Improve Parameter handling in SparsePauliOp (Qiskit/qiskit#9796)

* add reno

* Add assign_parameters and parameter in init

* add SPO.parameters and remove utils

* fix ParameterValueType typehint

* Update qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py

Co-authored-by: Ikko Hamamura <ikkoham@users.noreply.github.com>

* remove trailing print

* Elena's comments

Co-authored-by: Elena Peña Tapia <57907331+ElePT@users.noreply.github.com>

* fix line length

---------

Co-authored-by: Ikko Hamamura <ikkoham@users.noreply.github.com>
Co-authored-by: Elena Peña Tapia <57907331+ElePT@users.noreply.github.com>

qiskit_algorithms/time_evolvers/trotterization/trotter_qrte.py

@@ -26,8 +26,6 @@
 from qiskit.quantum_info import Pauli, SparsePauliOp
 from qiskit.synthesis import ProductFormula, LieTrotter
 
-from qiskit.algorithms.utils.assign_params import _assign_parameters, _get_parameters
-
 
 class TrotterQRTE(RealTimeEvolver):
     """Quantum Real Time Evolution using Trotterization.
@@ -165,16 +163,25 @@ def evolve(self, evolution_problem: TimeEvolutionProblem) -> TimeEvolutionResult
                 "The time evolution problem contained ``aux_operators`` but no estimator was "
                 "provided. The algorithm continues without calculating these quantities. "
             )
+
+        # ensure the hamiltonian is a sparse pauli op
         hamiltonian = evolution_problem.hamiltonian
         if not isinstance(hamiltonian, (Pauli, PauliSumOp, SparsePauliOp)):
             raise ValueError(
-                f"TrotterQRTE only accepts Pauli | PauliSumOp, {type(hamiltonian)} provided."
+                f"TrotterQRTE only accepts Pauli | PauliSumOp | SparsePauliOp, {type(hamiltonian)} "
+                "provided."
             )
+        if isinstance(hamiltonian, PauliSumOp):
+            hamiltonian = hamiltonian.primitive * hamiltonian.coeff
+        elif isinstance(hamiltonian, Pauli):
+            hamiltonian = SparsePauliOp(hamiltonian)
+
         t_param = evolution_problem.t_param
-        if t_param is not None and _get_parameters(hamiltonian.coeffs) != ParameterView([t_param]):
+        free_parameters = hamiltonian.parameters
+        if t_param is not None and free_parameters != ParameterView([t_param]):
             raise ValueError(
-                "Hamiltonian time parameter does not match evolution_problem.t_param "
-                "or contains multiple parameters"
+                f"Hamiltonian time parameters ({free_parameters}) do not match "
+                f"evolution_problem.t_param ({t_param})."
             )
 
         # make sure PauliEvolutionGate does not implement more than one Trotter step
@@ -213,9 +220,9 @@ def evolve(self, evolution_problem: TimeEvolutionProblem) -> TimeEvolutionResult
             # evolution for next step
             if t_param is not None:
                 time_value = (n + 1) * dt
-                bound_coeffs = _assign_parameters(hamiltonian.coeffs, [time_value])
+                bound_hamiltonian = hamiltonian.assign_parameters([time_value])
                 single_step_evolution_gate = PauliEvolutionGate(
-                    SparsePauliOp(hamiltonian.paulis, bound_coeffs),
+                    bound_hamiltonian,
                     dt,
                     synthesis=self.product_formula,
                 )

qiskit_algorithms/time_evolvers/variational/solvers/var_qte_linear_solver.py

@@ -23,8 +23,6 @@
 from qiskit.quantum_info import SparsePauliOp
 from qiskit.quantum_info.operators.base_operator import BaseOperator
 
-from qiskit.algorithms.utils.assign_params import _assign_parameters
-
 from ..variational_principles import VariationalPrinciple
 
 
@@ -115,13 +113,12 @@ def solve_lse(
 
         if self._time_param is not None:
             if time_value is not None:
-                bound_params_array = _assign_parameters(self._hamiltonian.coeffs, [time_value])
-                hamiltonian = SparsePauliOp(self._hamiltonian.paulis, bound_params_array)
+                hamiltonian = hamiltonian.assign_parameters([time_value])
             else:
                 raise ValueError(
-                    f"Providing a time_value is required for time-dependant hamiltonians, "
+                    "Providing a time_value is required for time-dependent hamiltonians, "
                     f"but got time_value = {time_value}. "
-                    f"Please provide a time_value to the solve_lse method."
+                    "Please provide a time_value to the solve_lse method."
                 )
 
         evolution_grad_lse_rhs = self._var_principle.evolution_gradient(

test/time_evolvers/test_trotter_qrte.py

@@ -20,7 +20,6 @@
 from numpy.testing import assert_raises
 
 from qiskit.algorithms.time_evolvers import TimeEvolutionProblem, TrotterQRTE
-from qiskit.algorithms.utils.assign_params import _assign_parameters
 from qiskit.primitives import Estimator
 from qiskit import QuantumCircuit
 from qiskit.circuit.library import ZGate
@@ -245,11 +244,8 @@ def _get_expected_trotter_qrte(operator, time, num_timesteps, init_state, observ
         for n in range(num_timesteps):
             if t_param is not None:
                 time_value = (n + 1) * dt
-                bound_coeffs = _assign_parameters(operator.coeffs, [time_value])
-                ops = [
-                    Pauli(op).to_matrix() * np.real(coeff)
-                    for op, coeff in SparsePauliOp(operator.paulis, bound_coeffs).to_list()
-                ]
+                bound = operator.assign_parameters([time_value])
+                ops = [Pauli(op).to_matrix() * np.real(coeff) for op, coeff in bound.to_list()]
             for op in ops:
                 psi = expm(-1j * op * dt).dot(psi)
             observable_results.append(