Codes of Matrix Product State (MPS)

General

This is a simple example code of Gradient Descent Method on Matrix Product State. I wrote it for my undergraduate thesis. This is not a formal project and it may have many bugs XD.

The tensor type is defined by Prof. B Clark at UIUC. See his Problem Set 3.

I developed SVRG/SCSG and Adam algorithms about Gradient Optimization on 1-dim Tensor Network (MPS).

Installation

Julia Programming Language

I recommend you to compiling from source code using the latest stable version. I'm using v1.6.0.

Jupyter Lab / Notebook

Please open these *.ipynb file via Jupyter Lab. You can install it here or use the following command in Julia:

using Pkg; Pkg.add("IJulia")

Alternative

If you already have Jupyter installed, IJulia can call up your Jupyter instead of installing a new one. You can click the IJulia here and follow this guide:

You can force it to use a specific jupyter installation by setting ENV["JUPYTER"] to the path of the jupyter program before Pkg.add, or before running Pkg.build("IJulia")

Usage

First Time

Run Julia, go into Package mode by entering ] and install some packages. This may take a long time, but you can see progressmeter bars of them to ensure the process is not stuck. (Do not copy codes before > or $. )

$ julia
julia> ]
(@v1.6) pkg> add Plots, FFTW, ColorSchemes, LinearAlgebra, StatsBase, ProgressMeter, TensorOperations
(@v1.6) pkg> build

Press Backspace and then Ctrl+D to exit.

Run Program

After the installation, enter this repository and call up Jupyter Lab by Julia:

$ julia -e 'using IJulia; jupyterlab(detached=true, dir=".")' 

To Professor Carlson

Tests about Heisanberg model was placed in Heisenberg.ipynb.