squlearn.observables.observable_derivatives.ObservableDerivatives

class squlearn.observables.observable_derivatives.ObservableDerivatives(observable: ObservableBase | list, optree_caching=True, split_paulis=False)

Class for calculating derivatives of observables.

The derivatives are calculated by automatic differentiation of parameter in the expectation operator. Also, squaring of the operator is implemented. The class can either applied on a single operator, or on a list of operators. results are cached for faster evaluation.

Parameters:

• observable (Union[ObservableBase, list]) – Expectation operator or list of observables from which the derivatives are obtained.

• optree_caching (bool) – If True, the optree structure of the observable is cached

Strings that are recognized by the get_derivative() method

String	Derivative
"O"	Expectation operator \(\hat{O}\)
"OO"	Squared observable \(\hat{O}^2\)
"dop" or "Odop"	First-order derivative of the observable: \(\frac{d}{dp}\hat{O}(p)\)
"dopdop" or "Odopdop"	Second-order derivative of the observable: \(\frac{d^2}{dp^2}\hat{O}(p)\)
"OOdop"	First-order derivative of the squared observable: \(\frac{d}{dp}\hat{O}^2(p)\)
"OOdopdop"	Second-order derivative of the squared observable: \(\frac{d^2}{dp^2}\hat{O}^2(p)\)
"I"	Returns a identity operator with the same number of qubits as the provided observable

Example: first-order derivative of the Ising Hamiltonian

from squlearn.observables import IsingHamiltonian
from squlearn.observables.observable_derivatives import ObservableDerivatives
op = IsingHamiltonian(num_qubits=3)
print(ObservableDerivatives(op).get_derivative("dop"))

[1.0*SparsePauliOp(['III'],
              coeffs=[1.+0.j]), 1.0*SparsePauliOp(['IIZ'],
              coeffs=[1.+0.j]), 1.0*SparsePauliOp(['IZI'],
              coeffs=[1.+0.j]), 1.0*SparsePauliOp(['ZII'],
              coeffs=[1.+0.j]), 1.0*SparsePauliOp(['IZZ'],
              coeffs=[1.+0.j]), 1.0*SparsePauliOp(['ZIZ'],
              coeffs=[1.+0.j]), 1.0*SparsePauliOp(['ZZI'],
              coeffs=[1.+0.j])]

Example: Squared summed Pauli Operator

from squlearn.observables import SummedPaulis
from squlearn.observables.observable_derivatives import ObservableDerivatives
op = SummedPaulis(num_qubits=3)
print(ObservableDerivatives(op).get_operator_squared())

SparsePauliOp(['III', 'IIZ', 'IZI', 'ZII', 'IZZ', 'ZIZ', 'ZZI'],
              coeffs=[ParameterExpression(1.0*p_op[0]**2 + 1.0*p_op[1]**2 + 1.0*p_op[2]**2 + 1.0*p_op[3]**2),
 ParameterExpression(2.0*p_op[0]*p_op[1]),
 ParameterExpression(2.0*p_op[0]*p_op[2]),
 ParameterExpression(2.0*p_op[0]*p_op[3]),
 ParameterExpression(2.0*p_op[1]*p_op[2]),
 ParameterExpression(2.0*p_op[1]*p_op[3]),
 ParameterExpression(2.0*p_op[2]*p_op[3])])

Attributes:

parameter_vector

Parameter vector used in the observable

Type:

ParameterVector

num_parameters

Total number of trainable parameters in the observable

Type:

int

num_operators

Number operators in case of multiple observables

Type:

int

Methods:

assign_parameters(operator: OpTreeElementBase, parameters: ndarray) → OpTreeElementBase

Assign parameters to a derivative that is obtained from this class.

Parameters:

• operator (OperatorBase) – Operator to which the parameters are assigned

• parameters (np.ndarray) – Parameters values that replace the parameters in the operator

Returns:

Operator with assigned parameters

get_derivative(derivative: str | tuple | list) → OpTreeElementBase

Determine the derivative of the observable.

Parameters:

derivative (str or tuple) – String or tuple of parameters for specifying the derivation. See ObservableDerivatives for more information.

Returns:

Differentiated observable in OpTree format

get_operator()

Returns the observable operator

get_operator_squared()

Returns the squared form of the observable OO=O^2