TeNPy TEBD backend

qiskit_addon_mpf.backends.tenpy_tebd

A tenpy-based TEBD backend.

pip install "qiskit-addon-mpf[tenpy]"

Underlying method

This module provides a time-evolution backend for computing dynamic MPF coefficients based on the time-evolving block decimation (TEBD) algorithm [1] implemented in the tenpy tensor network library.

The classes provided by this module serve two purposes:

1. Connecting tenpy’s implementation to the interface set out by qiskit_addon_mpf.backends.
2. Extending tenpy’s TEBD implementation to handle an internal MPO (rather than MPS) state (see also State for more details).

In the simplest sense, this module provides a straight-forward extension of the TEBD algorithm to evolve an internal MPO state. As such, if you wish to use this backend for your dynamic MPF algorithm, you must encode the Hamiltonian that you wish to time-evolve, in a tenpy-native form. To be more concrete, the TEBDEvolver class (which is a subclass of tenpy.algorithms.tebd.TEBDEngine) works with a Hamiltonian in the form of a Model. TeNPy provides a number of convenience methods for constructing such Hamiltonians in its tenpy.models module. If none of those fulfill your needs, you can consider using the LayerModel class which implements some conversion methods from Qiskit-native objects.

Code example

This section shows a simple example to get you started with using this backend. The example shows how to create the three factory functions required for the setup_dynamic_lse().

First of all, we define the Hamiltonian which we would like to time-evolve. Here, we simply choose one of tenpy’s convenience methods.

>>> from tenpy.models import XXZChain2
>>> hamil = XXZChain2(
...     {
...         "L": 10,
...         "Jz": 0.8,
...         "Jxx": 0.7,
...         "hz": 0.3,
...         "bc_MPS": "finite",
...         "sort_charge": False,
...     }
... )

Next, we can create the identity_factory which has to match the IdentityStateFactory protocol. We do so by using the initialize_from_lattice() convenience method which takes the lattice underlying the Hamiltonian which we just defined as its only input.

>>> from functools import partial
>>> from qiskit_addon_mpf.backends.tenpy_tebd import MPOState
>>> identity_factory = partial(MPOState.initialize_from_lattice, hamil.lat),

We can now construct the ExactEvolverFactory and ApproxEvolverFactory time-evolution instance factories. To do so, we can simply bind the pre-defined values of the TEBDEvolver initializer, reducing it to the correct interface as expected by the respective function protocols.

>>> from qiskit_addon_mpf.backends.tenpy_tebd import TEBDEvolver
>>> exact_evolver_factory = partial(
...     TEBDEvolver,
...     model=hamil,
...     dt=0.05,
...     options={
...         "order": 4,
...         "preserve_norm": False,
...     },
... )

Notice, how we have fixed the dt value to a small time step and have used a higher-order Suzuki-Trotter decomposition to mimic the exact time-evolution above.

Below, we do not fix the dt value and use only a second-order Suzuki-Trotter formula for the approximate time-evolution. Additionally, we also specify some truncation settings.

>>> approx_evolver_factory = partial(
...     TEBDEvolver,
...     model=hamil,
...     options={
...         "order": 2,
...         "preserve_norm": False,
...         "trunc_params": {
...             "chi_max": 10,
...             "svd_min": 1e-5,
...             "trunc_cut": None,
...         },
...     },
... )

Of course, you are not limited to the examples shown here, and we encourage you to play around with the other settings provided by TeNPy’s TEBDEngine implementation.

Limitations

Finally, we point out a few known limitations on what kind of Hamiltonians can be treated by this backend:

• all interactions must be 1-dimensional
• the interactions must use finite boundary conditions

Resources

[1]: https://en.wikipedia.org/wiki/Time-evolving_block_decimation