Hi,
When i coding HS.4.2a PrepSelPrep on the Walk operator, it show incorrect.
error log>>>
Incorrect: Something is off with your Hamiltonian!
my code>>>
offes = [1/4,1/4,1/2]
objs = [qml.Z(5),qml.Z(6),qml.Z(5)@qml.Z(6)]
H = qml.Hamiltonian(offes,objs)
dev = qml.device(“default.qubit”, wires = range(7))
walk_powers_1 = [qml.pow(qml.Qubitization(H, control = [3,4]), i) for i in range(0,3)]
walk_powers_2 = [qml.pow(qml.adjoint(qml.Qubitization(H, control = [3,4])), i) for i in reversed(range(1,3))]
bessel_1 = [0.765197686557943666, 0.44005058574493355, 0.11490348493190051]
J0, J1, J2 = bessel_1
norm_factor = J0 + 2J1 + 2J2
lcu_coeffs = [
J2 / norm_factor,
J1 / norm_factor,
J0 / norm_factor,
J1 / norm_factor,
J2 / norm_factor
]
lcu_ops = [
qml.s_prod(-1, walk_powers_2[0]), # - W^{-2}
qml.s_prod(-1j, walk_powers_2[1]), # -i W^{-1}
walk_powers_1[0], # I
qml.s_prod(1j, walk_powers_1[1]), # +i W^{1}
qml.s_prod(-1, walk_powers_1[2]) # - W^{2}
]
lcu = qml.dot(lcu_coeffs, lcu_ops)
@qml.qnode(dev)
def prep_sel_prep_walk():
qml.PrepSelPrep(lcu, control=[0,1,2])
return qml.state()
encoded_matrix = qml.matrix(prep_sel_prep_walk, wire_order=range(7))()[:4, :4]
print("The encoded matrix is: ", encoded_matrix)
output>>>
The encoded matrix is: [[0.286+1.930e-16j 0. +0.000e+00j 0. +0.000e+00j 0. +0.000e+00j]
[0. +0.000e+00j 0.469-1.039e-16j 0. +0.000e+00j 0. +0.000e+00j]
[0. +0.000e+00j 0. +0.000e+00j 0.469-1.047e-16j 0. +0.000e+00j]
[0. +0.000e+00j 0. +0.000e+00j 0. +0.000e+00j 0.531-1.501e-17j]]
Notice however that the last term of the Hamiltonian in the description of the Codercise is not a product of Pauli