TY - JOUR
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.
AU - Gharibian, Sevag
AU - Landau, Zeph
AU - Woo Shin, Seung
AU - Wang, Guoming
ID - 8168
IS - 9{\&}10
JF - Quantum Information & Computation
TI - Tensor network non-zero testing
VL - 15
ER -