.. _sphx_glr_api_gallery_quantum_tensor_networks:

Tensor networks
---------------

Matrix product states and time-evolving block decimation (TEBD) for spin
chains, checked against exact diagonalization.


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    <div class="sphx-glr-thumbcontainer" tooltip="The Hilbert space of N spins grows as 2^N, but the physically relevant states of 1D chains carry little entanglement and fit in a matrix product state (MPS) of bond dimension \chi. White&#x27;s DMRG (1992) found ground states this way; Vidal&#x27;s time-evolving block decimation (TEBD, 2003-2004) evolves an MPS in time by splitting e^{-iH\delta t} into two-site gates on even and odd bonds and truncating each bond back to \chi with an SVD. In imaginary time the same algorithm finds ground states.">

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  .. image:: /api/gallery/quantum/tensor_networks/images/thumb/sphx_glr_plot_tebd_matrix_product_states_thumb.png
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  :doc:`/api/gallery/quantum/tensor_networks/plot_tebd_matrix_product_states`

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      <div class="sphx-glr-thumbnail-title">TEBD on matrix product states: spin chains beyond exact diagonalization</div>
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    </div>


.. toctree::
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   /api/gallery/quantum/tensor_networks/plot_tebd_matrix_product_states