I am trying to optimise the code to construct a Hamiltonian as a sum of Hamiltonians. I have notised that using
qml.Hamiltonian with an array of coefficients and an array of observables is by far faster (running time in milliseconds even for 15 or more qubits) than constructing it as a sum of coefficient times observable (running time in minutes for 15 or more qubits). The code below constructs Hamiltonians using both methods.
import pennylane as qml N = 2 s = [(1/2 * (qml.Identity(i) - qml.PauliZ(i))) for i in range(2*N)] s_plus = s[:N] s_minus = s[N:] cost_h_from_coeffs_obs = qml.Hamiltonian(coeffs=[1 for i in range(4)], observables=[s_plus, (s_plus - 2*(s_plus @ s_minus) + s_minus), (s_plus - s_minus), (s_plus - s_minus) @ (s_plus - s_minus)]) print("Hamiltonian from coeffs. obs. construction") print(cost_h_from_coeffs_obs) cost_h_from_sum = sum([s_plus, (s_plus - 2*(s_plus @ s_minus) + s_minus), (s_plus - s_minus), (s_plus - s_minus) @ (s_plus - s_minus)]) print("Hamiltonian from sum") print(cost_h_from_sum) print("Equivalent Hamiltonians?", cost_h_from_coeffs_obs.compare(cost_h_from_sum))
However, when I run this code, it returns that both Hamiltonians are not equivalent. Moreover, when I print them, I see the PauliZ and Identity gates for the summed up Hamiltonian, but not for the one computed with
Hamiltonian from coeffs. obs. construction (1) [Hamiltonian0] + (1) [Hamiltonian1,3] + (1) [Hamiltonian0,2] + (1) [Hamiltonian0,1,2,3] Hamiltonian from sum (-1.0) [Z0] + (0.5) [Z2] + (1.0) [I0] + (-0.5) [Z1 Z3] + (-0.25) [Z0 Z3] + (-0.25) [Z2 Z1] + (0.25) [Z0 Z1] + (0.25) [Z2 Z3] Equivalent Hamiltonians? False
Can someone explain me why these two do not match?
Finally, when I try to use the Hamiltonian computed with
qml.Hamiltonian for QAOA, I get the following error message:
ValueError: hamiltonian must be written only in terms of PauliZ and Identity gates
How can I deal with it? Is there any other way to speed up the computation of a cost Hamiltonian from the sum of s_plus and s_minus elements times some fixed factors? Thank you very much in advance.