Differentiate a circuit with respect to its inputs by adjoint method.

Inherits From: `Differentiator`

The Adjoint differentiator follows along with the methods described here: arXiv:1912.10877 and doi: 10.1111/j.1365-246X.2006.02978.x. The Adjoint method differentiates the input circuits in roughly one forward and backward pass over the circuits, to calculate the gradient of a symbol only a constant number of gate operations need to be applied to the circuits state. When the number of parameters in a circuit is very large, this differentiator performs much better than all the others found in TFQ.

````my_op = tfq.get_expectation_op()`
`adjoint_differentiator = tfq.differentiators.Adjoint()`
`# Get an expectation op, with this differentiator attached.`
`op = adjoint_differentiator.generate_differentiable_op(`
`    analytic_op=my_op`
`)`
`qubit = cirq.GridQubit(0, 0)`
`circuit = tfq.convert_to_tensor([`
`    cirq.Circuit(cirq.X(qubit) ** sympy.Symbol('alpha'))`
`])`
`psums = tfq.convert_to_tensor([[cirq.Z(qubit)]])`
`symbol_values_array = np.array([[0.123]], dtype=np.float32)`
`# Calculate tfq gradient.`
`symbol_values_tensor = tf.convert_to_tensor(symbol_values_array)`
`with tf.GradientTape() as g:`
`    g.watch(symbol_values_tensor)`
`    expectations = op(circuit, ['alpha'], symbol_values_tensor, psums`
`)`
`grads = g.gradient(expectations, symbol_values_tensor)`
`grads`
`tf.Tensor([[-1.1839]], shape=(1, 1), dtype=float32)`
```

## Methods

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### `differentiate_sampled`

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Specify how to differentiate a circuit with sampled expectation.

This is called at graph runtime by TensorFlow. `differentiate_sampled` should calculate the gradient of a batch of circuits and return it formatted as indicated below. See `tfq.differentiators.ForwardDifference` for an example.

Args
`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 specified 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` of positive integers representing the number of samples per term in each term of pauli_sums used during the forward pass.
`forward_pass_vals` `tf.Tensor` of real numbers with shape [batch_size, n_ops] containing the output of the forward pass through the op you are differentiating.
`grad` `tf.Tensor` of real numbers with shape [batch_size, n_ops] representing the gradient backpropagated to the output of the op you are differentiating through.

Returns
A `tf.Tensor` with the same shape as `symbol_values` representing the gradient backpropageted to the `symbol_values` input of the op you are differentiating through.

### `generate_differentiable_op`

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Generate a differentiable op by attaching self to an op.

See `tfq.differentiators.Differentiator`. This has been partially re-implemented by the Adjoint differentiator to disallow the `sampled_op` input.

Args
`sampled_op` A `callable` op that you want to make differentiable using this differentiator's `differentiate_sampled` method.
`analytic_op` A `callable` op that you want to make differentiable using this differentiators `differentiate_analytic` method.

Returns
A `callable` op that who's gradients are now registered to be a call to this differentiators `differentiate_*` function.

### `refresh`

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Refresh this differentiator in order to use it with other ops.