Description
Neural Quantum States (NQS) are powerful tools used to represent complex quantum
many-body states in an increasingly wide range of applications. However, despite their
popularity, at present only a rudimentary understanding of their limitations exists. In
this work, we investigate the dependence of NQS on the choice of the computational ba-
sis, focusing on restricted Boltzmann machines. Considering a family of rotated Hamil-
tonians corresponding to the paradigmatic transverse-field Ising model, we discuss the
properties of ground states responsible for the dependence of NQS performance, namely
the presence of ground state degeneracies as well as the uniformity of amplitudes and
phases, carefully examining their interplay. We identify that the basis-dependence of
the performance is linked to the convergence properties of a cluster or cumulant ex-
pansion of multi-spin operators—providing a framework to directly connect physical,
basis-dependent properties, to performance itself. Our results provide insights that may
be used to gauge the applicability of NQS to new problems and to identify the optimal
basis for numerical computations.