Metadata-Version: 2.1
Name: pyqentangle
Version: 3.3.1
Summary: Quantum Entanglement in Python
Home-page: https://github.com/stephenhky/pyqentangle
Author: Kwan-Yuet Ho
Author-email: stephenhky@yahoo.com.hk
License: MIT
Description: # Quantum Entanglement in Python
        
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        ## 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 2.7 and 3.5 has been decomissioned.
        Since release 3.3.0, support for Python 3.6 is diminished, but that for Python 3.11 is added.
        
        ## Installation
        
        This package can be installed using `pip`.
        
        ```
        >>> pip install -U 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))
        ```
        
        ![alt](https://github.com/stephenhky/pyqentangle/raw/master/fig/three_harmonic_modes.png)
        
        
        ## 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)
        
Keywords: quantum physics Schmidt decompostion entanglement
Platform: UNKNOWN
Classifier: Topic :: Scientific/Engineering :: Physics
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Scientific/Engineering :: Chemistry
Classifier: License :: OSI Approved :: MIT License
Classifier: Programming Language :: Python :: 3.7
Classifier: Programming Language :: Python :: 3.8
Classifier: Programming Language :: Python :: 3.9
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Cython
Classifier: Programming Language :: C
Classifier: Intended Audience :: Science/Research
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Education
Description-Content-Type: text/markdown
