Reconstruction of Randomly Sampled Quantum Wavefunctions using Tensor Methods

TL;DR

This paper introduces tensor network algorithms that efficiently reconstruct quantum ground states from limited samples, leveraging entanglement minimization to achieve high fidelity in 1D lattice models.

Contribution

It presents novel tensor-based methods for wavefunction reconstruction from sparse data, demonstrating high accuracy and efficiency for local Hamiltonian ground states.

Findings

Successfully reconstructs ground states with minimal sampling

Achieves high fidelity close to double-precision limits

Effective for 1D local Hamiltonian models

Abstract

We propose and test several tensor network based algorithms for reconstructing the ground state of an (unknown) local Hamiltonian starting from a random sample of the wavefunction amplitudes. These algorithms, which are based on completing a wavefunction by minimizing the block Renyi entanglement entropy averaged over all local blocks, are numerically demonstrated to reliably reconstruct ground states of local Hamiltonians on 1D lattices to high fidelity, often at the limit of double-precision numerics, while potentially starting from a random sample of only a few percent of the total wavefunction amplitudes.