Adaptive sampling-based optimization of quantics tensor trains for noisy functions: applications to quantum simulations
arXiv:2405.12730 · doi:10.21468/SciPostPhys.19.2.038
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.
References in corpus (30)
- The density-matrix renormalization group in the age of matrix product states
- Continuous-variable optical quantum state tomography
- The ITensor Software Library for Tensor Network Calculations
- Variational ansatz-based quantum simulation of imaginary time evolution
- Qulacs: a fast and versatile quantum circuit simulator for research purpose
- Unsupervised Generative Modeling Using Matrix Product States
- Image compression and entanglement
- A Quantum Inspired Approach to Exploit Turbulence Structures
- Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
- Supervised Learning with Quantum-Inspired Tensor Networks
- Learning Feynman Diagrams with Tensor Trains
- TensorNetwork for Machine Learning
- Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond
- Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
- A variational quantum eigensolver for dynamic correlation functions
- Learning tensor networks with tensor cross interpolation: new algorithms and libraries
- A quantum-inspired method for solving the Vlasov-Poisson equations
- Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
- Error-resilient Monte Carlo quantum simulation of imaginary time
- Quantized tensor networks for solving the Vlasov-Maxwell equations
- Compactness of quantics tensor train representations of local imaginary-time propagators
- TTOpt: A Maximum Volume Quantized Tensor Train-based Optimization and its Application to Reinforcement Learning
- Quantum state tomography with tensor train cross approximation
- Learning parameter dependence for Fourier-based option pricing with tensor trains
- Numerical solution of the incompressible Navier-Stokes equations for chemical mixers via quantum-inspired Tensor Train Finite Element Method
- Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
- Error Analysis of Tensor-Train Cross Approximation
- Permutation of Tensor-Train Cores for Computing Moments on Stochastic Differential Equations
- A highly efficient tensor network algorithm for multi-asset Fourier options pricing
- Denoising Convolution Algorithms and Applications to SAR Signal Processing