# tfq.math.fidelity

Calculate the fidelity between circuits.

Compute (potentially many) fidelities between the given circuits and the symbol free comparison circuits.

Calculates out[i][j] = $| \langle \psi{ ext{programs[i]} } ( ext{symbol_values[i]}) | \psi { ext{other_programs[j]} } angle |^2$

symbols = sympy.symbols('alpha beta')
qubits = cirq.GridQubit.rect(1, 2)
reference_circuits = [
    cirq.Circuit((cirq.H**symbols[0]).on_each(qubits)),
    cirq.Circuit(
        cirq.X(qubits[0]) ** symbols[0],
        cirq.Y(qubits[1]) ** symbols[1])
]
other_circuits = [
    cirq.Circuit(cirq.X.on_each(qubits)),
    cirq.Circuit((cirq.Y**0.125).on_each(qubits)),
    cirq.Circuit((cirq.X**0.5).on_each(qubits))
]
reference_tensor = tfq.convert_to_tensor(reference_circuits)
symbol_tensor = tf.convert_to_tensor([s.name for s in symbols])
values_tensor = tf.convert_to_tensor(np.arange(4).reshape(2, 2))
other_tensor = tfq.convert_to_tensor([other_circuits, other_circuits])
fid = tfq.math.fidelity(reference_tensor, symbol_tensor,
                            values_tensor, other_tensor)
fid
tf.Tensor(
    [[ 0., 0.925, 0.25],
     [ 0., 0.036, 0.25]],shape=(2, 3), dtype=float32)


programs tf.Tensor of strings with shape [batch_size] containing the string representations of the circuits
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.
other_programs tf.Tensor of strings with shape [batch_size, n_others] containing the string representations of the circuits with which to compute the overlap on programs with. Must not contain any free symbols.

tf.Tensor with shape [batch_size, n_others] where out[i][j] is equal to the fidelity of programs[i] with symbol_values[i] resolved in and other_programs[i][j].

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