Quimb TEBD backend

qiskit_addon_mpf.backends.quimb_tebd

A quimb-based TEBD backend.

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

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 quimb tensor network library.

The classes provided by this module serve two purposes:

1. Connecting quimb’s implementation to the interface set out by qiskit_addon_mpf.backends.
2. Extending quimb’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 quimb-native form. To be more concrete, the TEBDEvolver class (which is a subclass of quimb.tensor.TEBD) works with a Hamiltonian in the form of a quimb.tensor.LocalHam1D. Quimb provides a number of convenience methods for constructing such Hamiltonians in its quimb.tensor.tensor_builder 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, we create the identity_factory which has to match the IdentityStateFactory protocol. We do so simply by using the quimb.tensor.MPO_identity() function and wrapping the resulting quimb.tensor.MatrixProductOperator with our custom MPOState interface.

>>> from qiskit_addon_mpf.backends.quimb_tebd import MPOState
>>> from quimb.tensor import MPO_identity
>>> num_qubits = 10
>>> identity_factory = lambda: MPOState(MPO_identity(num_qubits))

Next, before being able to define the ExactEvolverFactory and ApproxEvolverFactory protocols, we must define the Hamiltonian which we would like to time-evolve. Here, we simply choose one of quimb’s convenience methods.

>>> from quimb.tensor import ham_1d_heis
>>> hamil = ham_1d_heis(num_qubits, 0.8, 0.3, cyclic=False)

We can now construct the exact and approximate time-evolution instance factories. To do so, we can simply use functools.partial() to bind the pre-defined values of the TEBDEvolver initializer, reducing it to the correct interface as expected by the ExactEvolverFactory and ApproxEvolverFactory protocols, respectively.

>>> from functools import partial
>>> from qiskit_addon_mpf.backends.quimb_tebd import TEBDEvolver
>>> exact_evolver_factory = partial(
...     TEBDEvolver,
...     H=hamil,
...     dt=0.05,
...     order=4,
... )

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,
...     H=hamil,
...     order=2,
...     split_opts={"max_bond": 10, "cutoff": 1e-5},
... )

Of course, you are not limited to the examples shown here, and we encourage you to play around with the other settings provided by the quimb.tensor.TEBD 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 be acylic

Resources

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