Adaptive sampling-based optimization of quantics tensor trains for noisy functions: applications to quantum simulations

TL;DR

This paper introduces a noise-robust tensor train optimization method using adaptive sampling and non-linear least squares, enhancing quantum simulation accuracy for noisy functions.

Contribution

It develops a novel optimization approach for tensor trains with noisy data, improving robustness and accuracy in quantum simulations over existing methods.

Findings

Optimized tensor trains outperform traditional methods in noisy environments.

The approach yields higher accuracy in quantum ground-state energy calculations.

Demonstrated effectiveness on sine and correlation functions with noise.

Abstract

Tensor cross interpolation (TCI) is a powerful technique for learning a tensor train (TT) by adaptively sampling a target tensor based on an interpolation formula. However, when the tensor evaluations contain random noise, optimizing the TT is more advantageous than interpolating the noise. Here, we propose a new method that starts with an initial guess of TT and optimizes it using non-linear least-squares by fitting it to measured points obtained from TCI. We use quantics TCI (QTCI) in this method and demonstrate its effectiveness on sine and two-time correlation functions, with each evaluated with random noise. The resulting QTT exhibits increased robustness against noise compared to the QTCI method. Furthermore, we employ this optimized QTT of the correlation function in quantum simulation based on pseudo-imaginary-time evolution, resulting in ground-state energy with higher accuracy than the QTCI or Monte Carlo methods.