apply operator like spin hamiltonian inside a quantum kernel

Required prerequisites

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Describe the feature

In the tutorial of krylov example in the application page, The circuit is given by:

cudaq.kernel
def U_m(qubits: cudaq.qview, dt: float, coefficients: list[complex],
        words: list[cudaq.pauli_word]):
    # Compute U_m = exp(-i m dt H)
    for i in range(len(coefficients)):
        exp_pauli(dt * coefficients[i].real, qubits, words[i])

@cudaq.kernel
def U_n(qubits: cudaq.qview, dt: float, coefficients: list[complex],
        words: list[cudaq.pauli_word]):
    # Compute U_n = exp(-i n dt H)
    for i in range(len(coefficients)):
        exp_pauli(dt * coefficients[i].real, qubits, words[i])


# Applies the gate operations for a Hamiltonian Pauli Word
@cudaq.kernel
def apply_pauli(qubits: cudaq.qview, word: list[int]):
    # Add H (Hamiltonian operator)
    for i in range(len(word)):
        if word[i] == 1:
            x(qubits[i])
        if word[i] == 2:
            y(qubits[i])
        if word[i] == 3:
            z(qubits[i])


@cudaq.kernel
def qfd_kernel(dt_alpha: float, dt_beta: float, coefficients: list[complex],
               words: list[cudaq.pauli_word], word_list: list[int],
               vec: list[complex]):

    ancilla = cudaq.qubit()
    qreg = cudaq.qvector(vec)

    h(ancilla)

    x(ancilla)
    cudaq.control(U_m, ancilla, qreg, dt_alpha, coefficients, words)
    x(ancilla)

    cudaq.control(apply_pauli, ancilla, qreg, word_list)
    cudaq.control(U_n, ancilla, qreg, dt_beta, coefficients, words)

U_n, U_m are the exponential of hamiltonian operator. But apply_pauli is the spin hamiltonian operator. The hamiltonian is a linear combination of pauli string. Currently, to apply the hamiltonian pauli operator, I had to convert that into a list of integer number.

It would be good if cudaq allows applying an operator like spin hamiltonian inside the quantum kernel. That would make the code cleaner.

Start with the linked Krylov tutorial and inspect the existing U_m, U_n, and apply_pauli kernels. Determine how a spin Hamiltonian could be passed to or applied inside a quantum kernel without converting Pauli words to integer lists. Done means the tutorial can express the Hamiltonian operation directly and includes updated working usage.