arXiv subjects

Aleksei Malyshev

Publications and source records attributed to Aleksei Malyshev.

4 recordsLinked to original sources

arXiv2024

Neural Quantum States and Peaked Molecular Wave Functions: Curse or Blessing?

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 $\sim 10^{15}$ 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.

quant-ph↗

arXiv2024

Role of Spatial Coherence in Diffractive Optical Neural Networks

Diffractive optical neural networks (DONNs) have emerged as a promising optical hardware platform for ultra-fast and energy-efficient signal processing for machine learning tasks, particularly in computer vision. Previous experimental demonstrations of DONNs have only been performed using coherent light. However, many real-world DONN applications require consideration of the spatial coherence properties of the optical signals. Here, we study the role of spatial coherence in DONN operation and performance. We propose a numerical approach to efficiently simulate DONNs under incoherent and partially coherent input illumination and discuss the corresponding computational complexity. As a demonstration, we train and evaluate simulated DONNs on the MNIST dataset of handwritten digits to process light with varying spatial coherence.

physics.optics↗

arXiv2023

Autoregressive Neural Quantum States with Quantum Number Symmetries

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.

quant-ph↗

arXiv2022

Autoregressive neural-network wavefunctions for ab initio quantum chemistry

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.

physics.chem-ph↗