In recent years, neural-network quantum states have emerged as powerful tools for the study of quantum many-body systems. Electronic structure calculations are one such canonical many-body problem that have attracted sustained research efforts spanning multiple decades, whilst only recently being attempted with neural-network quantum states. However, the complex non-local interactions and high sample complexity are substantial challenges that call for bespoke solutions. Here, we parameterize the electronic wavefunction with an autoregressive neural network that permits highly efficient and scalable sampling, whilst also embedding physical priors reflecting the structure of molecular systems without sacrificing expressibility. This allows us to perform electronic structure calculations on molecules with up to 30 spin orbitals—at least an order of magnitude more Slater determinants than previous applications of conventional neural-network quantum states—and we find that our ansatz can outperform the de facto gold-standard coupled-cluster methods even in the presence of strong quantum correlations. With a highly expressive neural network for which sampling is no longer a computational bottleneck, we conclude that the barriers to further scaling are not associated with the wavefunction ansatz itself, but rather are inherent to any variational Monte Carlo approach.
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The molecular geometries used in this work are in the STO-3G basis as returned from the PubChem42 database by OpenFermion43. OpenFermion was also used to generate qubit Hamiltonians of the form of equation (4), with the backend calculations and baseline QC methods—Hartree–Fock, configuration interaction, CCSD, CCSD(T)—implemented using Psi444. The exact molecular data generated, along with a notebook to reproduce these steps, can be found in the supporting code at https://github.com/tomdbar/naqs-for-quantum-chemistry and published on Zenodo45.
Source code to reproduce the reported results can be found at https://github.com/tomdbar/naqs-for-quantum-chemistry and published on Zenodo45.
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We are grateful to G. Carleo for his insights regarding RBMs, and to M. Sapova for her assistance with quantum chemical calculations. A.I.L.’s research is partially supported by the Russian Science Foundation (19-71-10092).
The authors declare no competing interests.
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Barrett, T.D., Malyshev, A. & Lvovsky, A.I. Autoregressive neural-network wavefunctions for ab initio quantum chemistry. Nat Mach Intell 4, 351–358 (2022). https://doi.org/10.1038/s42256-022-00461-z
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