# tfq.layers.Expectation

A Layer that calculates an expectation value.

### Used in the notebooks

Used in the tutorials

Given an input circuit and set of parameter values, prepare a quantum state and output expectation values taken on that state with respect to some observables to the tensorflow graph.

First define a simple helper function for generating a parametrized quantum circuit that we will use throughout:

````def _gen_single_bit_rotation_problem(bit, symbols):`
`    """Generate a toy problem on 1 qubit."""`
`    starting_state = [0.123, 0.456, 0.789]`
`    circuit = cirq.Circuit(`
`        cirq.rx(starting_state[0])(bit),`
`        cirq.ry(starting_state[1])(bit),`
`        cirq.rz(starting_state[2])(bit),`
`        cirq.rz(symbols[2])(bit),`
`        cirq.ry(symbols[1])(bit),`
`        cirq.rx(symbols[0])(bit)`
`    )`
`    return circuit`
```

In quantum machine learning there are two very common use cases that align with keras layer constructs. The first is where the circuits represent the input data points (see the note at the bottom about using compiled models):

````bit = cirq.GridQubit(0, 0)`
`symbols = sympy.symbols('x, y, z')`
`ops = [-1.0 * cirq.Z(bit), cirq.X(bit) + 2.0 * cirq.Z(bit)]`
`circuit_list = [`
`    _gen_single_bit_rotation_problem(bit, symbols),`
`    cirq.Circuit(`
`        cirq.Z(bit) ** symbols[0],`
`        cirq.X(bit) ** symbols[1],`
`        cirq.Z(bit) ** symbols[2]`
`    ),`
`    cirq.Circuit(`
`        cirq.X(bit) ** symbols[0],`
`        cirq.Z(bit) ** symbols[1],`
`        cirq.X(bit) ** symbols[2]`
`    )`
`]`
`expectation_layer = tfq.layers.Expectation()`
`output = expectation_layer(`
`    circuit_list, symbol_names=symbols, operators = ops)`
`# Here output[i][j] corresponds to the expectation of all the ops`
`# in ops w.r.t circuits[i] where keras managed variables are`
`# placed in the symbols 'x', 'y', 'z'.`
`tf.shape(output)`
`tf.Tensor([3 2], shape=(2,), dtype=int32)`
```

Here, different `cirq.Circuit` instances sharing the common symbols 'x', 'y' and 'z' are used as input. Keras uses the `symbol_names` argument to map Keras managed variables to these circuits constructed with `sympy.Symbol`s. Note that you used a Python `list` containing your circuits, you could also specify a `tf.keras.Input` layer or any tensorlike object to specify the circuits you would like fed to the layer at runtime.

Another common use case is where there is a fixed circuit and the expectation operators vary:

````bit = cirq.GridQubit(0, 0)`
`symbols = sympy.symbols('x, y, z')`
`ops = [-1.0 * cirq.Z(bit), cirq.X(bit) + 2.0 * cirq.Z(bit)]`
`fixed_circuit = _gen_single_bit_rotation_problem(bit, symbols)`
`expectation_layer = tfq.layers.Expectation()`
`output = expectation_layer(`
`    fixed_circuit,`
`    symbol_names=symbols,`
`    operators=ops,`
`    initializer=tf.keras.initializers.RandomUniform(0, 2 * np.pi))`
`# Here output[i][j] corresponds to`
`# the expectation of operators[i][j] w.r.t the circuit where`
`# variable values are managed by keras and store numbers in`
`# the symbols 'x', 'y', 'z'.`
`tf.shape(output)`
`tf.Tensor([1 2], shape=(2,), dtype=int32)`
```

Note that in the above examples you used a `cirq.Circuit` object and a list of `cirq.PauliSum` objects as inputs to your layer. To allow for varying inputs your could change the line in the above code to: `expectation_layer(circuit_inputs, symbol_names=symbols, operators=ops)` with `circuit_inputs` is `tf.keras.Input(shape=(), dtype=tf.dtypes.string)` to allow you to pass in different circuits in a compiled model. Lastly you also supplied a `tf.keras.initializer` to the `initializer` argument. This argument is optional in the case that the layer itself will be managing the symbols of the circuit and not have them fed in from somewhere else in the model.

There are also some more complex use cases. Notably these use cases all make use of the `symbol_values` parameter that causes the `Expectation` layer to stop managing the `sympy.Symbol`s in the quantum circuits for the user and instead require them to supply input values themselves. Lets look at the case where there is a single fixed circuit, some fixed operators and symbols that must be common to all circuits:

````bit = cirq.GridQubit(0, 0)`
`symbols = sympy.symbols('x, y, z')`
`ops = [cirq.Z(bit), cirq.X(bit)]`
`circuit = _gen_single_bit_rotation_problem(bit, symbols)`
`values = [[1,1,1], [2,2,2], [3,3,3]]`
`expectation_layer = tfq.layers.Expectation()`
`output = expectation_layer(`
`    circuit,`
`    symbol_names=symbols,`
`    symbol_values=values,`
`    operators=ops)`
`# output[i][j] = The expectation of operators[j] with`
`# values[i] placed into the symbols of the circuit`
`# with the order specified by symbol_names.`
`# so output[1][2] = The expectation of your circuit with parameter`
`# values [2,2,2] w.r.t Pauli X.`
`output`
`tf.Tensor(`
`[[0.63005245 0.76338404]`
` [0.25707167 0.9632684 ]`
` [0.79086655 0.5441111 ]], shape=(3, 2), dtype=float32)`
```

Here is a simple model that uses this particular input signature of `tfq.layers.Expectation`, that learns to undo the random rotation of the qubit:

````bit = cirq.GridQubit(0, 0)`
`symbols = sympy.symbols('x, y, z')`
`circuit = _gen_single_bit_rotation_problem(bit, symbols)`
`control_input = tf.keras.Input(shape=(1,))`
`circuit_inputs = tf.keras.Input(shape=(), dtype=tf.dtypes.string)`
`d1 = tf.keras.layers.Dense(10)(control_input)`
`d2 = tf.keras.layers.Dense(3)(d1)`
`expectation = tfq.layers.Expectation()(`
`    circuit_inputs, # See note below!`
`    symbol_names=symbols,`
`    symbol_values=d2,`
`    operators=cirq.Z(bit))`
`data_in = np.array([[1], [0]], dtype=np.float32)`
`data_out = np.array([[1], [-1]], dtype=np.float32)`
`model = tf.keras.Model(`
`    inputs=[circuit_inputs, control_input], outputs=expectation)`
`model.compile(`
`    optimizer=tf.keras.optimizers.Adam(learning_rate=0.01),`
`    loss=tf.keras.losses.mean_squared_error)`
`history = model.fit(`
`    x=[tfq.convert_to_tensor([circuit] * 2), data_in],`
`    y=data_out,`
`    epochs=100)`
```

Lastly `symbol_values`, `operators` and circuit `inputs` can all be fed Python `list` objects. In addition to this they can also be fed `tf.Tensor` inputs, meaning that you can input all of these things from other Tensor objects (like `tf.keras.Dense` layer outputs or `tf.keras.Input`s etc).

`backend` Optional Backend to use to simulate states. Defaults to the native TensorFlow simulator (None), however users may also specify a preconfigured cirq simulation object to use instead, which must inherit `cirq.SimulatesFinalState`.
`differentiator` Optional Differentiator to use to calculate analytic derivative values of given operators_to_measure and circuit, which must inherit `tfq.differentiators.Differentiator` and implements `differentiate_analytic` method. Defaults to None, which uses `linear_combination.ForwardDifference()`.

`activity_regularizer` Optional regularizer function for the output of this layer.
`dtype`

`dynamic`

`input` Retrieves the input tensor(s) of a layer.

Only applicable if the layer has exactly one input, i.e. if it is connected to one incoming layer.

`input_mask` Retrieves the input mask tensor(s) of a layer.

Only applicable if the layer has exactly one inbound node, i.e. if it is connected to one incoming layer.

`input_shape` Retrieves the input shape(s) of a layer.

Only applicable if the layer has exactly one input, i.e. if it is connected to one incoming layer, or if all inputs have the same shape.

`input_spec`

`losses` Losses which are associated with this `Layer`.

Variable regularization tensors are created when this property is accessed, so it is eager safe: accessing `losses` under a `tf.GradientTape` will propagate gradients back to the corresponding variables.

`metrics`

`name` Returns the name of this module as passed or determined in the ctor.

`name_scope` Returns a `tf.name_scope` instance for this class.
`non_trainable_variables`

`non_trainable_weights`

`output` Retrieves the output tensor(s) of a layer.

Only applicable if the layer has exactly one output, i.e. if it is connected to one incoming layer.

`output_mask` Retrieves the output mask tensor(s) of a layer.

Only applicable if the layer has exactly one inbound node, i.e. if it is connected to one incoming layer.

`output_shape` Retrieves the output shape(s) of a layer.

Only applicable if the layer has one output, or if all outputs have the same shape.

`submodules` Sequence of all sub-modules.

Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on).

``````a = tf.Module()
b = tf.Module()
c = tf.Module()
a.b = b
b.c = c
assert list(a.submodules) == [b, c]
assert list(b.submodules) == [c]
assert list(c.submodules) == []
``````

`trainable`

`trainable_variables` Sequence of trainable variables owned by this module and its submodules.

`trainable_weights`

`updates`

`variables` Returns the list of all layer variables/weights.

Alias of `self.weights`.

`weights` Returns the list of all layer variables/weights.

## Methods

### `build`

Creates the variables of the layer (optional, for subclass implementers).

This is a method that implementers of subclasses of `Layer` or `Model` can override if they need a state-creation step in-between layer instantiation and layer call.

This is typically used to create the weights of `Layer` subclasses.

Arguments
`input_shape` Instance of `TensorShape`, or list of instances of `TensorShape` if the layer expects a list of inputs (one instance per input).

### `compute_mask`

Arguments
`inputs` Tensor or list of tensors.
`mask` Tensor or list of tensors.

Returns
None or a tensor (or list of tensors, one per output tensor of the layer).

### `compute_output_shape`

Computes the output shape of the layer.

If the layer has not been built, this method will call `build` on the layer. This assumes that the layer will later be used with inputs that match the input shape provided here.

Arguments
`input_shape` Shape tuple (tuple of integers) or list of shape tuples (one per output tensor of the layer). Shape tuples can include None for free dimensions, instead of an integer.

Returns
An input shape tuple.

### `count_params`

Count the total number of scalars composing the weights.

Returns
An integer count.

Raises
`ValueError` if the layer isn't yet built (in which case its weights aren't yet defined).

### `from_config`

Creates a layer from its config.

This method is the reverse of `get_config`, capable of instantiating the same layer from the config dictionary. It does not handle layer connectivity (handled by Network), nor weights (handled by `set_weights`).

Arguments
`config` A Python dictionary, typically the output of get_config.

Returns
A layer instance.

### `get_config`

Returns the config of the layer.

A layer config is a Python dictionary (serializable) containing the configuration of a layer. The same layer can be reinstantiated later (without its trained weights) from this configuration.

The config of a layer does not include connectivity information, nor the layer class name. These are handled by `Network` (one layer of abstraction above).

Returns
Python dictionary.

### `get_input_at`

Retrieves the input tensor(s) of a layer at a given node.

Arguments
`node_index` Integer, index of the node from which to retrieve the attribute. E.g. `node_index=0` will correspond to the first time the layer was called.

Returns
A tensor (or list of tensors if the layer has multiple inputs).

Raises
`RuntimeError` If called in Eager mode.

### `get_input_mask_at`

Retrieves the input mask tensor(s) of a layer at a given node.

Arguments
`node_index` Integer, index of the node from which to retrieve the attribute. E.g. `node_index=0` will correspond to the first time the layer was called.

Returns
A mask tensor (or list of tensors if the layer has multiple inputs).

### `get_input_shape_at`

Retrieves the input shape(s) of a layer at a given node.

Arguments
`node_index` Integer, index of the node from which to retrieve the attribute. E.g. `node_index=0` will correspond to the first time the layer was called.

Returns
A shape tuple (or list of shape tuples if the layer has multiple inputs).

Raises
`RuntimeError` If called in Eager mode.

### `get_losses_for`

Retrieves losses relevant to a specific set of inputs.

Arguments
`inputs` Input tensor or list/tuple of input tensors.

Returns
List of loss tensors of the layer that depend on `inputs`.

### `get_output_at`

Retrieves the output tensor(s) of a layer at a given node.

Arguments
`node_index` Integer, index of the node from which to retrieve the attribute. E.g. `node_index=0` will correspond to the first time the layer was called.

Returns
A tensor (or list of tensors if the layer has multiple outputs).

Raises
`RuntimeError` If called in Eager mode.

### `get_output_mask_at`

Retrieves the output mask tensor(s) of a layer at a given node.

Arguments
`node_index` Integer, index of the node from which to retrieve the attribute. E.g. `node_index=0` will correspond to the first time the layer was called.

Returns
A mask tensor (or list of tensors if the layer has multiple outputs).

### `get_output_shape_at`

Retrieves the output shape(s) of a layer at a given node.

Arguments
`node_index` Integer, index of the node from which to retrieve the attribute. E.g. `node_index=0` will correspond to the first time the layer was called.

Returns
A shape tuple (or list of shape tuples if the layer has multiple outputs).

Raises
`RuntimeError` If called in Eager mode.

### `get_updates_for`

Retrieves updates relevant to a specific set of inputs.

Arguments
`inputs` Input tensor or list/tuple of input tensors.

Returns
List of update ops of the layer that depend on `inputs`.

### `get_weights`

Returns the current weights of the layer.

Returns
Weights values as a list of numpy arrays.

### `set_weights`

Sets the weights of the layer, from Numpy arrays.

Arguments
`weights` a list of Numpy arrays. The number of arrays and their shape must match number of the dimensions of the weights of the layer (i.e. it should match the output of `get_weights`).

Raises
`ValueError` If the provided weights list does not match the layer's specifications.

### `with_name_scope`

Decorator to automatically enter the module name scope.

``````class MyModule(tf.Module):
@tf.Module.with_name_scope
def __call__(self, x):
if not hasattr(self, 'w'):
self.w = tf.Variable(tf.random.normal([x.shape[1], 64]))
return tf.matmul(x, self.w)
``````

Using the above module would produce `tf.Variable`s and `tf.Tensor`s whose names included the module name:

``````mod = MyModule()
mod(tf.ones([8, 32]))
# ==> <tf.Tensor: ...>
mod.w
# ==> <tf.Variable ...'my_module/w:0'>
``````

Args
`method` The method to wrap.

Returns
The original method wrapped such that it enters the module's name scope.

### `__call__`

Wraps `call`, applying pre- and post-processing steps.

Arguments
`inputs` input tensor(s).
`*args` additional positional arguments to be passed to `self.call`.
`**kwargs` additional keyword arguments to be passed to `self.call`.

Returns
Output tensor(s).

#### Note:

• The following optional keyword arguments are reserved for specific uses:
• `training`: Boolean scalar tensor of Python boolean indicating whether the `call` is meant for training or inference.
• `mask`: Boolean input mask.
• If the layer's `call` method takes a `mask` argument (as some Keras layers do), its default value will be set to the mask generated for `inputs` by the previous layer (if `input` did come from a layer that generated a corresponding mask, i.e. if it came from a Keras layer with masking support.

Raises
`ValueError` if the layer's `call` method returns None (an invalid value).