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arXiv:2310.04166

Autoregressive Neural Quantum States with Quantum Number Symmetries

Aleksei Malyshev, Juan Miguel Arrazola, Alexander I. Lvovsky

Published Oct 6, 2023• 4 citations
arXivHTMLPDF

Abstract

Neural quantum states have established themselves as a powerful and versatile family of ansatzes for variational Monte Carlo simulations of quantum many-body systems. Of particular prominence are autoregressive neural quantum states (ANQS), which enjoy the expressibility of deep neural networks, and are equipped with a procedure for fast and unbiased sampling. Yet, the non-selective nature of autoregressive sampling makes incorporating quantum number symmetries challenging. In this work, we develop a general framework to make the autoregressive sampling compliant with an arbitrary number of quantum number symmetries. We showcase its advantages by running electronic structure calculations for a range of molecules with multiple symmetries of this kind. We reach the level of accuracy reported in previous works with more than an order of magnitude speedup and achieve chemical accuracy for all studied molecules, which is a milestone unreported so far. Combined with the existing effort to incorporate space symmetries, our approach expands the symmetry toolbox essential for any variational ansatz and brings the ANQS closer to being a competitive choice for studying challenging quantum many-body systems.

DOI
10.48550/arxiv.2310.04166

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Neural quantum states have established themselves as a powerful and versatile family of ansatzes for variational Monte Carlo simulations of quantum many-body systems. Of particular prominence are autoregressive neural quantum states (ANQS), which enjoy the expressibility of deep neural networks, and are equipped with a procedure for fast and unbiased sampling. Yet, the non-selective nature of autoregressive sampling makes incorporating quantum number symmetries challenging. In this work, we develop a general framework to make the autoregressive sampling compliant with an arbitrary number of quantum number symmetries. We showcase its advantages by running electronic structure calculations for a range of molecules with multiple symmetries of this kind. We reach the level of accuracy reported in previous works with more than an order of magnitude speedup and achieve chemical accuracy for all studied molecules, which is a milestone unreported so far. Combined with the existing effort to incorporate space symmetries, our approach expands the symmetry toolbox essential for any variational ansatz and brings the ANQS closer to being a competitive choice for studying challenging quantum many-body systems.
In recent years, neural network quantum states (NNQS) 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 significant research efforts spanning multiple decades, whilst only recently being attempted with NNQS. However, the complex non-local interactions and high sample complexity are significant challenges that call for bespoke solutions. Here, we parameterise the electronic wavefunction with a novel autoregressive neural network (ARN) 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 NNQS -- 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.
Neural quantum states (NQS) have gained prominence in variational quantum Monte Carlo methods in approximating ground-state wavefunctions. Despite their success, they face limitations in optimization, scalability, and expressivity in addressing certain problems. In this work, we propose a quantum-neural hybrid framework that combines parametrized quantum circuits with neural networks to model quantum many-body wavefunctions. This approach combines the efficient sampling and optimization capabilities of autoregressive neural networks with the enhanced expressivity provided by quantum circuits. Numerical simulations demonstrate the scalability and accuracy of the hybrid ansatz in spin systems and quantum chemistry problems. Our results reveal that the hybrid method achieves notably lower relative energy compared to stand-alone NQS. These findings underscore the potential of quantum-neural hybrid methods for tackling challenging problems in quantum many-body simulations.
Neural quantum states (NQSs) have emerged as a powerful ansatz for variational quantum Monte Carlo studies of strongly correlated systems. Here, we apply recurrent neural networks (RNNs) and autoregressive transformer neural networks to the Fermi-Hubbard and the (non-Hermitian) Hatano-Nelson-Hubbard models in one and two dimensions. In both cases, we observe that the convergence of the RNN ansatz is challenged when increasing the interaction strength. We present a physically motivated and easy-to-implement strategy for improving the optimization, namely, by ramping of the model parameters. Furthermore, we investigate the advantages and disadvantages of the autoregressive sampling property of both network architectures. For the Hatano-Nelson-Hubbard model, we identify convergence issues that stem from the autoregressive sampling scheme in combination with the non-Hermitian nature of the model. Our findings provide insights into the challenges of the NQS approach and make the first step towards exploring strongly correlated electrons using this ansatz.
Accurately determining the ground-state properties of quantum many-body systems remains a central challenge. In this work, we introduce an autoregressive projective quantum Monte Carlo (PQMC) framework that leverages recurrent neural networks (RNNs) to guide the stochastic dynamics. By incorporating autoregressive sampling into PQMC, we demonstrate substantial improvements in accuracy compared to standard unguided PQMC, while retaining polynomial computational cost. We benchmark our approach against conventional variational RNN ansätze and find that the autoregressive PQMC consistently achieves lower energies and higher fidelity, regardless of system size or whether the Hamiltonian is Hermitian or non-Hermitian. Our results highlight the versatility and power of neural-guided PQMC methods, paving the way for promising scalable simulations of low-energy states in complex quantum many-body systems.
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The field of neural quantum states has recently experienced a tremendous progress, making them a competitive tool of computational quantum many-body physics. However, their largest achievements to date mostly concern interacting spin systems, while their utility for quantum chemistry remains yet to be demonstrated. Two main complications are the peaked structure of the molecular wave functions, which impedes sampling, and large number of terms in second quantised Hamiltonians, which hinders scaling to larger molecule sizes. In this paper we address these issues jointly and argue that the peaked structure might actually be key to drastically more efficient calculations. Specifically, we introduce a novel algorithm for autoregressive sampling without replacement and a procedure to calculate a computationally cheaper surrogate for the local energy. We complement them with a custom modification of the stochastic reconfiguration optimisation technique and a highly optimised GPU implementation. As a result, our calculations require substantially less resources and exhibit more than order of magnitude speedup compared to the previous works. 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\sim 10^{15}∼1015 Slater determinants, which is orders of magnitude larger than what was previously achieved. We believe that our work underscores the prospect of NQS for challenging quantum chemistry calculations and serves as a favourable ground for the future method development.