TeNPy TEBD backend
qiskit_addon_mpf.backends.tenpy_tebd
A tenpy
-based TEBD backend.
This backend is only available if the optional dependencies have been installed:
pip install "qiskit-addon-mpf[tenpy]"
TEBDEvolver | A TEBD algorithm for evolving an internal MPO. |
MPOState | A mediator class to make TeNPy's MPO match the State interface. |
MPS_neel_state | Constructs the Néel state as an MPS. |
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:
- Connecting
tenpy
’s implementation to the interface set out byqiskit_addon_mpf.backends
. - Extending
tenpy
’s TEBD implementation to handle an internal MPO (rather than MPS) state (see alsoState
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