Python implementation of quantum tensor network operations and simulations: matrix product states and operators, TDVP time evolution, support for quantum numbers, ...
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PyTeNet is a Python implementation of quantum tensor network operations and simulations within the matrix product state framework, using NumPy to handle tensors.

Example usage for TDVP time evolution:

import pytenet as ptn

# number of lattice sites (1D with open boundary conditions)
L = 10

# construct matrix product operator representation of
# Heisenberg XXZ Hamiltonian (arguments are L, J, \Delta, h)
mpoH = ptn.heisenberg_XXZ_MPO(L, 1.0, 0.8, -0.1)

# initial wavefunction as MPS with random entries
# maximally allowed virtual bond dimensions
D = [1, 2, 4, 8, 16, 28, 16, 8, 4, 2, 1]
psi = ptn.MPS(mpoH.qd, [Di*[0] for Di in D], fill='random')
# effectively clamp virtual bond dimension of initial state
Dinit = 8
for i in range(L):
    psi.A[i][:, Dinit:, :] = 0
    psi.A[i][:, :, Dinit:] = 0

# time step can have both real and imaginary parts;
# for real time evolution use purely imaginary dt!
dt = 0.01 - 0.05j
numsteps = 100

# run TDVP time evolution
ptn.integrate_local_singlesite(mpoH, psi, dt, numsteps, numiter_lanczos=5)
# psi now stores the (approximated) time-evolved state exp(-dt*numsteps H) psi


  • matrix product state and operator classes
  • construct common Hamiltonians as MPOs, straightforward to adapt to custom Hamiltonians
  • convert arbitrary operator chains to MPOs
  • TDVP time evolution (real and imaginary)
  • generate vector / matrix representations of matrix product states / operators
  • Krylov subspace methods for local operations
  • one-site local energy minimization using Lanczos iteration
  • built-in support for additive quantum numbers


To install PyTeNet, download the source code and run python install from within the main PyTeNet directory, or add the pytenet/ subfolder to your Python search path.


The full documentation is available at

Directory structure

  • pytenet: source code of the actual PyTeNet package
  • doc: documentation and tutorials
  • test: unit tests (might serve as detailed documentation, too)
  • experiments: numerical experiments on more advanced, in-depth topics
  • paper: JOSS manuscript


Feature requests, discussions and code contributions to PyTeNet in the form of pull requests are of course welcome. Creating an issue might be a good starting point. New code should be well documented (Google style docstrings) and unit-tested (see the test/ subfolder). For questions and additional support, fell free to contact


PyTeNet is published in the Journal of Open Source Software - if it's ever useful for a research project please consider citing it:

  author = {Mendl, C. B.},
  title = {PyTeNet: A concise Python implementation of quantum tensor network algorithms},
  journal = {Journal of Open Source Software},
  year = {2018},
  volume = {3},
  number = {30},
  pages = {948},
  doi = {10.21105/joss.00948},


PyTeNet is licensed under the BSD 2-Clause license.


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    The density-matrix renormalization group in the age of matrix product states
    Ann. Phys. 326, 96-192 (2011) arXiv:1008.3477, DOI
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    Unifying time evolution and optimization with matrix product states
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    From density-matrix renormalization group to matrix product states
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