https://github.com/stephenhky/pyqentangle
Quantum Entanglement in Python
https://github.com/stephenhky/pyqentangle
numerical-methods package physics python python-library quantum-entanglement schmidt-decomposition
Last synced: about 1 month ago
JSON representation
Quantum Entanglement in Python
- Host: GitHub
- URL: https://github.com/stephenhky/pyqentangle
- Owner: stephenhky
- License: mit
- Created: 2016-10-26T20:51:14.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2025-04-20T04:16:26.000Z (about 2 months ago)
- Last Synced: 2025-04-20T05:22:24.769Z (about 2 months ago)
- Topics: numerical-methods, package, physics, python, python-library, quantum-entanglement, schmidt-decomposition
- Language: Python
- Homepage: http://pyqentangle.readthedocs.io
- Size: 3.65 MB
- Stars: 20
- Watchers: 5
- Forks: 5
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Quantum Entanglement in Python
[](https://circleci.com/gh/stephenhky/pyqentangle.svg)
[](https://github.com/stephenhky/pyqentangle/releases)
[](https://pyqentangle.readthedocs.io/en/latest/?badge=latest)
[](https://pyup.io/repos/github/stephenhky/pyqentangle/)
[](https://pyup.io/repos/github/stephenhky/pyqentangle/)
[](https://pypi.org/project/pyqentangle/)
[](https://pypi.org/project/pyqentangle/)
## Version
The releases of `pyqentangle` 2.x.x is incompatible with previous releases.
The releases of `pyqentangle` 3.x.x is incompatible with previous releases.
Since release 3.1.0, the support for Python 2 was decomissioned.
## Installation
This package can be installed using `pip`.
```
>>> pip install pyqentangle
```
To use it, enter
```
>>> import pyqentangle
>>> import numpy as np
```
## Schmidt Decomposition for Discrete Bipartite States
We first express the bipartite state in terms of a tensor. For example, if the state is `|01>+|10>`, then express it as
```
>>> tensor = np.array([[0., np.sqrt(0.5)], [np.sqrt(0.5), 0.]])
```
To perform the Schmidt decompostion, just enter:
```
>>> pyqentangle.schmidt_decomposition(tensor)
[(0.7071067811865476, array([ 0., -1.]), array([-1., -0.])),
(0.7071067811865476, array([-1., 0.]), array([-0., -1.]))]
```
For each tuple in the returned list, the first element is the Schmidt coefficients, the second the component for first subsystem, and the third the component for the second subsystem.
## Schmidt Decomposition for Continuous Bipartite States
We can perform Schmidt decomposition on continuous systems too. For example, define the following normalized wavefunction:
```
>>> fcn = lambda x1, x2: np.exp(-0.5 * (x1 + x2) ** 2) * np.exp(-(x1 - x2) ** 2) * np.sqrt(np.sqrt(8.) / np.pi)
```
Then perform the Schmidt decomposition,
```
>>> modes = pyqentangle.continuous_schmidt_decomposition(biwavefcn, -10., 10., -10., 10., keep=10)
```
where it describes the ranges of x1 and x2 respectively, and `keep=10` specifies only top 10 Schmidt modes are kept. Then we can read the Schmidt coefficients:
```
>>> list(map(lambda dec: dec[0], modes))
[0.9851714310094161,
0.1690286950361957,
0.02900073920775954,
0.004975740210361192,
0.0008537020544076649,
0.00014647211608480773,
2.51306421011773e-05,
4.311736522272035e-06,
7.39777032460608e-07,
1.2692567250688184e-07]
```
The second and the third elements in each tuple in the list `decompositions` are lambda functions for the modes of susbsystems A and B respectively. The Schmidt functions can be plotted:
```
>>> xarray = np.linspace(-10., 10., 100)
plt.subplot(3, 2, 1)
plt.plot(xarray, modes[0][1](xarray))
plt.subplot(3, 2, 2)
plt.plot(xarray, modes[0][2](xarray))
plt.subplot(3, 2, 3)
plt.plot(xarray, modes[1][1](xarray))
plt.subplot(3, 2, 4)
plt.plot(xarray, modes[1][2](xarray))
plt.subplot(3, 2, 5)
plt.plot(xarray, modes[2][1](xarray))
plt.subplot(3, 2, 6)
plt.plot(xarray, modes[2][2](xarray))
```
## Useful Links
* Study of Entanglement in Quantum Computers: [https://datawarrior.wordpress.com/2017/09/20/a-first-glimpse-of-rigettis-quantum-computing-cloud/](https://datawarrior.wordpress.com/2017/09/20/a-first-glimpse-of-rigettis-quantum-computing-cloud/)
* Github page: [https://github.com/stephenhky/pyqentangle](https://github.com/stephenhky/pyqentangle)
* PyPI page: [https://pypi.python.org/pypi/pyqentangle/](https://pypi.python.org/pypi/pyqentangle/)
* Documentation: [http://pyqentangle.readthedocs.io/](http://pyqentangle.readthedocs.io/)
* RQEntangle: [https://CRAN.R-project.org/package=RQEntangle](https://CRAN.R-project.org/package=RQEntangle) (corresponding R library)
## Reference
* Artur Ekert, Peter L. Knight, "Entangled quantum systems and the Schmidt decomposition", *Am. J. Phys.* 63, 415 (1995).
## Acknowledgement
* [Hossein Seifoory](https://ca.linkedin.com/in/hosseinseifoory?trk=public_profile_card_url)