We present a whole series of methods to alleviate the sign problem of the fermionic shadow wave function in the context of variational Monte Carlo. The effectiveness of our techniques is demonstrated on liquid ^{3}He. We found that although the variance is reduced, the gain in efficiency is restricted by the increased computational cost. Yet, this development not only extends the scope of the fermionic shadow wave function, but also facilitates highly accurate quantum Monte Carlo simulations previously thought not feasible.

Inspired by the universal approximation theorem and widespread adoption of artificial neural network techniques in a diversity of fields, feed‐forward neural networks are proposed as a general purpose trial wave function for quantum Monte Carlo simulations of continuous many‐body systems. Whereas for simple model systems the whole many‐body wave function can be represented by a neural network, the antisymmetry condition of non‐trivial fermionic systems is incorporated by means of a Slater determinant. To demonstrate the accuracy of the trial wave functions, an exactly solvable model system of two trapped interacting particles, as well as the hydrogen dimer, is studied.

-We demonstrate that extending the Shadow Wave Function to fermionic systems facilitates to accurately calculate strongly-correlated multi-reference systems such as the stretched H2 molecule. This development considerably extends the scope of electronic structure calculations and enables to efficiently recover the static correlation energy using just a single Slater determinant.Introduction. -One of the most outstanding problems of computational physics and quantum chemistry is the ability to devise a quantitatively precise, yet computationally tractable, method to accurately break a chemical bond across an entire reaction coordinate. A particularly simple example is the H 2 molecule, in particular when the covalent bond between the H atoms is stretched. Effective single-particle theories, such as the widely employed Hartree-Fock (HF) or Density Functional Theory (DFT) methods, describe the covalent bond well, but the energy is severely overestimated upon dissociation [1]. This wellknown problem is attributed to the multi-reference character of the stretched H 2 molecule, or static electron correlation that arises in situations with degeneracy or neardegeneracy, as in transition metal chemistry and stronglycorrelated systems in general [2]. As a consequence, the stretched H 2 molecule and similar problems are typically dealt with using multi-determinant wave functions [3]. However, for larger systems with many degeneracies, the number of determinants quickly becomes unfeasible [4,5].

We revisit the pressure-induced metal-insulator-transition of solid hydrogen by means of variational quantum Monte Carlo simulations based on the antisymmetric shadow wave function. In order to facilitate studying the electronic structure of large-scale fermionic systems, the shadow wave function formalism is extended by a series of technical improvements, such as a revised optimization method for the employed shadow wave function and an enhanced treatment of periodic systems with long-range interactions. It is found that the superior accuracy of the antisymmetric shadow wave function results in a significantly increased transition pressure. arXiv:1604.05804v3 [physics.comp-ph]