def __grad_shift_rule(unitary, g, i, variable, hamiltonian):
'''
function for getting the gradients of directly differentiable gates. Expects precompiled circuits.
:param unitary: QCircuit: the QCircuit object containing the gate to be differentiated
:param g: a parametrized: the gate being differentiated
:param i: Int: the position in unitary at which g appears
:param variable: Variable or String: the variable with respect to which gate g is being differentiated
:param hamiltonian: the hamiltonian with respect to which unitary is to be measured, in the case that unitary
is contained within an ExpectationValue
:return: an Objective, whose calculation yields the gradient of g w.r.t variable
'''
# possibility for overwride in custom gate construction
if hasattr(g, "shifted_gates"):
inner_grad=__grad_inner(g.parameter, variable)
shifted = g.shifted_gates()
dOinc = Objective()
for x in shifted:
w,g = x
Ux = unitary.replace_gates(positions=[i], circuits=[g])
wx = w*inner_grad
Ex = Objective.ExpectationValue(U=Ux, H=hamiltonian)
dOinc += wx*Ex
return dOinc
else:
raise TequilaException('No shift found for gate {}\nWas the compiler called?'.format(g))
def __grad_shift_rule(unitary, g, i, variable, hamiltonian):
'''
function for getting the gradients of directly differentiable gates. Expects precompiled circuits.
:param unitary: QCircuit: the QCircuit object containing the gate to be differentiated
:param g: a parametrized: the gate being differentiated
:param i: Int: the position in unitary at which g appears
:param variable: Variable or String: the variable with respect to which gate g is being differentiated
:param hamiltonian: the hamiltonian with respect to which unitary is to be measured, in the case that unitary
is contained within an ExpectationValue
:return: an Objective, whose calculation yields the gradient of g w.r.t variable
'''
# possibility for overwride in custom gate construction
if hasattr(g, "shifted_gates"):
inner_grad = __grad_inner(g.parameter, variable)
shifted = g.shifted_gates()
dOinc = Objective()
for x in shifted:
w, g = x
Ux = unitary.replace_gates(positions=[i], circuits=[g])
wx = w * inner_grad
Ex = Objective.ExpectationValue(U=Ux, H=hamiltonian)
dOinc += wx * Ex
return dOinc
if not hasattr(g, "eigenvalues_magnitude"):
raise TequilaException(
"No shift-rule found for gate {}. Neither shifted_gates nor eigenvalues_magnitude not defined"
.format(g))
# neo_a and neo_b are the shifted versions of gate g needed to evaluate its gradient
shift_a = g._parameter + pi / (4 * g.eigenvalues_magnitude)
shift_b = g._parameter - pi / (4 * g.eigenvalues_magnitude)
neo_a = copy.deepcopy(g)
neo_a._parameter = shift_a
neo_b = copy.deepcopy(g)
neo_b._parameter = shift_b
U1 = unitary.replace_gates(positions=[i], circuits=[neo_a])
w1 = g.eigenvalues_magnitude * __grad_inner(g.parameter, variable)
U2 = unitary.replace_gates(positions=[i], circuits=[neo_b])
w2 = -g.eigenvalues_magnitude * __grad_inner(g.parameter, variable)
Oplus = ExpectationValueImpl(U=U1, H=hamiltonian)
Ominus = ExpectationValueImpl(U=U2, H=hamiltonian)
dOinc = w1 * Objective(args=[Oplus]) + w2 * Objective(args=[Ominus])
return dOinc