Turning quantum nodes into Keras Layers

Creating neural networks in Keras is easy. Models are constructed from elementary layers and can be trained using a high-level API. For example, the following code defines a two-layer network that could be used for binary classification:

import tensorflow as tf

layer_1 = tf.keras.layers.Dense(2)
layer_2 = tf.keras.layers.Dense(2, activation="softmax")

model = tf.keras.Sequential([layer_1, layer_2])
model.compile(loss="mae")

The model can then be trained using model.fit().

What if we want to add a quantum layer to our model? This is possible in PennyLane: QNodes can be converted into Keras layers and combined with the wide range of built-in classical layers to create truly hybrid models. This tutorial will guide you through a simple example to show you how it’s done!

Note

A similar demo explaining how to turn quantum nodes into Torch layers is also available.

Fixing the dataset and problem

Let us begin by choosing a simple dataset and problem to allow us to focus on how the hybrid model is constructed. Our objective is to classify points generated from scikit-learn’s binary-class make_moons() dataset:

import matplotlib.pyplot as plt
from sklearn.datasets import make_moons

X, y = make_moons(n_samples=200, noise=0.1)
y_hot = tf.keras.utils.to_categorical(y, num_classes=2)  # one-hot encoded labels

c = ["#1f77b4" if y_ == 0 else "#ff7f0e" for y_ in y]  # colours for each class
plt.axis("off")
plt.scatter(X[:, 0], X[:, 1], c=c)
plt.show()
tutorial qnn module tf

Defining a QNode

Our next step is to define the QNode that we want to interface with Keras. Any combination of device, operations and measurements that is valid in PennyLane can be used to compose the QNode. However, the QNode arguments must satisfy additional conditions including having an argument called inputs. All other arguments must be arrays or tensors and are treated as trainable weights in the model. We fix a two-qubit QNode using the default.qubit simulator and operations from the templates module.

import pennylane as qml

n_qubits = 2
dev = qml.device("default.qubit", wires=n_qubits)

@qml.qnode(dev)
def qnode(inputs, weights):
    qml.templates.AngleEmbedding(inputs, wires=range(n_qubits))
    qml.templates.BasicEntanglerLayers(weights, wires=range(n_qubits))
    return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_qubits)]

Interfacing with Keras

With the QNode defined, we are ready to interface with Keras. This is achieved using the KerasLayer class of the qnn module, which converts the QNode to the elementary building block of Keras: a layer. We shall see in the following how the resultant layer can be combined with other well-known neural network layers to form a hybrid model.

We must first define the weight_shapes dictionary. Recall that all of the arguments of the QNode (except the one named inputs) are treated as trainable weights. For the QNode to be successfully converted to a layer in Keras, we need to provide the details of the shape of each trainable weight for them to be initialized. The weight_shapes dictionary maps from the argument names of the QNode to corresponding shapes:

n_layers = 6
weight_shapes = {"weights": (n_layers, n_qubits)}

In our example, the weights argument of the QNode is trainable and has shape given by (n_layers, n_qubits), which is passed to BasicEntanglerLayers().

Now that weight_shapes is defined, it is easy to then convert the QNode:

qlayer = qml.qnn.KerasLayer(qnode, weight_shapes, output_dim=n_qubits)

With this done, the QNode can now be treated just like any other Keras layer and we can proceed using the familiar Keras workflow.

Creating a hybrid model

Let’s create a basic three-layered hybrid model consisting of:

  1. a 2-neuron fully connected classical layer
  2. our 2-qubit QNode converted into a layer
  3. another 2-neuron fully connected classical layer
  4. a softmax activation to convert to a probability vector

A diagram of the model can be seen in the figure below.

../_images/qnn_keras.png

We can construct the model using the Sequential API:

clayer_1 = tf.keras.layers.Dense(2)
clayer_2 = tf.keras.layers.Dense(2, activation="softmax")
model = tf.keras.models.Sequential([clayer_1, qlayer, clayer_2])

Training the model

We can now train our hybrid model on the classification dataset using the usual Keras approach. We’ll use the standard SGD optimizer and the mean absolute error loss function:

opt = tf.keras.optimizers.SGD(learning_rate=0.2)
model.compile(opt, loss="mae", metrics=["accuracy"])

Note that there are more advanced combinations of optimizer and loss function, but here we are focusing on the basics.

The model is now ready to be trained!

X = X.astype("float32")
y_hot = y_hot.astype("float32")
fitting = model.fit(X, y_hot, epochs=6, batch_size=5, validation_split=0.25, verbose=2)

Out:

Epoch 1/6
30/30 - 11s - loss: 0.4372 - accuracy: 0.6267 - val_loss: 0.3729 - val_accuracy: 0.6600
Epoch 2/6
30/30 - 11s - loss: 0.3350 - accuracy: 0.6800 - val_loss: 0.2872 - val_accuracy: 0.7600
Epoch 3/6
30/30 - 11s - loss: 0.2782 - accuracy: 0.7333 - val_loss: 0.2274 - val_accuracy: 0.8000
Epoch 4/6
30/30 - 11s - loss: 0.2345 - accuracy: 0.8000 - val_loss: 0.1818 - val_accuracy: 0.8600
Epoch 5/6
30/30 - 10s - loss: 0.2113 - accuracy: 0.8200 - val_loss: 0.1531 - val_accuracy: 0.8600
Epoch 6/6
30/30 - 10s - loss: 0.1914 - accuracy: 0.8333 - val_loss: 0.1508 - val_accuracy: 0.9000

How did we do? The model looks to have successfully trained and the accuracy on both the training and validation datasets is reasonably high. In practice, we would aim to push the accuracy higher by thinking carefully about the model design and the choice of hyperparameters such as the learning rate.

Creating non-sequential models

The model we created above was composed of a sequence of classical and quantum layers. This type of model is very common and is suitable in a lot of situations. However, in some cases we may want a greater degree of control over how the model is constructed, for example when we have multiple inputs and outputs or when we want to distribute the output of one layer into multiple subsequent layers.

Suppose we want to make a hybrid model consisting of:

  1. a 4-neuron fully connected classical layer
  2. a 2-qubit quantum layer connected to the first two neurons of the previous classical layer
  3. a 2-qubit quantum layer connected to the second two neurons of the previous classical layer
  4. a 2-neuron fully connected classical layer which takes a 4-dimensional input from the combination of the previous quantum layers
  5. a softmax activation to convert to a probability vector

A diagram of the model can be seen in the figure below.

../_images/qnn2_keras.png

This model can also be constructed using the Functional API:

# re-define the layers
clayer_1 = tf.keras.layers.Dense(4)
qlayer_1 = qml.qnn.KerasLayer(qnode, weight_shapes, output_dim=n_qubits)
qlayer_2 = qml.qnn.KerasLayer(qnode, weight_shapes, output_dim=n_qubits)
clayer_2 = tf.keras.layers.Dense(2, activation="softmax")

# construct the model
inputs = tf.keras.Input(shape=(2,))
x = clayer_1(inputs)
x_1, x_2 = tf.split(x, 2, axis=1)
x_1 = qlayer_1(x_1)
x_2 = qlayer_2(x_2)
x = tf.concat([x_1, x_2], axis=1)
outputs = clayer_2(x)

model = tf.keras.Model(inputs=inputs, outputs=outputs)

As a final step, let’s train the model to check if it’s working:

opt = tf.keras.optimizers.SGD(learning_rate=0.2)
model.compile(opt, loss="mae", metrics=["accuracy"])

fitting = model.fit(X, y_hot, epochs=6, batch_size=5, validation_split=0.25, verbose=2)

Out:

Epoch 1/6
30/30 - 20s - loss: 0.4333 - accuracy: 0.6933 - val_loss: 0.2892 - val_accuracy: 0.8400
Epoch 2/6
30/30 - 20s - loss: 0.2542 - accuracy: 0.7933 - val_loss: 0.1912 - val_accuracy: 0.8400
Epoch 3/6
30/30 - 20s - loss: 0.2108 - accuracy: 0.8133 - val_loss: 0.1587 - val_accuracy: 0.9000
Epoch 4/6
30/30 - 20s - loss: 0.1930 - accuracy: 0.8400 - val_loss: 0.1475 - val_accuracy: 0.9000
Epoch 5/6
30/30 - 20s - loss: 0.1852 - accuracy: 0.8133 - val_loss: 0.1324 - val_accuracy: 0.9000
Epoch 6/6
30/30 - 20s - loss: 0.1790 - accuracy: 0.8267 - val_loss: 0.1233 - val_accuracy: 0.9000

Great! We’ve mastered the basics of constructing hybrid classical-quantum models using PennyLane and Keras. Can you think of any interesting hybrid models to construct? How do they perform on realistic datasets?

Total running time of the script: ( 3 minutes 9.699 seconds)

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