---
_id: '8168'
abstract:
- lang: eng
text: "Tensor networks are a central tool in condensed matter physics. In this paper,
we initiate the study of tensor network non-zero testing (TNZ): Given a tensor
network T, does T represent a non-zero vector? We show that TNZ is not in the
Polynomial-Time Hierarchy unless the hierarchy collapses. We next show (among
other results) that the special cases of TNZ on non-negative and injective tensor
networks are in NP. Using this, we make a simple observation: The commuting variant
of the MA-complete stoquastic k-SAT problem on D-dimensional qudits is in NP for
logarithmic k and constant D. This reveals the first class of quantum Hamiltonians
whose commuting variant is known to be in NP for all (1) logarithmic k, (2) constant
D, and (3) for arbitrary interaction graphs.\r\n"
article_type: original
author:
- first_name: Sevag
full_name: Gharibian, Sevag
id: '71541'
last_name: Gharibian
orcid: 0000-0002-9992-3379
- first_name: Zeph
full_name: Landau, Zeph
last_name: Landau
- first_name: Seung
full_name: Woo Shin, Seung
last_name: Woo Shin
- first_name: Guoming
full_name: Wang, Guoming
last_name: Wang
citation:
ama: Gharibian S, Landau Z, Woo Shin S, Wang G. Tensor network non-zero testing.
Quantum Information & Computation. 2015;15(9{\ & }10):885-899.
apa: Gharibian, S., Landau, Z., Woo Shin, S., & Wang, G. (2015). Tensor network
non-zero testing. Quantum Information & Computation, 15(9{\
& }10), 885–899.
bibtex: '@article{Gharibian_Landau_Woo Shin_Wang_2015, title={Tensor network non-zero
testing}, volume={15}, number={9{\ & }10}, journal={Quantum Information &
Computation}, author={Gharibian, Sevag and Landau, Zeph and Woo Shin, Seung and
Wang, Guoming}, year={2015}, pages={885–899} }'
chicago: 'Gharibian, Sevag, Zeph Landau, Seung Woo Shin, and Guoming Wang. “Tensor
Network Non-Zero Testing.” Quantum Information & Computation 15, no.
9{\ & }10 (2015): 885–99.'
ieee: S. Gharibian, Z. Landau, S. Woo Shin, and G. Wang, “Tensor network non-zero
testing,” Quantum Information & Computation, vol. 15, no. 9{\ &
}10, pp. 885–899, 2015.
mla: Gharibian, Sevag, et al. “Tensor Network Non-Zero Testing.” Quantum Information
& Computation, vol. 15, no. 9{\ & }10, 2015, pp. 885–99.
short: S. Gharibian, Z. Landau, S. Woo Shin, G. Wang, Quantum Information &
Computation 15 (2015) 885–899.
date_created: 2019-03-01T11:53:08Z
date_updated: 2023-02-28T11:02:35Z
department:
- _id: '623'
- _id: '7'
extern: '1'
external_id:
arxiv:
- '1406.5279'
intvolume: ' 15'
issue: 9{\&}10
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1406.5279
oa: '1'
page: 885-899
publication: Quantum Information & Computation
publication_status: published
status: public
title: Tensor network non-zero testing
type: journal_article
user_id: '71541'
volume: 15
year: '2015'
...