Fast Randomized Iteration

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

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

1. O. Vahtras, J. Almlöf, and M. W. Feyereisen, Chem. Phys. Lett. 213, 5–6, 514–518 (1993).
2. M. Vose, IEEE Transactions on Software Engineering 17, 9, 972–975 (1991).
3. Practical account on the alias method
4. T. Y. Takeshita, W. A. de Jong, D. Neuhauser, R. Baer, and E. Rabani, J. Chem. Theory Comput. 13, 4605–4610 (2017).