# Understanding and improving the efficiency of full configuration interaction quantum Monte Carlo.

@article{Vigor2016UnderstandingAI, title={Understanding and improving the efficiency of full configuration interaction quantum Monte Carlo.}, author={W. A. Vigor and James S. Spencer and Michael J. Bearpark and Alex J. W. Thom}, journal={The Journal of chemical physics}, year={2016}, volume={144 9}, pages={ 094110 } }

Within full configuration interaction quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per time step and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree…

## 14 Citations

### Validation of the Ability of Full Configuration Interaction Quantum Monte Carlo for Studying the 2D Hubbard Model

- Physics
- 2017

To validate the ability of full configuration interaction quantum Monte Carlo (FCIQMC) for studying the 2D Hubbard model near half-filling regime, the ground state energies of a 4 x 4 square lattice…

### The HANDE-QMC Project: Open-Source Stochastic Quantum Chemistry from the Ground State Up.

- PhysicsJournal of chemical theory and computation
- 2019

The HANDE-QMC code is described, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations, allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively.

### Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations.

- Physics, ChemistryThe Journal of chemical physics
- 2019

The recently proposed idea of identifying the most important higher-than-doubly excited determinants in the ground-state coupled-cluster (CC) calculations through stochastic configuration interaction Quantum Monte Carlo propagations is extended to excited electronic states via the equation-of-motion (EOM) CC methodology.

### Improved Fast Randomized Iteration Approach to Full Configuration Interaction.

- MathematicsJournal of chemical theory and computation
- 2020

Three modifications to the recently introduced fast randomized iteration method for full configuration interaction (FCI-FRI) are presented and a new approach to sampling excitations is developed that yields consistent improvements in statistical efficiency and reductions in computational cost.

### Stochastic coupled cluster theory: Efficient sampling of the coupled cluster expansion.

- ChemistryThe Journal of chemical physics
- 2017

We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behavior of a…

### Iterative multireference configuration interaction

- Chemistry, Physics
- 2019

Iterative multireference configuration interaction (IMRCI) is proposed. It is exploited to compute the electronic energies of H $_2$ O and CH $_2$ (singlet and triplet states) at equilibrium and…

### Investigating anharmonic effects in condensed matter systems

- Physics
- 2018

This thesis presents work done on the calculation of the effects of anharmonic nuclear motion on the properties of solid materials from first principles. Such anharmonic effects can be significant in…

### Approximating Matrix Eigenvalues by Subspace Iteration with Repeated Random Sparsification

- Computer ScienceSIAM J. Sci. Comput.
- 2022

This work presents a general approach to extending Iterative random sparsification methods for the estimation of multiple eigenvalues and demonstrates its performance for several benchmark problems in quantum chemistry.

### Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification.

- ChemistryJournal of chemical theory and computation
- 2022

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full…

### Approximating matrix eigenvalues by randomized subspace iteration

- Computer ScienceArXiv
- 2021

This work presents a general approach to extending Randomized iterative methods for the estimation of multiple eigenvalues and demonstrates its performance for problems in quantum chemistry with matrices as large as 28 million by 28 million.

## References

SHOWING 1-10 OF 47 REFERENCES

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

- PhysicsThe Journal of chemical physics
- 2012

It is explained 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.

### Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application.

- Computer ScienceThe Journal of chemical physics
- 2015

An alternate method for generating the deterministic space without a priori knowledge of the wave function is presented and stochastic efficiencies for a variety of both molecular and lattice systems are presented.

### Interaction picture density matrix quantum Monte Carlo.

- PhysicsThe Journal of chemical physics
- 2015

It is demonstrated that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions, and benchmark calculations for a four-electron system are provided.

### An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo.

- ChemistryThe Journal of chemical physics
- 2012

Pilot calculations on the binding curve for the carbon dimer demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FC IQMC calculations, and that the F12 correction improves results equivalent to increasing the quality of the one-electron basis by two cardinal numbers.

### Strategies for improving the efficiency of quantum Monte Carlo calculations.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

A technique to maximize the efficiency of the linear extrapolation of diffusion Monte Carlo results to zero time step is proposed, finding that a relative time-step ratio of 1:4 is optimal.

### Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states.

- PhysicsThe Journal of chemical physics
- 2013

A novel quantum Monte Carlo method in configuration space, which stochastically samples the contribution from a large secondary space to the effective Hamiltonian in the energy dependent partitioning of Löwdin avoiding significant amount of the negative sign problem.

### Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo.

- PhysicsThe Journal of chemical physics
- 2015

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.

### Minimising biases in full configuration interaction quantum Monte Carlo.

- BusinessThe Journal of chemical physics
- 2015

It is shown that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov chain in its present form and a reweight ing scheme to remove the bias caused by population control commonly used in diffusion Monte Carlo is effective.

### Communication: Excited states, dynamic correlation functions and spectral properties from full configuration interaction quantum Monte Carlo.

- PhysicsThe Journal of chemical physics
- 2012

This method allows for stable sampling with respect to collapse to lower energy states and requires no uncontrolled approximations, and it is shown that the propagator can directly yield frequency-domain correlation functions and spectral functions such as the density of states which are difficult to obtain within a traditional quantum Monte Carlo framework.

### Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models.

- PhysicsThe Journal of chemical physics
- 2012

The fixed-shift phase of the i-FCIQMC can be used to effectively assess stochastic and initiator error, and the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds.