Parallelized tensor network simulator with belief propagation

This repository provides a parallelized simulator for estimating expectation values of quantum circuits using belief propagation on tensor networks, built on top of the Tensor Computing Interface (TCI).

The library targets tensor-product-state representations—primarily MPS and PEPS—and provides utilities to construct circuit-induced factor graphs, run BP (loopy BP where appropriate), and aggregate observables efficiently across distributed computing resources.

Key points

• Focus: expectation-value evaluation of quantum circuits via tensor network simulation with belief propagation
• Built as an application-layer library on top of the Tensor Computing Interface (TCI)
• Tensor network formats: tensor product states such as MPS and PEPS
• Parallelism: thread-level and MPI-style process-level parallel execution
• Use cases: benchmark typical circuits/problems for paper-ready test calculations

Note: This repository is intended as a foundation for test codes and benchmarking; the API may evolve as features are added.

Tensor Computing Interface (TCI)

This project was originally developed in connection with the Tensor Computing Interface (TCI) project.

For details, see:

Sun, R.-Y., Shirakawa, T., Kohshiro, H., Sheng, D. N., Yunoki, S.
Tensor Computing Interface: An Application-Oriented, Lightweight Interface for Portable High-Performance Tensor Network Applications
https://arxiv.org/abs/2512.23917

This repository provides a lightweight TCI implementation and supports multiple TCI backends.

Minimal testing implementation

A simplified implementation of the TCI interface is provided for testing and development:

external/min-tci

TCI backends

The simulator can also be used with external TCI implementations:

• gqten backend implementation
  https://github.com/gracequantum/tensor-ng-dev

• Cytnx backend implementation
  https://github.com/r-ccs-cms/tensor-computing-interface-backend-cytnx

Requirements

To use this TCI, you need to install GraceQ/tensor-ng-dev.
For details on installation, please refer to the README.md of tensor-ng-dev.

The repository is registered as a Git submodule and can be initialized as follows:

git submodule init
git submodule update

This will place the original tensor-ng-dev under

/external/tensor-ng-dev

Sample Programs

1. Simulation of estimator for kicked ising model on a lattice (apps/kicked_ising_lattice)

The sample program under

/apps/kicked_ising_lattice

provides a simulator to estimate the expectation value after the kicked Ising Floquet dynamics on the lattice. See the /apps/kicked_ising_lattice/README.md for more details.

2. Simulation of estimator for sparse Pauli operator after gate operations defined by qasm file (apps/estimator)

The apps program under

/apps/estimator/

provides a simulator for estimating the expectation value of sparse Pauli operator after gate operations defined by qasm file. See the /sample/estimator/README.md for more details.

Citation

If you use this code in your research, please cite:

@misc{Sun2025TCI,
  title        = {Tensor Computing Interface: An Application-Oriented, Lightweight Interface for Portable High-Performance Tensor Network Applications},
  author       = {Rong-Yang Sun and Tomonori Shirakawa and Hidehiko Kohshiro and D. N. Sheng and Seiji Yunoki},
  year         = {2025},
  eprint       = {2512.23917},
  archivePrefix= {arXiv},
  primaryClass = {quant-ph}
}

Authors

• Tomonori Shirakawa
• Rongyang Sun
• Hidehiko Kohshiro