Add LUCJ ansatz as parameterized Qiskit circuit

[kevinsung]

Traditionally, the LUCJ ansatz has this form:

U1 -> J1 -> U1dag -> U2 -> J2 -> U2dag -> ...

but when we convert it to a quantum circuit, we merge the orbital rotations and the resulting circuit has this form:

U1 -> J1 -> U2 -> J2 -> ...

This form is more natural for optimizing a Qiskit circuit using, for example, AQC-Tensor.

The function we add should have the same behavior as this:

from qiskit.circuit import QuantumCircuit, QuantumRegister
from qiskit_addon_aqc_tensor import parametrize_circuit

import ffsim


def ucj_spin_balanced_ansatz(
    norb: int,
    n_reps: int,
    interaction_pairs: tuple[
        list[tuple[int, int]] | None, list[tuple[int, int]] | None
    ],
) -> QuantumCircuit:
    ucj_op = ffsim.random.random_ucj_op_spin_balanced(
        norb,
        n_reps=n_reps,
        interaction_pairs=interaction_pairs,
    )
    qubits = QuantumRegister(2 * norb)
    circuit = QuantumCircuit(qubits)
    circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)
    circuit = ffsim.qiskit.PRE_INIT.run(circuit).decompose()
    ansatz, parameters = parametrize_circuit(circuit)
    return ansatz

Here the parameters are discarded, but we should also have a function to generate the parameters from t2 amplitudes.