tfq.differentiators.Differentiator

Interface that defines how to specify gradients for a quantum circuit.

Used in the notebooks

Used in the tutorials

This abstract class allows for the creation of gradient calculation procedures for (expectation values from) quantum circuits, with respect to a set of input parameter values. This allows one to backpropagate through a quantum circuit.

Methods

differentiate_analytic

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@tf.function
differentiate_analytic(
    programs, symbol_names, symbol_values, pauli_sums, forward_pass_vals, grad
)

Differentiate a circuit with analytical expectation.

This is called at graph runtime by TensorFlow. differentiate_analytic calls he inheriting differentiator's get_gradient_circuits and uses those components to construct the gradient.

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.
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.

differentiate_sampled

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@tf.function
differentiate_sampled(
    programs,
    symbol_names,
    symbol_values,
    pauli_sums,
    num_samples,
    forward_pass_vals,
    grad
)

Differentiate a circuit with sampled expectation.

This is called at graph runtime by TensorFlow. differentiate_sampled calls he inheriting differentiator's get_gradient_circuits and uses those components to construct the gradient.

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_differentiable_op(
    *, sampled_op=None, analytic_op=None
)

Generate a differentiable op by attaching self to an op.

This function returns a tf.function that passes values through to forward_op during the forward pass and this differentiator (self) to backpropagate through the op during the backward pass. If sampled_op is provided the differentiators differentiate_sampled method will be invoked (which requires sampled_op to be a sample based expectation op with num_samples input tensor). If analytic_op is provided the differentiators differentiate_analytic method will be invoked (which requires analytic_op to be an analytic based expectation op that does NOT have num_samples as an input). If both sampled_op and analytic_op are provided an exception will be raised.

This generate_differentiable_op() can be called only ONCE because of the one differentiator per op policy. You need to call refresh() to reuse this differentiator with another op.

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.

get_gradient_circuits

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@abc.abstractmethod
get_gradient_circuits(
    programs, symbol_names, symbol_values
)

Return circuits to compute gradients for given forward pass circuits.

Prepares (but does not execute) all intermediate circuits needed to calculate the gradients for the given forward pass circuits specified by programs, symbol_names, and symbol_values. The returned tf.Tensor objects give all necessary information to recreate the internal logic of the differentiator.

This base class defines the standard way to use the outputs of this function to obtain either analytic gradients or sample gradients. Below is code that is copied directly from the differentiate_analytic default implementation, which is then compared to how one could automatically get this gradient. The point is that the derivatives of some functions cannot be calculated via the available auto-diff (such as when the function is not expressible efficiently as a PauliSum), and then one would need to use get_gradient_circuits the manual way.

Suppose we have some inputs programs, symbol_names, and symbol_values. To get the derivative of the expectation values of a tensor of PauliSums pauli_sums with respect to these inputs, do:

diff = <some differentiator>()
(
    batch_programs, new_symbol_names, batch_symbol_values,
    batch_weights, batch_mapper
) = diff.get_gradient_circuits(
    programs, symbol_names, symbol_values)
exp_layer = tfq.layers.Expectation()
batch_pauli_sums = tf.tile(
    tf.expand_dims(pauli_sums, 1),
    [1, tf.shape(batch_programs)[1], 1])
n_batch_programs = tf.reduce_prod(tf.shape(batch_programs))
n_symbols = tf.shape(new_symbol_names)[0]
n_ops = tf.shape(pauli_sums)[1]
batch_expectations = tfq.layers.Expectation()(
    tf.reshape(batch_programs, [n_batch_programs]),
    symbol_names=new_symbol_names,
    symbol_values=tf.reshape(
        batch_symbol_values, [n_batch_programs, n_symbols]),
    operators=tf.reshape(
        batch_pauli_sums, [n_batch_programs, n_ops]))
batch_expectations = tf.reshape(
    batch_expectations, tf.shape(batch_pauli_sums))
batch_jacobian = tf.map_fn(
    lambda x: tf.einsum(&#x27;km,kmp->kp', x[0], tf.gather(x[1], x[2])),
    (batch_weights, batch_expectations, batch_mapper),
    fn_output_signature=tf.float32)
grad_manual = tf.reduce_sum(batch_jacobian, -1)

To perform the same gradient calculation automatically:

with tf.GradientTape() as g:
    g.watch(symbol_values)
    exact_outputs = tfq.layers.Expectation()(
        programs, symbol_names=symbol_names,
        symbol_values=symbol_values, operators=pauli_sums)
grad_auto = g.gradient(exact_outputs, symbol_values)
tf.math.reduce_all(grad_manual == grad_auto).numpy()
True

Args
programs tf.Tensor of strings with shape [batch_size] containing the string representations of the circuits to be executed during the forward pass.
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 during the forward pass, following the ordering dictated by symbol_names.

Returns
batch_programs 2-D tf.Tensor of strings representing circuits to run to evaluate the gradients. The first dimension is the length of the input programs. At each index i in the first dimension is the tensor of circuits required to evaluate the gradient of the input circuit programs[i]. The size of the second dimension is determined by the inheriting differentiator.
new_symbol_names tf.Tensor of strings, containing the name of every symbol used in every circuit in batch_programs. The length is determined by the inheriting differentiator.
batch_symbol_values 3-D tf.Tensor of DType tf.float32 containing values to fill in to every parameter in every circuit. The first two dimensions are the same shape as batch_programs; the last dimension is the length of new_symbol_names. Thus, at each index i in the first dimension is the 2-D tensor of parameter values to fill in to batch_programs[i].
batch_weights 3-D tf.Tensor of DType tf.float32 which defines how much weight to give to each program when computing the derivatives. First dimension is the length of the input programs, second dimension is the length of the input symbol_names, and the third dimension is determined by the inheriting differentiator.
batch_mapper 3-D tf.Tensor of DType tf.int32 which defines how to map expectation values of the circuits generated by this differentiator to the derivatives of the original circuits. It says which indices of the returned programs are relevant for the derivative of each symbol, for use by tf.gather. The first dimension is the length of the input programs, the second dimension is the length of the input symbol_names, and the third dimension is the length of the last dimension of the output batch_weights.

refresh

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refresh()

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