  Due to the strong correlations present in quantum systems, classical machine
learning algorithms like stochastic gradient descent are often insufficient for
the training of neural network quantum states (NQSs). These difficulties can be
overcome by using physically inspired learning algorithm, the most prominent of
which is the stochastic reconfiguration (SR) which mimics imaginary time
evolution. Here we explore an alternative algorithms for the optimization of
complex valued NQSs based on the linear method (LM), and present the explicit
formulation in terms of complex valued parameters. Beyond the theoretical
formulation, we present numerical evidence that the LM can be used successfully
for the optimization of complex valued NQSs, to our knowledge for the first
time. We compare the LM to the state-of-the-art SR algorithm and find that the
LM requires up to an order of magnitude fewer iterations for convergence,
albeit at a higher cost per epoch. We further demonstrate that the LM becomes
the more efficient training algorithm whenever the cost of sampling is high.
This advantage, however, comes at the price of a larger variance.
