English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes

Zheng, Y., He, H., Regnault, N., & Bernevig, B. A. (2019). Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes. Physical Review B, 99(15): 155129. doi:10.1103/PhysRevB.99.155129.

Item is

Files

show Files
hide Files
:
PhysRevB.99.155129.pdf (Publisher version), 3MB
 
File Permalink:
-
Name:
PhysRevB.99.155129.pdf
Description:
Archivkopie
OA-Status:
Visibility:
Private
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show
hide
Locator:
https://doi.org/10.1103/PhysRevB.99.155129 (Publisher version)
Description:
-
OA-Status:

Creators

show
hide
 Creators:
Zheng, Yunqin1, Author
He, Huan1, Author
Regnault, Nicolas1, Author
Bernevig, B. Andrei2, Author
Affiliations:
1External Organizations, ou_persistent22              
2Max Planck Institute of Microstructure Physics, Max Planck Society, Weinberg 2, 06120 Halle, DE, ou_2415691              

Content

show
hide
Free keywords: -
 Abstract: We discuss the relations between restricted Boltzmann machine (RBM) states and the matrix product states (MPS) for the ground states of 1D translational invariant stabilizer codes. A generic translational invariant and finitely connected RBM state can be expressed as an MPS, and the matrices of the resulting MPS are of rank 1. We dub such an MPS as an RBM-MPS. This provides a necessary condition for exactly realizing a quantum state as an RBM state, if the quantum state can be written as an MPS. For generic 1D stabilizer codes having a nondegenerate ground state with periodic boundary condition, we obtain an expression for the lower bound of their MPS bond dimension, and an upper bound for the rank of their MPS matrices. In terms of RBM, we provide an algorithm to derive the RBM for the cocycle Hamiltonians whose MPS matrices are proved to be of rank 1. Moreover, the RBM-MPS produced by our algorithm has the minimal bond dimension. A family of examples is provided to explain the algorithm. We finally conjecture that these features hold true for all the 1D stabilizer codes having a nondegenerate ground state with periodic boundary condition, as long as their MPS matrices are of rank 1.

Details

show
hide
Language(s):
 Dates: 2019-04-152019-04-15
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: P13738
DOI: 10.1103/PhysRevB.99.155129
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Physical Review B
  Abbreviation : Phys. Rev. B
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: Woodbury, NY : American Physical Society
Pages: - Volume / Issue: 99 (15) Sequence Number: 155129 Start / End Page: - Identifier: ISSN: 1098-0121
CoNE: https://pure.mpg.de/cone/journals/resource/954925225008