TY - JOUR
T1 - Tensor network non-zero testing
JF - Quantum Information & Computation
Y1 - 2015
A1 - Sevag Gharibian
A1 - Zeph Landau
A1 - Seung Woo Shin
A1 - Guoming Wang
AB - 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.
VL - 15
U4 - 885-899
UR - http://arxiv.org/abs/1406.5279
CP - 9-10
ER -