Gate operations · Measurements · Time evolution · Quantum teleportation · Quantum energy teleportation · Gauge theory · Green’s functions · Hadamard tests
This repository provides a compact but research-oriented collection of Qiskit tutorials for quantum information science, quantum many-body physics, and quantum simulation. Materials are based on lectures at UMass Boston.
The notebooks begin with the foundations of quantum circuits and measurements, then progress toward advanced topics including:
- universal quantum gate operations,
- quantum measurement and expectation values,
- time evolution and quench dynamics,
- Ising-model simulations and phase transitions,
- adiabatic algorithms and adiabatic state preparation,
- quantum teleportation,
- quantum energy teleportation,
- lattice gauge theory simulations,
- Green’s functions, two-point functions, and Hadamard tests.
The goal is to provide practical, executable examples of quantum-computing techniques that are useful for modern quantum physics research.
| Topic | Notebook | Run |
|---|---|---|
| Qiskit fundamentals, measurement, time evolution, Ising model, phase transition | Qiskit_Tutorial.ipynb |
 |
| Quantum teleportation | Quantum_Teleportation.ipynb |
|
| Quantum energy teleportation | Quantum_Energy_Teleportation.ipynb |
|
| Quantum simulation of gauge theory: Schwinger model | Quantum_simulation_of_Schwinger_model.ipynb |
|
| Green’s functions, two-point functions, n-point correlation functions, Hadamard test | Quantum_computation_of_n_point_correpation_functions.ipynb |
|
Note: the filename
Quantum_computation_of_n_point_correpation_functions.ipynbis kept as it appears in the repository.
Start with:
Qiskit_Tutorial.ipynb
This notebook introduces the basic workflow of quantum programming with Qiskit:
- creating quantum circuits,
- applying one-qubit and two-qubit gates,
- measuring quantum states,
- running circuits on simulators,
- visualizing measurement outcomes,
- computing expectation values,
- working with density matrices,
- computing entanglement entropy,
- simulating time evolution,
- studying the Ising model and phase-transition dynamics.
Continue with:
Quantum_Teleportation.ipynb
This notebook demonstrates the standard quantum teleportation protocol using elementary quantum gates, entanglement, Bell measurements, and classical feed-forward operations.
It provides a useful bridge between basic circuit construction and more advanced protocols based on local operations and classical communication.
The notebook
Quantum_Energy_Teleportation.ipynb
introduces the circuit-level implementation of quantum energy teleportation.
For the complete research code and updated hardware demonstrations, see the related repository:
https://github.com/IKEDAKAZUKI/Quantum-Energy-Teleportation
This tutorial is connected to 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
arXiv: 2301.02666
The notebook
Quantum_simulation_of_Schwinger_model.ipynb
develops a Qiskit-based tutorial for the quantum simulation of the massive Schwinger model, a 1+1 dimensional U(1) lattice gauge theory.
Topics include:
- the Schwinger-model Lagrangian,
- lattice Hamiltonian formulation,
- Jordan-Wigner transformation,
- spin Hamiltonian representation,
- local charge operators,
- static and dynamical simulations,
- adiabatic state preparation,
- phase-transition demonstrations using time-dependent Hamiltonians.
This notebook is intended as a gateway from introductory quantum circuits to quantum simulation in high-energy physics.
The notebook
Quantum_computation_of_n_point_correpation_functions.ipynb
covers quantum-computing methods for correlation functions and Hadamard-test-based measurements.
Topics include:
- Hadamard test circuits,
- real and imaginary parts of transition amplitudes,
- two-point correlation functions,
- n-point correlation functions,
- Green’s-function-style observables,
- quantum simulation workflows relevant to lattice field theory.
This part is connected to the research context of real-time quantum simulation for timelike correlation functions:
J. Barata, K. Ikeda, S. Mukherjee, J. Raghoonanan,
“Towards a real-time computation of timelike hadronic vacuum polarization and light-by-light scattering: Schwinger Model tests,”
Journal of High Energy Physics 2025, 118 (2025).
DOI: 10.1007/JHEP02(2025)118
Clone the repository:
git clone https://github.com/IKEDAKAZUKI/Qiskit-Tutorial.git
cd Qiskit-TutorialCreate a Python virtual environment:
python -m venv .venv
source .venv/bin/activateFor Windows PowerShell:
.venv\Scripts\Activate.ps1Install the recommended packages:
pip install qiskit qiskit-aer numpy scipy matplotlib jupyterLaunch Jupyter Notebook:
jupyter notebookThen open any of the tutorial notebooks.
Each notebook can also be opened directly in Google Colab using the badges in the table above.
For Colab execution, run the package-installation cell at the beginning of each notebook before executing the remaining cells.
For students and researchers new to Qiskit, the recommended order is:
1. Qiskit_Tutorial.ipynb
2. Quantum_Teleportation.ipynb
3. Quantum_Energy_Teleportation.ipynb
4. Quantum_simulation_of_Schwinger_model.ipynb
5. Quantum_computation_of_n_point_correpation_functions.ipynb
This sequence moves from basic circuit operations to research-level applications in quantum many-body dynamics and lattice gauge theory.
.
├── Qiskit_Tutorial.ipynb
├── Quantum_Teleportation.ipynb
├── Quantum_Energy_Teleportation.ipynb
├── Quantum_simulation_of_Schwinger_model.ipynb
├── Quantum_computation_of_n_point_correpation_functions.ipynb
├── LICENSE
└── README.md
For the complete implementation of quantum energy teleportation on IBM Quantum systems, see:
https://github.com/IKEDAKAZUKI/Quantum-Energy-Teleportation
That repository includes the full QET demonstration, updated 2025 workflows, and error-mitigation examples for IBM Quantum hardware.
K. Ikeda,
“Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware,”
Physical Review Applied 20, 024051 (2023).
DOI: 10.1103/PhysRevApplied.20.024051
arXiv: 2301.02666
J. Barata, K. Ikeda, S. Mukherjee, J. Raghoonanan,
“Towards a real-time computation of timelike hadronic vacuum polarization and light-by-light scattering: Schwinger Model tests,”
Journal of High Energy Physics 2025, 118 (2025).
DOI: 10.1007/JHEP02(2025)118
If you use the quantum energy teleportation tutorial, please cite:
@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}
}If you use the Green’s-function, two-point-function, or Hadamard-test tutorial in connection with real-time Schwinger-model simulations, please cite:
@article{Barata:2024bzk,
author = "Barata, Jo{\~a}o and Ikeda, Kazuki and Mukherjee, Swagato and Raghoonanan, Jonathan",
title = "{Towards a real-time computation of timelike hadronic vacuum polarization and light-by-light scattering: Schwinger Model tests}",
eprint = "2406.03536",
archivePrefix = "arXiv",
primaryClass = "hep-ph",
doi = "10.1007/JHEP02(2025)118",
journal = "JHEP",
volume = "02",
pages = "118",
year = "2025"
}This repository is released under the MIT License.
Qiskit Tutorial · Quantum Simulation · Quantum Information · Lattice Gauge Theory