Efficient Generative Modeling with Unitary MPS Using Riemannian Optimization (Code)

This repository provides the MATLAB implementation for the paper:

Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization

The code implements a generative modeling framework based on unitary Matrix Product States (MPS) and Riemannian optimization, and is used for experiments on datasets including Bars and Stripes, and EMNIST (includes the MNIST dataset). Overall, our approach achieves substantially faster convergence—up to 27× higher efficiency compared with the original MPS-based generative model.

---

Requirements

• MATLAB (R2022a or later is recommended)
• No additional toolboxes are required

---

Running the Code

To run the code, please follow the steps below:

1. Add required folders to the MATLAB path

   • datasets
   • figure

   Alternatively, run the following commands in MATLAB:

   addpath(genpath('datasets'));
   addpath(genpath('figure'));

2. Run the main script

   Execute:

   main_generate_sample_mnist.m

   This script trains the unitary MPS generative model and generates samples for the MNIST dataset.

---

Dataset Notes

1. Bars and Stripes Dataset

• The Bars and Stripes (BAS) dataset is located in the datasets folder.
• The dataset can be generated using:

  % H -> height, W -> width
  generate_bas(H,W) 

• Dataset parameters can be adjusted inside the function as needed.

---

2. EMNIST Dataset

• The EMNIST dataset can be downloaded from:

  https://www.nist.gov/itl/products-and-services/emnist-dataset

• After downloading, use the following function to read and preprocess the dataset:

  save_images_emnist.m

---

Comparison Experiments

The comparison experiments reported in the paper can be found in the following repository:

https://github.com/congzlwag/UnsupGenModbyMPS

This repository provides baseline implementations for unsupervised generative modeling using Matrix Product States.

---

Citation

If you use this code in your research, please cite the corresponding paper.

---

"Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization"

https://arxiv.org/abs/2603.12026

Authors: Haotong Duan, Zhongming Chen, Ngai Wong.