Stochastic Exact Diagonalization for Quantum Many-Body Problems on Supercomputers

Representing and solving quantum many-body problems on classical computers is extremely challenging due to the immense size of the Hilbert space, and while quantum computers hold promise, they are still decades away from being able to model complex, realistic quantum systems. This makes the development of efficient algorithms for classical computing crucial. A robust quantum many-body solver, optimized for classical supercomputers, could significantly advance quantum science in the coming years. We have implemented the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm in our open-source package Rimu.jl, written in the modern programming language Julia. This flavor of projector quantum Monte Carlo can be seen as a simple stochastic extension of exact diagonalization of a quantum man-body Hamiltonian in Fock space. Our implementation utilizes Julia's native threading and MPI.jl for inter-node parallelism, enabling high-performance execution on supercomputing platforms. We will demonstrate how Rimu.jl handles quantum impurity problems in the Bose-Hubbard model with Hilbert spaces of dimension greater than 10⁶⁰ and achieves favorable scaling across over 1,000 nodes on the Frontier supercomputer at Oak Ridge National Laboratory. Additionally, Rimu.jl’s flexible interfaces support the easy implementation of custom many-body models and the modification of stochastic algorithms.