Autoregressive neural quantum states for ab initio quantum chemistry

Thesis

Neural quantum states are a powerful and versatile family of ansatzes for variational Monte Carlo simulations of quantum many-body systems. However, their utility for ab initio quantum chemistry is yet to be demonstrated. The main complications are (i) taking into account multiple quantum number symmetries, inherent to molecules; (ii) the peaked structure of the molecular wave functions, which impedes sampling; and (iii) large numbers of terms in second quantised Hamiltonians, which hinder scaling to larger molecule sizes.

In this thesis, we address these issues with autoregressive neural quantum states (ANQS). ANQS enjoy the expressibility of deep neural networks, and enable fast and unbiased sampling.

First, we develop a framework to make the autoregressive sampling compliant with arbitrary numbers of quantum number symmetries. We run electronic structure calculations for a range of molecules with multiple symmetries of this kind and reach the accuracy reported in previous works with more than an order of magnitude speedup.

Second, we argue that the peaked structure might be key to drastically more efficient calculations. We introduce a novel algorithm for autoregressive sampling without replacement and a procedure to calculate a computationally cheaper energy surrogate. We complement them with a custom modification of the stochastic reconfiguration technique and a highly optimised GPU implementation. As a result, our calculations require substantially less resources and exhibit an additional order of magnitude speedup. On a single GPU we study molecules comprising up to 118 qubits and outperform the "golden standard" CCSD(T) benchmark in Hilbert spaces of ~10¹⁵ Slater determinants, which is orders of magnitude larger than what was previously achieved. We believe that our work underscores the prospect of ANQS for challenging quantum chemistry calculations and serves as a favourable ground for the future method development.

Authors: Malyshev, A

• DOI: 10.5287/ora-gapqobdre
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: neural quantum states; autoregressive neural quantum states; electronic structure calculations
• Subjects: Quantum chemistry; Neural networks (Computer science); Quantum Monte Carlo methods