Estimates (via sampling) expectation values using monte-carlo simulation.

Simulate the final state of programs given symbol_values are placed inside of the symbols with the name in symbol_names in each circuit. Channels in this simulation will be "tossed" to a certain realization during simulation. This simulation is repeated num_samples times and bitstring based expectation calculations with the given pauli_sums are calculated after each run. Once all the runs are finished, these quantities are averaged together.

# Prepare some inputs.
qubit = cirq.GridQubit(0, 0)
my_symbol = sympy.Symbol('alpha')
my_circuit_tensor = tfq.convert_to_tensor([
        cirq.H(qubit) ** my_symbol,
my_values = np.array([[0.123]])
my_paulis = tfq.convert_to_tensor([[
    3.5 * cirq.X(qubit) - 2.2 * cirq.Y(qubit)
my_num_samples = np.array([[100]])
# This op can now be run with:
output = tfq.noise.sampled_expectation(
    my_circuit_tensor, ['alpha'], my_values, my_paulis, my_num_samples)
tf.Tensor([[0.71530885]], shape=(1, 1), dtype=float32)

In order to make the op differentiable, a tfq.differentiator object is needed. see tfq.differentiators for more details. Below is a simple example of how to make the from the above code block differentiable:

diff = tfq.differentiators.ForwardDifference()
my_differentiable_op = diff.generate_differentiable_op(

programs tf.Tensor of strings with shape [batch_size] containing the string representations of the circuits to be executed.
symbol_names tf.Tensor of strings with shape [n_params], which is used to specify the order in which the values in symbol_values should be placed inside of the circuits in programs.
symbol_values tf.Tensor of real numbers with shape [batch_size, n_params] specifying parameter values to resolve into the circuits specificed by programs, following the ordering dictated by symbol_names.
pauli_sums tf.Tensor of strings with shape [batch_size, n_ops] containing the string representation of the operators that will be used on all of the circuits in the expectation calculations.
num_samples tf.Tensor with num_samples[i][j] is equal to the number of times programs[i] will be simulated to estimate pauli_sums[i][j]. Therefore, num_samples must have the same shape as pauli_sums. Note: internally this quantity can get rounded up to the nearest multiple of the number of available threads to TensorFlow. For best performance ensure that the quantities in num_samples are a multiple of the number of available threads.

tf.Tensor with shape [batch_size, n_ops] that holds the expectation value for each circuit with each op applied to it (after resolving the corresponding parameters in).