May I ask how to implement the time evolution in qiskit, given an initialized state?
In quantum mechanics, a quantum state evolves over time with the governing Hamiltonian.
$$ \exp{(-i \int H dt )} \ket{\psi} $$
For example, in the 2-qubit Ising model,
$$ H = -Z_1 Z_2 + h_1 X_1 + h_2 X_2 $$
where $h_1$ and $h_2$ are the transverse field for qubit 1 and qubit 2. The initial state is in the ferromagnetic state $\ket{11}$. So I encode the initial state with a 2-qubit quantum circuit.
from qiskit import QuantumCircuit
qc = QuantumCircuit(2)
qc.initialize('11', qc.qubits)
How can I define a time-dependent quantum gate $ \exp{(-i \int H dt )} $ to act on the quantum circuit?