Tensor network non-zero testing
Abstract
Tensor networks are a central tool in condensed matter physics. In this paper, we study the task 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.
Keywords
Cite
@article{arxiv.1406.5279,
title = {Tensor network non-zero testing},
author = {Sevag Gharibian and Zeph Landau and Seung Woo Shin and Guoming Wang},
journal= {arXiv preprint arXiv:1406.5279},
year = {2019}
}
Comments
15 pages, 4 figures. v2: Published version (QIC)