A Caltech Library Service

Improving the efficiency of variational tensor network algorithms

Evenbly, Glen and Pfeifer, Robert N. C. (2014) Improving the efficiency of variational tensor network algorithms. Physical Review B, 89 (24). Art. No. 245118. ISSN 1098-0121. doi:10.1103/PhysRevB.89.245118.

PDF - Published Version
See Usage Policy.

[img] Other (Matlab .m) - Supplemental Material
See Usage Policy.

PDF (Instructions) - Supplemental Material
See Usage Policy.

PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed tensor network T, we prove that if the environment of a single tensor from the network can be evaluated with computational cost κ, then the environment of any other tensor from T can be evaluated with identical cost κ. Moreover, we describe how the set of all single tensor environments from T can be simultaneously evaluated with fixed cost 3κ. The usefulness of these results, which are applicable to a variety of tensor network methods, is demonstrated for the optimization of a multiscale entanglement renormalization Ansatz for the ground state of a one-dimensional quantum system, where they are shown to substantially reduce the computation time.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper DOIArticle Material
Additional Information:© 2014 American Physical Society. Received 7 February 2014; revised manuscript received 13 May 2014; published 12 June 2014. G.E. is supported by the Sherman Fairchild foundation. R.N.C.P. gratefully acknowledges the Ontario Ministry of Research and Innovation Early Researcher Awards for financial support. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Ontario Ministry of Research and Innovation Early Researcher AwardsUNSPECIFIED
Government of CanadaUNSPECIFIED
Industry CanadaUNSPECIFIED
Province of Ontario Ministry of Research and InnovationUNSPECIFIED
Issue or Number:24
Classification Code:PACS: 05.30.−d, 02.70.−c, 75.10.Jm, 04.60.Pp
Record Number:CaltechAUTHORS:20140807-101932641
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48177
Deposited By: Tony Diaz
Deposited On:07 Aug 2014 20:59
Last Modified:10 Nov 2021 18:04

Repository Staff Only: item control page