Wavefunction Completion with Tensor Networks
Author: Aaron Stahl (2024) // aaaron.m.stahl@gmail.com
Author's note: a more comprehensive repository is
available in Matlab; please email if interested.
OVERVIEW
----------------
This project introduces several new tensor network algorithms
for reconstructing ("completing") low energy eigenstates of an
unknown Hamiltonian using a random sample of the wavefunction
coefficient amplitudes. The completion algorithms leverage
truncated matrix product states (MPS), randomized tensor tree
networks (TTN), and other tensor-oriented structures to offer
powerful tools for wavefunction completion. Starting from only a
sparse sampling of amplitudes, these routines commonly obtain
completed states with fidelity values near the limits of numerical
precision.
CITATION
-------------
This repository is associated with the article, "Reconstruction of
Randomly Sampled Quantum Wavefunctions using Tensor
Methods" by Aaron Stahl and Glen Evenbly (2023). For a detailed
theoretical background and numerical results, please refer to:
https://arxiv.org/abs/2310.01628
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 1-D 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.
FEATURES
----------------
* Exact diagonalization of local Hamiltonians for calculating
eigenvalues and eigenstates
* Wavefunction completion using tensor network methods
* Support for various model options including the critical XX model,
Ising model, and randomly generated homogenous and
inhomogenous Hamiltonians with arbitrary interaction lengths
INSTALLATION
---------------------
Core functionality included in:
- applyHam.py
- genLocalHams.py
- ncon.py
- truncatedMPS.py
- allCutSweep.py
- compHelperFunctions.py
- genBlocksTree.py
- oneLayerTree.py
- reverseLayerTree.py
Sample implementations:
- exactDiagEx.py (exact diagonalization)
- wavefunctionCompEx.py (example: MPS and ACS)
- wavefunctionTreeCompEx.py (example: tree tensor network)
ACKNOWLEDGMENTS
--------------------------------
Thank you to Glen Evenbly for his assistance in developing this project.astahl3/wavefunction_completion
Implementation of tensor network algorithms for completion of sparsely sampled quantum states
Python