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View Code? Open in Web Editor NEWImplementation of tensor network algorithms for completion of sparsely sampled quantum states
Implementation of tensor network algorithms for completion of sparsely sampled quantum states
Wavefunction Completion with Tensor Networks Author: Aaron Stahl (2024) // [email protected] 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.
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