Quimb circuit-based backend (qiskit_addon_mpf.backends.quimb_circuit)

A circuit-based time-evolution backend using quimb.

Warning

This backend is only available if the optional dependencies have been installed:

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

CircuitEvolver	A time-evolution engine based on quantum circuits.
CircuitState	An MPO-like representation of a time-evolution state based on quantum circuits.

Underlying method

Quimb boasts direct support for the simulation of quantum circuits in the form of its tensor-network based quimb.tensor.Circuit representation. We can leverage this, to bypass any explicit time-evolution algorithm and instead directly encode the time-evolution in a QuantumCircuit and use quimb to compute the overlap between two such circuits. For more information, check out their guide on Quantum Circuits.

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().

The IdentityStateFactory protocol is already fulfilled by the CircuitState constructor, rendering the identity_factory argument trivial:

>>> from qiskit_addon_mpf.backends.quimb_circuit import CircuitState
>>> identity_factory = CircuitState

The setup of the CircuitEvolver is slightly more involved. It requires a parameterized QuantumCircuit object as its input where the Parameter should take the place of the Trotter methods time step (dt).

To show how such a parameterized Trotter circuit template is constructed, we reuse the same Hamiltonian and second-order Suzuki-Trotter formula as in quimb_layers.

>>> from qiskit.quantum_info import SparsePauliOp
>>> hamil = SparsePauliOp.from_sparse_list(
...     [("ZZ", (i, i+1), 1.0) for i in range(0, 9, 2)] +
...     [("Z", (i,), 0.5) for i in range(10)] +
...     [("ZZ", (i, i+1), 1.0) for i in range(1, 9, 2)] +
...     [("X", (i,), 0.25) for i in range(10)],
...     num_qubits=10,
... )

But this time, we specify a Parameter as the time argument when constructing the actual circuits.

>>> from functools import partial
>>> from qiskit.circuit import Parameter
>>> from qiskit.synthesis import SuzukiTrotter
>>> from qiskit_addon_mpf.backends.quimb_circuit import CircuitEvolver
>>> from qiskit_addon_utils.problem_generators import generate_time_evolution_circuit
>>> dt = Parameter("dt")
>>> suzuki_2 = generate_time_evolution_circuit(hamil, time=dt, synthesis=SuzukiTrotter(order=2))
>>> approx_evolver_factory = partial(CircuitEvolver, circuit=suzuki_2)

Caution

It is necessary that the name of the Parameter is dt!

We can choose a higher order Trotter formula for the exact_evolver_factory. But note, that we must once again use a parameterized circuit, even if we immediately bind its parameter when constructing the partial function.

>>> suzuki_4 = generate_time_evolution_circuit(hamil, time=dt, synthesis=SuzukiTrotter(order=4))
>>> exact_evolver_factory = partial(CircuitEvolver, circuit=suzuki_4, dt=0.05)

These factory functions may now be used to run the setup_dynamic_lse(). Refer to its documentation for more details on that.