

Abstract

We present 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 technique 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.

Additional Information

© 2018 American Physical Society. Received 6 September 2017; published 14 March 2018. We would like to thank Ning Bao, ChunJun (Charles) Cao, and Jess Riedel for helpful discussions during the course of this project. We are also thankful to an anonymous reviewer for their comments to help improve the manuscript. This material is based upon work supported by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, as well as by the Walter Burke Institute for Theoretical Physics at Caltech and the Foundational Questions Institute.

Attached Files

Published - PhysRevA.97.032111.pdf

Submitted - 1709.01066.pdf

Files

PhysRevA.97.032111.pdf
Files (511.1 kB)
Name Size Download all
md5:04f5f1db7eea1ae0b7c6f9aec13ac7c4
241.2 kB Preview Download
md5:d76e50a48f035e9acd67da8b199b98cf
269.8 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023