qml.math.expectation_value¶

expectation_value(operator_matrix, state_vector, check_state=False, check_operator=False, c_dtype='complex128')[source]¶

Compute the expectation value of an operator with respect to a pure state.

The expectation value is the probabilistic expected result of an experiment. Given a pure state, i.e., a state which can be represented as a single vector \(\ket{\psi}\) in the Hilbert space, the expectation value of an operator \(A\) can computed as

\[\langle A \rangle_\psi = \bra{\psi} A \ket{\psi}\]

Parameters:

operator_matrix (tensor_like) – operator matrix with shape (2**N, 2**N) or (batch_dim, 2**N, 2**N).
state_vector (tensor_like) – state vector with shape (2**N) or (batch_dim, 2**N).
check_state (bool) – if True, the function will check the validity of the state vector via its shape and the norm.
check_operator (bool) – if True, the function will check the validity of the operator via its shape and whether it is hermitian.
c_dtype (str) – complex floating point precision type.

Returns:

Expectation value of the operator for the state vector.

Return type:

float

Example

The expectation value for any operator can obtained by passing their matrix representation as an argument. For example, for a 2 qubit state, we can compute the expectation value of the operator \(Z \otimes I\) as

>>> import pennylane as qml
>>> import numpy as np
>>> state_vector = [1 / np.sqrt(2), 0, 1 / np.sqrt(2), 0]
>>> operator_matrix = qml.matrix(qml.PauliZ(0), wire_order=[0, 1])
>>> qml.math.expectation_value(operator_matrix, state_vector)
tensor(-2.23711432e-17+0.j, requires_grad=True)

qml.math.expectation_value¶

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