Neural network enhanced measurement efficiency for molecular groundstates

Abstract

It is believed that one of the first useful applications for a quantum computer will be the preparation of groundstates of molecular Hamiltonians. A crucial task involving state preparation and readout is obtaining physical observables of such states, which are typically estimated using projective measurements on the qubits. At present, measurement data is costly and time-consuming to obtain on any quantum computing architecture, which has significant consequences for the statistical errors of estimators. In this paper, we adapt common neural network models (restricted Boltzmann machines and recurrent neural networks) to learn complex groundstate wavefunctions for several prototypical molecular qubit Hamiltonians from typical measurement data. By relating the accuracy $\epsilon$ of the reconstructed groundstate energy to the number of measurements, we find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables. This enhancement yields an asymptotic scaling near ${\epsilon }^{-1}$ for the model-based approaches, as opposed to ${\epsilon }^{-2}$ in the case of classical shadow tomography.

7 pages, 5 figures

References in corpus (4)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Experimental single-setting quantum state tomography
• On the Origin of Implicit Regularization in Stochastic Gradient Descent
• Data-Enhanced Variational Monte Carlo Simulations for Rydberg Atom Arrays

Cited by in corpus (5)

• Ab-initio quantum chemistry with neural-network wavefunctions
• Enhancing variational Monte Carlo using a programmable quantum simulator
• Empirical Sample Complexity of Neural Network Mixed State Reconstruction
• Observing Schrödinger's Cat with Artificial Intelligence: Emergent Classicality from Information Bottleneck
• Neural network enhanced cross entropy benchmark for monitored circuits