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# 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 'noiseless' simulator, options include {'noiseless', 'noisy'}. In the noisy case a `repetitions` call argument must be provided. Users may also specify a preconfigured cirq object to use instead, which must inherit `cirq.sim.simulator.SimulatesExpectationValues`.
`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 `tfq.differentiators.ParameterShift()`. If `backend` is also 'noiseless' then default is `tfq.differentiators.Adjoint`.

`activity_regularizer` Optional regularizer function for the output of this layer.
`compute_dtype` The dtype of the layer's computations.

This is equivalent to `Layer.dtype_policy.compute_dtype`. Unless mixed precision is used, this is the same as `Layer.dtype`, the dtype of the weights.

Layers automatically cast their inputs to the compute dtype, which causes computations and the output to be in the compute dtype as well. This is done by the base Layer class in `Layer.call`, so you do not have to insert these casts if implementing your own layer.

Layers often perform certain internal computations in higher precision when `compute_dtype` is float16 or bfloat16 for numeric stability. The output will still typically be float16 or bfloat16 in such cases.

`dtype` The dtype of the layer weights.

This is equivalent to `Layer.dtype_policy.variable_dtype`. Unless mixed precision is used, this is the same as `Layer.compute_dtype`, the dtype of the layer's computations.

`dtype_policy` The dtype policy associated with this layer.

This is an instance of a `tf.keras.mixed_precision.Policy`.

`dynamic` Whether the layer is dynamic (eager-only); set in the constructor.
`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_spec` `InputSpec` instance(s) describing the input format for this layer.

When you create a layer subclass, you can set `self.input_spec` to enable the layer to run input compatibility checks when it is called. Consider a `Conv2D` layer: it can only be called on a single input tensor of rank 4. As such, you can set, in `__init__()`:

``````self.input_spec = tf.keras.layers.InputSpec(ndim=4)
``````

Now, if you try to call the layer on an input that isn't rank 4 (for instance, an input of shape `(2,)`, it will raise a nicely-formatted error:

``````ValueError: Input 0 of layer conv2d is incompatible with the layer:
expected ndim=4, found ndim=1. Full shape received: [2]
``````

Input checks that can be specified via `input_spec` include:

• Structure (e.g. a single input, a list of 2 inputs, etc)
• Shape
• Rank (ndim)
• Dtype

For more information, see `tf.keras.layers.InputSpec`.

`losses` List of losses added using the `add_loss()` API.

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.

````class MyLayer(tf.keras.layers.Layer):`
`  def call(self, inputs):`
`    self.add_loss(tf.abs(tf.reduce_mean(inputs)))`
`    return inputs`
`l = MyLayer()`
`l(np.ones((10, 1)))`
`l.losses`
`[1.0]`
```
````inputs = tf.keras.Input(shape=(10,))`
`x = tf.keras.layers.Dense(10)(inputs)`
`outputs = tf.keras.layers.Dense(1)(x)`
`model = tf.keras.Model(inputs, outputs)`
`# Activity regularization.`
`len(model.losses)`
`0`
`model.add_loss(tf.abs(tf.reduce_mean(x)))`
`len(model.losses)`
`1`
```
````inputs = tf.keras.Input(shape=(10,))`
`d = tf.keras.layers.Dense(10, kernel_initializer='ones')`
`x = d(inputs)`
`outputs = tf.keras.layers.Dense(1)(x)`
`model = tf.keras.Model(inputs, outputs)`
`# Weight regularization.`
`model.add_loss(lambda: tf.reduce_mean(d.kernel))`
`model.losses`
`[<tf.Tensor: shape=(), dtype=float32, numpy=1.0>]`
```

`metrics` List of metrics added using the `add_metric()` API.

````input = tf.keras.layers.Input(shape=(3,))`
`d = tf.keras.layers.Dense(2)`
`output = d(input)`
`d.add_metric(tf.reduce_max(output), name='max')`
`d.add_metric(tf.reduce_min(output), name='min')`
`[m.name for m in d.metrics]`
`['max', 'min']`
```

`name` Name of the layer (string), set in the constructor.
`name_scope` Returns a `tf.name_scope` instance for this class.
`non_trainable_weights` List of all non-trainable weights tracked by this layer.

Non-trainable weights are not updated during training. They are expected to be updated manually in `call()`.

`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.

`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`
`list(a.submodules) == [b, c]`
`True`
`list(b.submodules) == [c]`
`True`
`list(c.submodules) == []`
`True`
```

`supports_masking` Whether this layer supports computing a mask using `compute_mask`.
`trainable`

`trainable_weights` List of all trainable weights tracked by this layer.

Trainable weights are updated via gradient descent during training.

`variable_dtype` Alias of `Layer.dtype`, the dtype of the weights.
`weights` Returns the list of all layer variables/weights.

## Methods

### `add_loss`

Add loss tensor(s), potentially dependent on layer inputs.

Some losses (for instance, activity regularization losses) may be dependent on the inputs passed when calling a layer. Hence, when reusing the same layer on different inputs `a` and `b`, some entries in `layer.losses` may be dependent on `a` and some on `b`. This method automatically keeps track of dependencies.

This method can be used inside a subclassed layer or model's `call` function, in which case `losses` should be a Tensor or list of Tensors.

#### Example:

``````class MyLayer(tf.keras.layers.Layer):
def call(self, inputs):
return inputs
``````

This method can also be called directly on a Functional Model during construction. In this case, any loss Tensors passed to this Model must be symbolic and be able to be traced back to the model's `Input`s. These losses become part of the model's topology and are tracked in `get_config`.

#### Example:

``````inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Activity regularization.
``````

If this is not the case for your loss (if, for example, your loss references a `Variable` of one of the model's layers), you can wrap your loss in a zero-argument lambda. These losses are not tracked as part of the model's topology since they can't be serialized.

#### Example:

``````inputs = tf.keras.Input(shape=(10,))
d = tf.keras.layers.Dense(10)
x = d(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Weight regularization.
``````

Arguments
`losses` Loss tensor, or list/tuple of tensors. Rather than tensors, losses may also be zero-argument callables which create a loss tensor.
`**kwargs` Additional keyword arguments for backward compatibility. Accepted values: inputs - Deprecated, will be automatically inferred.

### `add_metric`

Adds metric tensor to the layer.

This method can be used inside the `call()` method of a subclassed layer or model.

``````class MyMetricLayer(tf.keras.layers.Layer):
def __init__(self):
super(MyMetricLayer, self).__init__(name='my_metric_layer')
self.mean = tf.keras.metrics.Mean(name='metric_1')

def call(self, inputs):
return inputs
``````

This method can also be called directly on a Functional Model during construction. In this case, any tensor passed to this Model must be symbolic and be able to be traced back to the model's `Input`s. These metrics become part of the model's topology and are tracked when you save the model via `save()`.

``````inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
``````
``````inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
``````

Args
`value` Metric tensor.
`name` String metric name.
`**kwargs` Additional keyword arguments for backward compatibility. Accepted values: `aggregation` - When the `value` tensor provided is not the result of calling a `keras.Metric` instance, it will be aggregated by default using a `keras.Metric.Mean`.

### `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_weights`

Returns the current weights of the layer.

The weights of a layer represent the state of the layer. This function returns both trainable and non-trainable weight values associated with this layer as a list of Numpy arrays, which can in turn be used to load state into similarly parameterized layers.

For example, a Dense layer returns a list of two values-- per-output weights and the bias value. These can be used to set the weights of another Dense layer:

````a = tf.keras.layers.Dense(1,`
`  kernel_initializer=tf.constant_initializer(1.))`
`a_out = a(tf.convert_to_tensor([[1., 2., 3.]]))`
`a.get_weights()`
`[array([[1.],`
`       [1.],`
`       [1.]], dtype=float32), array([0.], dtype=float32)]`
`b = tf.keras.layers.Dense(1,`
`  kernel_initializer=tf.constant_initializer(2.))`
`b_out = b(tf.convert_to_tensor([[10., 20., 30.]]))`
`b.get_weights()`
`[array([[2.],`
`       [2.],`
`       [2.]], dtype=float32), array([0.], dtype=float32)]`
`b.set_weights(a.get_weights())`
`b.get_weights()`
`[array([[1.],`
`       [1.],`
`       [1.]], dtype=float32), array([0.], dtype=float32)]`
```

Returns
Weights values as a list of numpy arrays.

### `set_weights`

Sets the weights of the layer, from Numpy arrays.

The weights of a layer represent the state of the layer. This function sets the weight values from numpy arrays. The weight values should be passed in the order they are created by the layer. Note that the layer's weights must be instantiated before calling this function by calling the layer.

For example, a Dense layer returns a list of two values-- per-output weights and the bias value. These can be used to set the weights of another Dense layer:

````a = tf.keras.layers.Dense(1,`
`  kernel_initializer=tf.constant_initializer(1.))`
`a_out = a(tf.convert_to_tensor([[1., 2., 3.]]))`
`a.get_weights()`
`[array([[1.],`
`       [1.],`
`       [1.]], dtype=float32), array([0.], dtype=float32)]`
`b = tf.keras.layers.Dense(1,`
`  kernel_initializer=tf.constant_initializer(2.))`
`b_out = b(tf.convert_to_tensor([[10., 20., 30.]]))`
`b.get_weights()`
`[array([[2.],`
`       [2.],`
`       [2.]], dtype=float32), array([0.], dtype=float32)]`
`b.set_weights(a.get_weights())`
`b.get_weights()`
`[array([[1.],`
`       [1.],`
`       [1.]], dtype=float32), array([0.], dtype=float32)]`
```

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], 3]))`
`    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([1, 2]))`
`<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>`
`mod.w`
`<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,`
`numpy=..., dtype=float32)>`
```

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
`*args` Positional arguments to be passed to `self.call`.
`**kwargs` 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).
`RuntimeError` if `super().__init__()` was not called in the constructor.

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