Minimising biases in full configuration interaction quantum Monte Carlo

Abstract

Articles you may be interested in A deterministic alternative to the full configuration interaction quantum Monte Carlo method J. Chem. Phys. 145, 044112 (2016); 10.1063/1.4955109 Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application Approaching exact hyperpolarizabilities via sum-overstates Monte Carlo configuration interaction Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models Unbiased stochastic sampling of the one-and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation. C 2015 AIP Publishing LLC. [http://dx.

Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo

“…We observed this systematic deviation of the two estimators for different systems and was also reported in Ref. [8]. To understand it, let us consider Eq.…”

“…The population control bias has often been neglected in FCIQMC because it is usually much smaller than the statistical error bars or other biases [8]. Indeed, for any system with a fermionic sign problem, the original full FCIQMC algorithm needs a minimum number of walkers, below which the sign-incoherent noise dominates the simulation and the dynamics of the walkers become unstable.…”

“…Ref. [8] borrowed a reweighting procedure developed originally for DMC and showed numerically that it effectively corrects the projected energy estimates. We provide a derivation of this reweighting procedure within FCIQMC and adapt it for correcting the shift estimator.…”

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

“…Otherwise, their value becomes v i = t. In practice, we usually set t = 1. By using this approach, the length of the vectors c (n) can be much smaller than the dimension of the Hilbert space while the expectation value of c (n) still approaches the exact eigenvector of the ground state of H. At the same time, the shift S (n) equilibrates to fluctuating around the ground state eigenvalue with a small stochastic bias [68,71]. The spawning process described above differs from the original one of Ref.…”

Improved Fast Randomized Iteration Approach to Full Configuration Interaction

“…Even with this constraint, the average of the iterates does not converge to the exact groundstate eigenvector after infinitely many iterations, as they depend on a quotient of correlated random numbers (eq A3). 50 In typical calculations, the magnitude of this bias is often less than the standard error.…”