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We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.

Tensor contractions are ubiquitous in computational chemistry andphysics, where tensors generally represent states or operators andcontractions express the algebra of these quantities. In this context,the states and operators often preserve physical conservation laws,which are manifested as group symmetries in the tensors. These groupsymmetries imply that each tensor has block sparsity and can be storedin a reduced form. For nontrivial contractions, the memory footprint andcost are lowered, respectively, by a linear and a quadratic factor inthe number of symmetry sectors. State-of-the-art tensor contractionsoftware libraries exploit this opportunity by iterating over blocks orusing general block-sparse tensor representations. Both approachesentail overhead in performance and code complexity. With intuition aidedby tensor diagrams, we present a technique, irreducible representationalignment, which enables efficient handling of Abelian group symmetriesvia only dense tensors, by using contraction-specific reduced forms.This technique yields a general algorithm for arbitrary group symmetriccontractions, which we implement in Python and apply to a variety ofrepresentative contractions from quantum chemistry and tensor networkmethods. As a consequence of relying on only dense tensor contractions,we can easily make use of efficient batched matrix multiplication viaIntel’s MKL and distributed tensor contraction via the Cyclops library,achieving good efficiency and parallel scalability on up to 4096 KnightsLanding cores of a supercomputer.

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.