The best way to learn quantum Monte Carlo is to do a calculation, and the CASINO manual is now written for that: its first chapter says what a calculation computes, how the two principal methods work, what limits the accuracy of their results and what a calculation costs, for a reader who knows the Schrödinger equation and has met Hartree-Fock or density functional theory but has not used quantum Monte Carlo; a later chapter works through a first calculation from trial wave function to diffusion Monte Carlo; and the methods are then derived in full. The summer schools held at Vallico Sotto taught the same material over a week, with more than twenty hours of lectures.

Reviews

• W. M. C. Foulkes, L. Mitas, R. J. Needs and G. Rajagopal, Quantum Monte Carlo simulations of solids, Rev. Mod. Phys. 73, 33 (2001). The standard review of variational and diffusion Monte Carlo, and still the place to start.
• R. J. Needs, M. D. Towler, N. D. Drummond and P. López Ríos, Continuum variational and diffusion quantum Monte Carlo calculations, J. Phys.: Condens. Matter 22, 023201 (2010) [PDF]. The methods as CASINO implements them.
• R. J. Needs, M. D. Towler, N. D. Drummond, P. López Ríos and J. R. Trail, Variational and diffusion quantum Monte Carlo calculations with the CASINO code, J. Chem. Phys. 152, 154106 (2020) [link]. The paper that describes the program, and the one to cite for results obtained with it.
• M. D. Towler, Quantum Monte Carlo, or, how to solve the many-particle Schrödinger equation accurately whilst retaining favourable scaling with system size [PDF], the preprint of his chapter in Computational Methods for Large Systems, edited by J. R. Reimers (Wiley, 2011) [link]. An introduction for chemists and physicists who are new to the method.
• M. D. Towler, The quantum Monte Carlo method, Phys. Status Solidi B 243, 2573 (2006) [link].
• M. J. Gillan, M. D. Towler and D. Alfè, Petascale computing opens new vistas for quantum Monte Carlo, Psi-k Scientific Highlight of the Month, No. 103 (2011) [PDF]. What quantum Monte Carlo does with a hundred thousand cores.
• J. Kolorenč and L. Mitas, Applications of quantum Monte Carlo methods in condensed systems, Rep. Prog. Phys. 74, 026502 (2011) [link].
• B. M. Austin, D. Yu. Zubarev and W. A. Lester Jr., Quantum Monte Carlo and related approaches, Chem. Rev. 112, 263 (2012) [link].
• W. A. Lester Jr., L. Mitas and B. Hammond, Quantum Monte Carlo for atoms, molecules and solids, Chem. Phys. Lett. 478, 1 (2009) [link].

Books

• B. L. Hammond, W. A. Lester Jr. and P. J. Reynolds, Monte Carlo Methods in Ab Initio Quantum Chemistry (World Scientific, 1994) [link]. Old, and still the right first book for a beginner.
• W. Schattke and R. Díez Muiño, Quantum Monte Carlo Programming for Atoms, Molecules, Clusters and Solids (Wiley-VCH, 2013) [link]. Teaches the method by writing the programs.
• F. Becca and S. Sorella, Quantum Monte Carlo Approaches for Correlated Systems (Cambridge University Press, 2017). The methods for lattice models as well as continuum systems, with reptation Monte Carlo among them.

Lectures

Slides from the summer schools and from talks on quantum Monte Carlo and CASINO are collected in the talk archive. For what the random walks of quantum Monte Carlo have, and have not, to do with the trajectories of pilot-wave theory, see the de Broglie-Bohm page.