# Quantum Energy Teleportation (QET)
### The world's first zero temperature QET with superconducting qubits
[](https://doi.org/10.1103/PhysRevApplied.20.024051)
[](https://arxiv.org/abs/2301.02666)
[](https://www.ibm.com/quantum/qiskit)
[](https://www.ibm.com/quantum)
[](LICENSE)
---
## Overview
This repository provides complete quantum-circuit implementations for demonstrating **quantum energy teleportation** on IBM Quantum systems.
The code can be run in two modes:
- **Local simulation** — run the circuits on a classical simulator without an IBM Quantum account.
- **Real quantum hardware** — execute the experiment on IBM Quantum devices with an IBM Quantum account and API token.
The default workflow is designed to be accessible: no IBM Quantum credentials are required for local simulation, and the notebooks are written so that the circuit construction, measurement procedure, and energy-estimation logic can be inspected step by step.
---
## What this repository contains
This project accompanies the experimental demonstration reported in:
> K. Ikeda,
> **“Demonstration of quantum energy teleportation on superconducting quantum hardware,”**
> *Physical Review Applied* **20**, 024051 (2023).
> DOI: [10.1103/PhysRevApplied.20.024051](https://doi.org/10.1103/PhysRevApplied.20.024051)
> arXiv: [2301.02666](https://arxiv.org/abs/2301.02666)
The repository includes:
- A complete notebook for the original QET demonstration.
- Local simulator workflows for laptop execution.
- IBM Quantum hardware execution workflows.
- A 2025 update using modern Qiskit Runtime workflows.
- Error-mitigation demonstrations using **M3**, **dynamical decoupling**, and **Pauli twirling**.
- Slides and documentation for understanding the physics and implementation.
---
## Highlights
- **Quantum Energy Teleportation on IBM Quantum hardware**
- **No IBM Quantum account required for the default simulator run**
- **Circuit-level implementation of Alice’s measurement and Bob’s conditional operation**
- **Energy-injection and energy-extraction estimation**
- **Updated 2025 notebooks with modern error-mitigation techniques**
- **Compatible with Qiskit 1.4.0 in the 2025 update notebooks**
- **Educational notebooks for both quantum-information and quantum-hardware demonstrations**
---
## Quick start
Clone the repository:
```bash
git clone https://github.com/IKEDAKAZUKI/Quantum-Energy-Teleportation.git
cd Quantum-Energy-Teleportation
```
Create and activate a Python environment:
```bash
python -m venv .venv
source .venv/bin/activate
```
For Windows:
```bash
.venv\Scripts\activate
```
Install the recommended packages:
```bash
pip install qiskit==1.4.0 qiskit-aer qiskit-ibm-runtime mthree numpy matplotlib jupyter
```
Launch Jupyter:
```bash
jupyter notebook
```
Then open:
```text
Quantum_Energy_Teleportation.ipynb
```
---
## Running on a local simulator
The default demonstration can be executed on a classical simulator.
This mode does **not** require an IBM Quantum account or API token.
Recommended starting point:
```text
Quantum_Energy_Teleportation.ipynb
```
This notebook walks through the basic QET protocol, including:
1. Preparation of the ground state.
2. Alice’s local measurement.
3. Bob’s conditional operation.
4. Estimation of injected and teleported energy.
---
## Running on IBM Quantum hardware
To run the experiment on a real IBM Quantum device:
1. Create or sign in to your IBM Quantum account:
[https://www.ibm.com/quantum](https://www.ibm.com/quantum)
2. Obtain your IBM Quantum API token.
3. Replace the placeholder token in the relevant notebook or script:
```python
"My_API_Token"
```
with your own token.
> **Important:** never commit your real API token to a public GitHub repository.
> For production use, store the token in an environment variable or a local configuration file excluded by `.gitignore`.
---
## Latest update 2025
The `Latest update 2025` directory contains an updated implementation using recent Qiskit workflows and error-mitigation techniques.
```text
Latest update 2025/
├── QET.py
├── QET_Experiment_Estimator.ipynb
└── QET_Experiment_M3_Error_Mitigation.ipynb
```
### Included techniques
- **Estimator-based execution**
- **M3 measurement mitigation**
- **Dynamical decoupling**
- **Pauli twirling**
- **Qiskit Runtime workflows**
- **Fake backend testing**
Recommended notebooks:
- [`QET_Experiment_Estimator.ipynb`](Latest%20update%202025/QET_Experiment_Estimator.ipynb)
- [`QET_Experiment_M3_Error_Mitigation.ipynb`](Latest%20update%202025/QET_Experiment_M3_Error_Mitigation.ipynb)
The 2025 update was tested with:
```text
Qiskit 1.4.0
```
---
## Repository structure
```text
.
├── Quantum_Energy_Teleportation.ipynb
├── Latest update 2025/
│ ├── QET.py
│ ├── QET_Experiment_Estimator.ipynb
│ └── QET_Experiment_M3_Error_Mitigation.ipynb
├── PRApplied.pdf
├── QET slides.gif
├── QET slides.pdf
├── CITATION.cff
├── LICENSE
└── README.md
```
---
## Documentation and slides
Additional documentation:
> K. Ikeda,
> **“Quantum Games and Economics through Teleportation”**
> March 06, 2025.
> SSRN: [https://ssrn.com/abstract=5168193](https://ssrn.com/abstract=5168193)
Slides:
- [Overview of Quantum Energy Teleportation — SlideShare](https://www.slideshare.net/slideshow/overview-of-quantum-energy-teleportation/287987616)
- [`QET slides.pdf`](QET%20slides.pdf)
---
## References
### Main experimental paper
K. Ikeda,
**“Demonstration of quantum energy teleportation on superconducting quantum hardware,”**
*Physical Review Applied* **20**, 024051 (2023).
DOI: [10.1103/PhysRevApplied.20.024051](https://doi.org/10.1103/PhysRevApplied.20.024051)
arXiv: [2301.02666](https://arxiv.org/abs/2301.02666)
### IBM Quantum
IBM Quantum website:
[https://www.ibm.com/quantum](https://www.ibm.com/quantum)
---
## Citation
If you use this repository in your research, please cite:
```bibtex
@article{PhysRevApplied.20.024051,
title = {Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware},
author = {Ikeda, Kazuki},
journal = {Phys. Rev. Appl.},
volume = {20},
issue = {2},
pages = {024051},
numpages = {12},
year = {2023},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevApplied.20.024051},
url = {https://link.aps.org/doi/10.1103/PhysRevApplied.20.024051}
}
```
You can also use the included [`CITATION.cff`](CITATION.cff) file.
---
## License
This project is released under the [MIT License](LICENSE).
---
## Funding
The work was supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under Contract No.DESC0012704.
---
**Quantum Energy Teleportation · IBM Quantum · Qiskit · Error Mitigation**