Ajwt3: Created page with "= Project Title = Fast Randomized Iteration approach to Coupled Cluster = Project Phase = proto == Project aims/abstract == L.-H. Lim and J. Weare, Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra, SIAM Rev. 59 (2017), 547–587, DOI 10.1137/15M1040827. J. Lu and Z. Wang, The full configuration interaction quantum Monte Carlo method through the lens of inexact power iteration, SIAM J. Sci. Comput. 42 (2020), B1–B29, DOI 1..."

2025-09-14T07:45:50Z

Created page with "= Project Title = Fast Randomized Iteration approach to Coupled Cluster = Project Phase = proto == Project aims/abstract == L.-H. Lim and J. Weare, Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra, SIAM Rev. 59 (2017), 547–587, DOI 10.1137/15M1040827. J. Lu and Z. Wang, The full configuration interaction quantum Monte Carlo method through the lens of inexact power iteration, SIAM J. Sci. Comput. 42 (2020), B1–B29, DOI 1..."

New page

= Project Title =
Fast Randomized Iteration approach to Coupled Cluster

= Project Phase =
proto

== Project aims/abstract ==
L.-H. Lim and J. Weare, Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra, SIAM Rev. 59 (2017), 547–587, DOI 10.1137/15M1040827.

J. Lu and Z. Wang, The full configuration interaction quantum Monte Carlo method through the lens of inexact power iteration, SIAM J. Sci. Comput. 42 (2020), B1–B29, DOI 10.1137/18M1166626.

S. M. Greene, R. J. Webber, T. C. Berkelbach, and J. Weare, Approximating matrix eigenvalues by subspace iteration with repeated random sparsification, SIAM J. Sci. Comput. 44 (2022), A3067–A3097, DOI 10.1137/21M1422513.

S. M. Greene, R. J. Webber, J. E. T. Smith, J. Weare, and T. C. Berkelbach, Full configuration interaction excited-state energies in large active spaces from subspace iteration with repeated random sparsification, J. Chem. Theory Comput. 18 (2022), 7218–7232, DOI 10.1021/acs.jctc.2c00435.

S. M. Greene, R. J. Webber, J. Weare, and T. C. Berkelbach, Beyond walkers in stochastic quantum chemistry: reducing error using fast randomized iteration, J. Chem. Theory Comput. 15 (2019), 4834–4850, DOI 10.1021/acs.jctc.9b00422.

S. M. Greene, R. J. Webber, J. Weare, and T. C. Berkelbach, Improved fast randomized iteration approach to full configuration interaction, J. Chem. Theory Comput. 16 (2020), 5572–5585, DOI 10.1021/acs.jctc.0c00437.

As a consequence, FRI produces solutions as accurate as FCIQMC with a number of time steps that is smaller by a factor of 10---10000
Randomly sparsified Richardson iteration: A dimension-independent sparse linear solver
Jonathan Weare, Robert J. Webber
First published: 08 September 2025 https://doi.org/10.1002/cpa.70012

== Current state of the project and next steps ==

== Useful skills and knowledge ==
This project requires the knowledge of the following:

=== Theoretical ===
* Familiarity with the integral types of electronic structure theory (including their symmetries), and the efficient process of integral transformation
* Basic notions of linear algebra, and matrix decomposition techniques
* Understanding the mindset of scaling arguments (memory and computational)
* Understanding of Hartree-Fock and MP2 theory, and the basic notions of coupled cluster theory (derivation is not required)

=== Practical ===
* Basic understanding of the C++ syntax (or understanding the syntax of another programming language (e.g., Python) and willingness to explore how the other language works)
* Some familiarity with terminal commands, bash scripting, and the VI editor

== Learning outcomes ==

=== Theoretical ===
* Navigating electronic structure literature on integrals, and finding relevant information for understanding/implementation purposes
* Knowledge on existing approximation techniques that are extensively used in concurrent literature
* Understanding the context of fitting (where and why we use it in the methods we are interested in, and what the advantage/limitations of the proposed technique are)
* Knowledge on relevant statistical measures for performance testing

=== Practical ===
* Knowledge on C++ specific structures
* Familiarity and usage of the OpenMP/MPI parallelisation techniques in practice
* Efficiency optimisation of codes: using relevant matrix operation packages, and appropriate computational algorithms
* Efficient ways of dealing with test sets and extracting data (bash/Python scripting)
* Using Linux-based systems, computer clusters and schedulers

== Interesting references ==
# O. Vahtras, J. Almlöf, and M. W. Feyereisen, ''Chem. Phys. Lett.'' 213, 5–6, 514–518 (1993).
# M. Vose, ''IEEE Transactions on Software Engineering'' 17, 9, 972–975 (1991).
# [https://www.keithschwarz.com/darts-dice-coins/ Practical account on the alias method]
# T. Y. Takeshita, W. A. de Jong, D. Neuhauser, R. Baer, and E. Rabani, ''J. Chem. Theory Comput.'' 13, 4605–4610 (2017).

Fast Randomized Iteration - Revision history