tensor-disentangler 0.0.1

Numerical optimization of tensor network disentanglers

Tensor Disentangler

tensor-disentangler is a Python package that optimizes 'disentangling' unitary matrices to reduce bond-dimension in a given tensor. It is built on Pymanopt and designed to be used in tensor network algorithms for quantum many-body calculations and beyond. For example, disentangling is important for tensor network renormalization, isometric tensor network states, MERA, purified mixed-state MPS, and unitary tensor networks.

The user provides the tensor, dimensions of the tensor on which the unitary matrix is applied, and dimensions across which entanglement is minimized.

Installation

We should make this available via pip

Usage

disentangle(X, dis_legs, svd_legs, **kwargs)

• X: The input tensor (NumPy array) to be disentangled.
• dis_legs: A list of legs of X on which the unitary disentangling matrix acts.
• svd_legs: A list of legs of X across which the entanglement is minimized.

For example, if X is a 4D NumPy array then

Q, U, S, V = disentangle(X, dis_legs=[0, 1], svd_legs=[0, 2], **kwargs)

optimizes a unitary matrix Q to minimize the error when truncating the SVD in the following tensor network diagram

Features

tensor-disentangler has support for various optimizers and objective functions for disentangling. The optimizer, objective function, and other options can be specified with keyword arguments. For a comprehensive list we should write some documentation.

• Optimization algorithm: Alternating, Riemannian Conjugate Gradient, Riemannian Steepest Descent, and more
• Optimization objective function: Renyi entropy, Von-Neumann entropy, or truncation error
• Initial disentangler: identity, random, or user-supplied
• Maximum wall time and other optimizer specific stopping criteria
• Other advanced options