Qurrium 📏 - The python package for measuring quantum entanglement entropy and wave function overlap.

The python package that makes the randomized measurement easy.

The major function includes the measurement of quantum Renyi Entropy and Wave Function Overlap based on the randomized measurement protocol. When interfaced with IBM Qiskit, the package automates the workflow from creating experiment objects, job submission and recall and postprocessing.
There are several additional features, such as measurement of magnetization and error mitigation. Please check them out!

Documentation

More infomation can be found in the documentation of Qurrium 📏.

Installation

By PyPI - Stable Release

• The package can be found in pip list as qurrium-x.y.z
• Pip downloads the most stable release, but not necessarily the latest version.

bash pip install qurrium

By TestPyPI - Nightly Release

• This package can be found in pip list as qurry-x.y.z.devW
• This version includes new features and minor bug fixes, but may not be stable.

```bash pip install qiskit tqdm requests

the installation from testPyPI can' t find these dependencies

pip install -i https://test.pypi.org/simple/ qurry ```

Maually by Git

Qurry can be installed from source. Since this package relies on Cython and Rust, it requires "C complier" and "Rust complier" which you need to install first.

To install rust, run the following command:

bash curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh

Then install qurrium by the following command:

bash git clone https://github.com/qurrium/qurrium.git --recursive cd qurrium pip install -e .

Test Installation

pytest is used for testing. Simply run the following command after the installation:

bash pytest

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Environment

Qurry currently SUPPORT qiskit 0.46.0+ and qiskit 1.0.0+, other lower versions are no longer available. The package has been tested on the following systems.

• Ubuntu 18.04+ LTS (All ManyLinux 2014 compatible distro)
  • on x86_64 (recommended)
  • on x86_64 Windows 10/11 WSL2 (recommended)
  • on aarch64
  • We strongly recommend to use Linux based systems because Python multiprocessing may exist issues on Windows and the NVIDIA CUDA acceleration of Qiskit, qiskit-aer-gpu are supported only on Linux.
• Windows 10/11
  • on x86_64

• MacOS 11+

  • on aarch64 (Apple Silicon, M1/M2/M3/M4 chips)
  • on x86_64 (Intel chips)
  • The depedent modules are as follows.

• with required modules:

  • qiskit, tqdm, requests

• with optional modules:

  • qiskit-aer: The complete simulator package of qiskit
  • qiskit-aer-gpu: The gpu acceleration of qiskit-aer on Linux with Nvidia GPU
  • qiskit-aer-gpu-cu11: A package for CUDA 11
  • qiskit-ibm-runtime: The API to access IBM Quantum Device
  • qiskit-ibm-provider: The API to access IBM Quantum Device, but will be deprecated soon.
  • qiskit-ibmq-provider: The API to access IBM Quantum Device, which has been deprecated.

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Measurement -- made randomized measurement easy.

qurrent - The Quantum Renyi Entropy Measurement

The major function of this module is to measure the quantum Renyi entropy to quantify entanglement.

qurrech - The Wave Function Overlap Measurement

This module evaluates the overlap between any two given quantum states.

In each of the modules, two methods are implemented to perform the measurements:

• Hadamard Test

  • Ref: Entanglement spectroscopy on a quantum computer - Sonika Johri, Damian S. Steiger, and Matthias Troyer, PhysRevB.96.195136

• Haar Randomized Measure

  • Ref: Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states - A. Elben, B. Vermersch, C. F. Roos, and P. Zoller, PhysRevA.99.052323

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Citation

If you use this tool in your research, please cite the following paper in your publication:

```bibtex @article{PhysRevResearch.7.013043, title = {Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers}, author = {Chang, Huai-Chun and Hsu, Hsiu-Chuan and Lin, Yu-Cheng}, journal = {Phys. Rev. Res.}, volume = {7}, issue = {1}, pages = {013043}, numpages = {12}, year = {2025}, month = {Jan}, publisher = {American Physical Society}, doi = {10.1103/PhysRevResearch.7.013043}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.7.013043} } @mastersthesis{Chang2024, title = {Probing Entanglement Entropy on Near-term Quantum Computers}, author = {Huai-Chun Chang}, year = {2024}, school = {National Chengchi University}, department = {Graduate Institute of Applied Physics}, advisor = {Hsiu-Chuan Hsu}, committee = {Yu-Cheng Lin, Ying-Jer Kao, Chiao-Hsuan Wang}, degree = {Master's}, abstract = {In this thesis, we explore the quench dynamics of the Su–Schrieffer–Heeger (SSH) model and quantum entanglement using Noisy Intermediate-Scale Quantum (NISQ) computers, specifically on the IBM Quantum platform. We investigate the second-order Renyi entropy through randomized measurements to characterize the entanglement of quantum states. To simulate partial-dimerized quench Hamiltonians, we employ Trotter decomposition with an adaptive step size to reduce circuit depth. In the fully dimerized limit, the time evolution operator is exactly mapped to quantum gates, which minimizes noise. After applying error mitigation techniques, we find that the entanglement entropy oscillations align with theoretical predictions. Additionally, we developed a Python package called Qurry to manage workflows and facilitate parallel post-processing. Finally, we analyze the error scaling of Renyi entropy measurements and discuss the challenges encountered when simulating larger systems.}, keywords = {Noisy Intermediate-Scale Quantum Device, IBM Quantum, Quench dynamics, Su–Schrieffer–Heeger model, Renyi entropy, Randomized measurement, Error mitigation}, language = {zh-TW}, pages = {134}, url = {https://hdl.handle.net/11296/828e7d} }

```

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Acknowledgments

The authors acknowledge the support from National Chengchi University, NSTC-Quantum Virtual Machine project, National Center for Theoretical Sciences (NCTS). and IBM Quantum Hub at National Taiwan University (NTU).

Special thank to IBM Quantum Hub at NTU for providing the access right of IBM Quantum that allows us to fully test the tool and execute our experiments.

The author @harui2019 is grateful to the NTU hub of NCTS that supported him as a Research Assistiant in the early stage of the development.

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