N. S. Blunt

The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method

The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of the nodal structure of the ground-state wave function. We investigate the nature of the sign problem in this method and how its severity depends on the system studied. We explain how cancellation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations.

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.

Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application

We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.

An excited-state approach within full configuration interaction quantum Monte Carlo

We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method due to a comparable computational cost. As a first application, we consider the carbon dimer in basis sets up to quadruple-zeta quality and compare to existing results where available.

PySCF: the Python‐based simulations of chemistry framework

Python‐based simulations of chemistry framework (PySCF) is a general‐purpose electronic structure platform designed from the ground up to emphasize code simplicity, so as to facilitate new method development and enable flexible computational workflows. The package provides a wide range of tools to support simulations of finite‐size systems, extended systems with periodic boundary conditions, low‐dimensional periodic systems, and custom Hamiltonians, using mean‐field and post‐mean‐field methods with standard Gaussian basis functions. To ensure ease of extensibility, PySCF uses the Python language to implement almost all of its features, while computationally critical paths are implemented with heavily optimized C routines. Using this combined Python/C implementation, the package is as efficient as the best existing C or Fortran‐based quantum chemistry programs. In this paper, we document the capabilities and design philosophy of the current version of the PySCF package. WIREs Comput Mol Sci 2018, 8:e1340. doi: 10.1002/wcms.1340

Density-matrix quantum Monte Carlo method

We present a quantum Monte Carlo method capable of sampling the full density matrix of a many-particle system at finite temperature. This allows arbitrary reduced density matrix elements and expectation values of complicated nonlocal observables to be evaluated easily. The method resembles full configuration interaction quantumMonteCarlobutworksinthespaceofmany-particleoperatorsinsteadofthespaceofmany-particlewave functions. One simulation provides the density matrix at all temperatures simultaneously, from T =∞ to T = 0, allowing the temperature dependence of expectation values to be studied. The direct sampling of the density matrix also allows the calculation of some previously inaccessible entanglement measures. We explain the theory underlying the method, describe the algorithm, and introduce an importance-sampling procedure to improve the stochastic efficiency. To demonstrate the potential of our approach, the energy and staggered magnetization of the isotropic antiferromagnetic Heisenberg model on small lattices, the concurrence of one-dimensional spin rings, and the Renyi S2 entanglement entropy of various sublattices of the 6 × 6 Heisenberg model are calculated. The nature of the sign problem in the method is also investigated.

Interaction picture density matrix quantum Monte Carlo

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

Open-Source Development Experiences in Scientific Software: The HANDE Quantum Monte Carlo Project

J. S. Spencer, 2, ∗ N. S. Blunt, W. A. Vigor, F. D. Malone, W. M. C. Foulkes, James J. Shepherd, and A. J. W. Thom ∗ Department of Materials, Imperial College London, Exhibition Road, London, SW7 2AZ, United Kingdom Department of Physics, Imperial College London, Exhibition Road, London, SW7 2AZ, United Kingdom University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW, United Kingdom Department of Chemistry, Imperial College London, Exhibition Road, London, SW7 2AZ, United Kingdom Department of Chemistry, Rice University, Houston, TX 77005-1892, USA (Dated: July 22, 2014)

QMCPACK: An open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids

QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the programs capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.

Density matrices in full configuration interaction quantum Monte Carlo: Excited states, transition dipole moments, and parallel distribution

We present developments in the calculation of reduced density matrices (RDMs) in the full configuration interaction quantum Monte Carlo (FCIQMC) method. An efficient scheme is described to allow storage of RDMs across distributed memory, thereby allowing their calculation and storage in large basis sets. We demonstrate the calculation of RDMs for general states by using the recently introduced excited-state FCIQMC approach [N. S. Blunt et al., J. Chem. Phys. 143, 134117 (2015)] and further introduce calculation of transition density matrices in the method. These approaches are combined to calculate excited-state dipole and transition dipole moments for heteronuclear diatomic molecules, including LiH, BH, and MgO, and initiator error is investigated in these quantities.