Accelerating Quantum Many Body Calculations for Strongly Correlated Systems

José M. Arias, María Isabel Gallardo, Manuel Lozano

Bowen Kan, Honghui Shang

Quantum many-body calculations are fundamentally limited by the exponential growth of the configuration space, making accurate treatment of strongly correlated systems computationally prohibitive. Here we present the Generative Transformer Neural Network Selected Configuration Interaction (GTNN-SCI), a Transformer-based machine learning approach that generatively samples important configurations to accelerate many-body quantum chemistry calculations. By leveraging the Transformer architecture’s self-attention mechanism to capture long-range electron correlations, GTNN-SCI achieves up to 10× speedup compared to state-of-the-art neural network methods while maintaining high accuracy. We demonstrate the efficacy of GTNN-SCI by calculating correlation and binding energies for representative molecules including N 2, H 2 O, and C 2 using both Gaussian (cc-pVDZ) and plane-wave basis sets, achieving faster convergence and lower energies than previously reported neural network-based selected CI techniques. Most significantly, our generative approach identifies higher-order excitations missed by conventional coupling schemes, yielding lower variational energies than established methods including heat-bath CI. This capability enables GTNN-SCI to accurately treat the strongly correlated [Fe 2 S 2 (SCH 3 ) 4 ] 2– ([2Fe–2S]) cluster system, achieving ground-state energies within chemical accuracy of DMRG benchmarks, whereas conventional selected CI methods have failed on this system. The GTNN-SCI method thus combines modern deep learning with high-performance electronic structure computation, providing an efficient and precise avenue for solving the electronic Schrödinger equation in challenging molecular systems.

S. Zhang, E. C. Allman

S. I. Mistakidis, Artem G. Volosniev, R. E. Barfknecht +5 more

Cold atomic gases have become a paradigmatic system for exploring fundamental physics, which at the same time allows for applications in quantum technologies. The accelerating developments in the field have led to a highly advanced set of engineering techniques that, for example, can tune interactions, shape the external geometry, select among a large set of atomic species with different properties, or control the number of atoms. In particular, it is possible to operate in lower dimensions and drive atomic systems into the strongly correlated regime. In this review, we discuss recent advances in few-body cold atom systems confined in low dimensions from a theoretical viewpoint. We mainly focus on bosonic systems in one dimension and provide an introduction to the static properties before we review the state-of-the-art research into quantum dynamical processes stimulated by the presence of correlations. Besides discussing the fundamental physical phenomena arising in these systems, we also provide an overview of the calculational and numerical tools and methods that are commonly used, thus delivering a balanced and comprehensive overview of the field. We conclude by giving an outlook on possible future directions that are interesting to explore in these correlated systems.

John Sturt, Evgeny Kozik

Diagrammatic expansions are a paradigmatic and powerful tool of quantum many-body theory. Their evaluation to high order, e.g., by the Diagrammatic Monte Carlo technique, can provide unbiased results in strongly correlated and challenging regimes. However, calculating a factorial number of terms to acceptable precision remains very costly even for state-of-the-art methods. We achieve a dramatic acceleration of evaluating Feynman's diagrammatic series by use of specialised hardware architecture within the recently introduced combinatorial summation (CoS) framework. We present how exploiting the massive parallelism and concurrency available from GPUs leads to orders of magnitude improvement in computation time even on consumer-grade hardware. This provides a platform for making probes of novel phenomena of strong correlations much more accessible.

James K. Freericks, Jeffrey Cohn, Khadijeh Najafi +1 more