量子卷积神经网络

在 TensorFlow.org 上查看 在 Google Colab 中运行 在 GitHub 上查看源代码 下载笔记本

本教程实现了一个简化的 量子卷积神经网络 (QCNN)，它是一个经典卷积神经网络的量子模拟，也是平移不变的。

此示例演示如何检测量子数据源的某些属性，例如来自设备的量子传感器或复杂模拟。量子数据源是一个 簇态，它可能具有激发，也可能没有激发，而 QCNN 将学会检测这一点（论文中使用的数据集是 SPT 相位分类）。

设置

pip install tensorflow==2.15.0

安装 TensorFlow Quantum

pip install tensorflow-quantum==0.7.3

# Update package resources to account for version changes.
import importlib, pkg_resources
importlib.reload(pkg_resources)

/tmpfs/tmp/ipykernel_26901/1875984233.py:2: DeprecationWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html
  import importlib, pkg_resources
<module 'pkg_resources' from '/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/pkg_resources/__init__.py'>

现在导入 TensorFlow 和模块依赖项

import tensorflow as tf
import tensorflow_quantum as tfq

import cirq
import sympy
import numpy as np

# visualization tools
%matplotlib inline
import matplotlib.pyplot as plt
from cirq.contrib.svg import SVGCircuit

2024-05-18 11:45:09.533738: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:9261] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
2024-05-18 11:45:09.533782: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:607] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
2024-05-18 11:45:09.535253: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1515] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2024-05-18 11:45:12.910225: E external/local_xla/xla/stream_executor/cuda/cuda_driver.cc:274] failed call to cuInit: CUDA_ERROR_NO_DEVICE: no CUDA-capable device is detected

1. 构建 QCNN

1.1 在 TensorFlow 图中组装电路

TensorFlow Quantum (TFQ) 提供了专为图内电路构建而设计的层类。一个示例是 tfq.layers.AddCircuit 层，它继承自 tf.keras.Layer。此层可以预先添加到或附加到输入批次的电路，如下图所示。

以下代码段使用此层

qubit = cirq.GridQubit(0, 0)

# Define some circuits.
circuit1 = cirq.Circuit(cirq.X(qubit))
circuit2 = cirq.Circuit(cirq.H(qubit))

# Convert to a tensor.
input_circuit_tensor = tfq.convert_to_tensor([circuit1, circuit2])

# Define a circuit that we want to append
y_circuit = cirq.Circuit(cirq.Y(qubit))

# Instantiate our layer
y_appender = tfq.layers.AddCircuit()

# Run our circuit tensor through the layer and save the output.
output_circuit_tensor = y_appender(input_circuit_tensor, append=y_circuit)

检查输入张量

print(tfq.from_tensor(input_circuit_tensor))

[cirq.Circuit([
     cirq.Moment(
         cirq.X(cirq.GridQubit(0, 0)),
     ),
 ])
 cirq.Circuit([
     cirq.Moment(
         cirq.H(cirq.GridQubit(0, 0)),
     ),
 ])                                   ]

并检查输出张量

print(tfq.from_tensor(output_circuit_tensor))

[cirq.Circuit([
     cirq.Moment(
         cirq.X(cirq.GridQubit(0, 0)),
     ),
     cirq.Moment(
         cirq.Y(cirq.GridQubit(0, 0)),
     ),
 ])
 cirq.Circuit([
     cirq.Moment(
         cirq.H(cirq.GridQubit(0, 0)),
     ),
     cirq.Moment(
         cirq.Y(cirq.GridQubit(0, 0)),
     ),
 ])                                   ]

虽然可以在不使用 tfq.layers.AddCircuit 的情况下运行以下示例，但这是一个了解如何将复杂功能嵌入到 TensorFlow 计算图中的好机会。

1.2 问题概述

你将准备一个簇态，并训练一个量子分类器来检测它是否“受激”。簇态高度纠缠，但对于经典计算机来说并不一定困难。为了清楚起见，这是一个比论文中使用的数据集更简单的数据集。

对于此分类任务，您将实现类似于 MERA 的深度 QCNN 架构，因为

  1. 与 QCNN 一样，环上的簇态具有平移不变性。
  2. 簇态高度纠缠。

此架构应能有效减少纠缠，通过读取单个量子比特来获取分类。

“激发”簇态定义为对任何量子比特应用 cirq.rx 门的簇态。Qconv 和 QPool 将在本教程的后面讨论。

1.3 TensorFlow 的构建模块

使用 TensorFlow Quantum 解决此问题的一种方法是实现以下内容

  1. 模型的输入是电路张量——空电路或特定量子比特上的 X 门，表示激发。
  2. 模型的其余量子组件使用 tfq.layers.AddCircuit 层构建。
  3. 对于推理，使用 tfq.layers.PQC 层。这会读取 \(\langle \hat{Z} \rangle\) 并将其与激发态的标签 1 或非激发态的标签 -1 进行比较。

1.4 数据

在构建模型之前，您可以生成数据。在这种情况下，它将是对簇态的激发（原始论文使用更复杂的数据集）。激发用 cirq.rx 门表示。足够大的旋转被视为激发，并标记为 1，而不够大的旋转则标记为 -1，并被视为非激发。

def generate_data(qubits):
    """Generate training and testing data."""
    n_rounds = 20  # Produces n_rounds * n_qubits datapoints.
    excitations = []
    labels = []
    for n in range(n_rounds):
        for bit in qubits:
            rng = np.random.uniform(-np.pi, np.pi)
            excitations.append(cirq.Circuit(cirq.rx(rng)(bit)))
            labels.append(1 if (-np.pi / 2) <= rng <= (np.pi / 2) else -1)

    split_ind = int(len(excitations) * 0.7)
    train_excitations = excitations[:split_ind]
    test_excitations = excitations[split_ind:]

    train_labels = labels[:split_ind]
    test_labels = labels[split_ind:]

    return tfq.convert_to_tensor(train_excitations), np.array(train_labels), \
        tfq.convert_to_tensor(test_excitations), np.array(test_labels)

您可以看到，就像使用常规机器学习一样，您创建训练集和测试集以用于对模型进行基准测试。您可以使用以下方法快速查看一些数据点

sample_points, sample_labels, _, __ = generate_data(cirq.GridQubit.rect(1, 4))
print('Input:', tfq.from_tensor(sample_points)[0], 'Output:', sample_labels[0])
print('Input:', tfq.from_tensor(sample_points)[1], 'Output:', sample_labels[1])

Input: (0, 0): ───X^0.701─── Output: -1
Input: (0, 1): ───X^-0.136─── Output: 1

1.5 定义层

现在在 TensorFlow 中定义上图所示的层。

1.5.1 簇态

第一步是使用 Google 提供的量子电路编程框架 Cirq 定义 簇态。由于这是模型的静态部分，因此使用 tfq.layers.AddCircuit 功能将其嵌入。

def cluster_state_circuit(bits):
    """Return a cluster state on the qubits in `bits`."""
    circuit = cirq.Circuit()
    circuit.append(cirq.H.on_each(bits))
    for this_bit, next_bit in zip(bits, bits[1:] + [bits[0]]):
        circuit.append(cirq.CZ(this_bit, next_bit))
    return circuit

显示 cirq.GridQubit 矩形的簇态电路

SVGCircuit(cluster_state_circuit(cirq.GridQubit.rect(1, 4)))

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1.5.2 QCNN 层

使用 Cong 和 Lukin QCNN 论文 定义构成模型的层。有一些先决条件

  • 来自 Tucci 论文 的一量子比特和二量子比特参数化酉矩阵。
  • 一个通用的参数化二量子比特池化操作。
def one_qubit_unitary(bit, symbols):
    """Make a Cirq circuit enacting a rotation of the bloch sphere about the X,
    Y and Z axis, that depends on the values in `symbols`.
    """
    return cirq.Circuit(
        cirq.X(bit)**symbols[0],
        cirq.Y(bit)**symbols[1],
        cirq.Z(bit)**symbols[2])


def two_qubit_unitary(bits, symbols):
    """Make a Cirq circuit that creates an arbitrary two qubit unitary."""
    circuit = cirq.Circuit()
    circuit += one_qubit_unitary(bits[0], symbols[0:3])
    circuit += one_qubit_unitary(bits[1], symbols[3:6])
    circuit += [cirq.ZZ(*bits)**symbols[6]]
    circuit += [cirq.YY(*bits)**symbols[7]]
    circuit += [cirq.XX(*bits)**symbols[8]]
    circuit += one_qubit_unitary(bits[0], symbols[9:12])
    circuit += one_qubit_unitary(bits[1], symbols[12:])
    return circuit


def two_qubit_pool(source_qubit, sink_qubit, symbols):
    """Make a Cirq circuit to do a parameterized 'pooling' operation, which
    attempts to reduce entanglement down from two qubits to just one."""
    pool_circuit = cirq.Circuit()
    sink_basis_selector = one_qubit_unitary(sink_qubit, symbols[0:3])
    source_basis_selector = one_qubit_unitary(source_qubit, symbols[3:6])
    pool_circuit.append(sink_basis_selector)
    pool_circuit.append(source_basis_selector)
    pool_circuit.append(cirq.CNOT(source_qubit, sink_qubit))
    pool_circuit.append(sink_basis_selector**-1)
    return pool_circuit

要查看创建的内容，请打印出一量子比特酉电路

SVGCircuit(one_qubit_unitary(cirq.GridQubit(0, 0), sympy.symbols('x0:3')))

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以及二量子比特酉电路

SVGCircuit(two_qubit_unitary(cirq.GridQubit.rect(1, 2), sympy.symbols('x0:15')))

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以及二量子比特池化电路

SVGCircuit(two_qubit_pool(*cirq.GridQubit.rect(1, 2), sympy.symbols('x0:6')))

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1.5.2.1 量子卷积

与 Cong 和 Lukin 论文中一样，将一维量子卷积定义为将二量子比特参数化酉矩阵应用于每对相邻量子比特，步长为 1。

def quantum_conv_circuit(bits, symbols):
    """Quantum Convolution Layer following the above diagram.
    Return a Cirq circuit with the cascade of `two_qubit_unitary` applied
    to all pairs of qubits in `bits` as in the diagram above.
    """
    circuit = cirq.Circuit()
    for first, second in zip(bits[0::2], bits[1::2]):
        circuit += two_qubit_unitary([first, second], symbols)
    for first, second in zip(bits[1::2], bits[2::2] + [bits[0]]):
        circuit += two_qubit_unitary([first, second], symbols)
    return circuit

显示（非常水平的）电路

SVGCircuit(
    quantum_conv_circuit(cirq.GridQubit.rect(1, 8), sympy.symbols('x0:15')))

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1.5.2.2 量子池化

量子池化层使用上面定义的二量子比特池从 \(N\) 个量子比特池化到 \(\frac{N}{2}\) 个量子比特。

def quantum_pool_circuit(source_bits, sink_bits, symbols):
    """A layer that specifies a quantum pooling operation.
    A Quantum pool tries to learn to pool the relevant information from two
    qubits onto 1.
    """
    circuit = cirq.Circuit()
    for source, sink in zip(source_bits, sink_bits):
        circuit += two_qubit_pool(source, sink, symbols)
    return circuit

检查池化组件电路

test_bits = cirq.GridQubit.rect(1, 8)

SVGCircuit(
    quantum_pool_circuit(test_bits[:4], test_bits[4:], sympy.symbols('x0:6')))

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1.6 模型定义

现在使用已定义的层构建一个纯量子 CNN。从八个量子比特开始，池化到一个，然后测量 \(\langle \hat{Z} \rangle\)。

def create_model_circuit(qubits):
    """Create sequence of alternating convolution and pooling operators 
    which gradually shrink over time."""
    model_circuit = cirq.Circuit()
    symbols = sympy.symbols('qconv0:63')
    # Cirq uses sympy.Symbols to map learnable variables. TensorFlow Quantum
    # scans incoming circuits and replaces these with TensorFlow variables.
    model_circuit += quantum_conv_circuit(qubits, symbols[0:15])
    model_circuit += quantum_pool_circuit(qubits[:4], qubits[4:],
                                          symbols[15:21])
    model_circuit += quantum_conv_circuit(qubits[4:], symbols[21:36])
    model_circuit += quantum_pool_circuit(qubits[4:6], qubits[6:],
                                          symbols[36:42])
    model_circuit += quantum_conv_circuit(qubits[6:], symbols[42:57])
    model_circuit += quantum_pool_circuit([qubits[6]], [qubits[7]],
                                          symbols[57:63])
    return model_circuit


# Create our qubits and readout operators in Cirq.
cluster_state_bits = cirq.GridQubit.rect(1, 8)
readout_operators = cirq.Z(cluster_state_bits[-1])

# Build a sequential model enacting the logic in 1.3 of this notebook.
# Here you are making the static cluster state prep as a part of the AddCircuit and the
# "quantum datapoints" are coming in the form of excitation
excitation_input = tf.keras.Input(shape=(), dtype=tf.dtypes.string)
cluster_state = tfq.layers.AddCircuit()(
    excitation_input, prepend=cluster_state_circuit(cluster_state_bits))

quantum_model = tfq.layers.PQC(create_model_circuit(cluster_state_bits),
                               readout_operators)(cluster_state)

qcnn_model = tf.keras.Model(inputs=[excitation_input], outputs=[quantum_model])

# Show the keras plot of the model
tf.keras.utils.plot_model(qcnn_model,
                          show_shapes=True,
                          show_layer_names=False,
                          dpi=70)

png

1.7 训练模型

为了简化此示例，在整个批次上训练模型。

# Generate some training data.
train_excitations, train_labels, test_excitations, test_labels = generate_data(
    cluster_state_bits)


# Custom accuracy metric.
@tf.function
def custom_accuracy(y_true, y_pred):
    y_true = tf.squeeze(y_true)
    y_pred = tf.map_fn(lambda x: 1.0 if x >= 0 else -1.0, y_pred)
    return tf.keras.backend.mean(tf.keras.backend.equal(y_true, y_pred))


qcnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.02),
                   loss=tf.losses.mse,
                   metrics=[custom_accuracy])

history = qcnn_model.fit(x=train_excitations,
                         y=train_labels,
                         batch_size=16,
                         epochs=25,
                         verbose=1,
                         validation_data=(test_excitations, test_labels))

Epoch 1/25
7/7 [==============================] - 2s 146ms/step - loss: 0.8633 - custom_accuracy: 0.6875 - val_loss: 0.8743 - val_custom_accuracy: 0.5833
Epoch 2/25
7/7 [==============================] - 1s 105ms/step - loss: 0.7570 - custom_accuracy: 0.7321 - val_loss: 0.8544 - val_custom_accuracy: 0.6458
Epoch 3/25
7/7 [==============================] - 1s 104ms/step - loss: 0.6833 - custom_accuracy: 0.7679 - val_loss: 0.8004 - val_custom_accuracy: 0.7083
Epoch 4/25
7/7 [==============================] - 1s 103ms/step - loss: 0.6179 - custom_accuracy: 0.8304 - val_loss: 0.7718 - val_custom_accuracy: 0.7083
Epoch 5/25
7/7 [==============================] - 1s 103ms/step - loss: 0.6308 - custom_accuracy: 0.8393 - val_loss: 0.7734 - val_custom_accuracy: 0.6667
Epoch 6/25
7/7 [==============================] - 1s 101ms/step - loss: 0.6147 - custom_accuracy: 0.7768 - val_loss: 0.7765 - val_custom_accuracy: 0.7083
Epoch 7/25
7/7 [==============================] - 1s 100ms/step - loss: 0.6029 - custom_accuracy: 0.8036 - val_loss: 0.7487 - val_custom_accuracy: 0.7292
Epoch 8/25
7/7 [==============================] - 1s 102ms/step - loss: 0.5764 - custom_accuracy: 0.8036 - val_loss: 0.7421 - val_custom_accuracy: 0.7083
Epoch 9/25
7/7 [==============================] - 1s 101ms/step - loss: 0.5695 - custom_accuracy: 0.8125 - val_loss: 0.7577 - val_custom_accuracy: 0.7083
Epoch 10/25
7/7 [==============================] - 1s 101ms/step - loss: 0.5777 - custom_accuracy: 0.8214 - val_loss: 0.7220 - val_custom_accuracy: 0.7292
Epoch 11/25
7/7 [==============================] - 1s 101ms/step - loss: 0.5630 - custom_accuracy: 0.8214 - val_loss: 0.7224 - val_custom_accuracy: 0.7500
Epoch 12/25
7/7 [==============================] - 1s 102ms/step - loss: 0.5558 - custom_accuracy: 0.8393 - val_loss: 0.7251 - val_custom_accuracy: 0.7500
Epoch 13/25
7/7 [==============================] - 1s 100ms/step - loss: 0.5592 - custom_accuracy: 0.8393 - val_loss: 0.7175 - val_custom_accuracy: 0.7708
Epoch 14/25
7/7 [==============================] - 1s 102ms/step - loss: 0.5563 - custom_accuracy: 0.8393 - val_loss: 0.7030 - val_custom_accuracy: 0.7292
Epoch 15/25
7/7 [==============================] - 1s 101ms/step - loss: 0.5590 - custom_accuracy: 0.8125 - val_loss: 0.7180 - val_custom_accuracy: 0.7292
Epoch 16/25
7/7 [==============================] - 1s 100ms/step - loss: 0.5666 - custom_accuracy: 0.8304 - val_loss: 0.7338 - val_custom_accuracy: 0.7292
Epoch 17/25
7/7 [==============================] - 1s 99ms/step - loss: 0.5675 - custom_accuracy: 0.8214 - val_loss: 0.7164 - val_custom_accuracy: 0.7500
Epoch 18/25
7/7 [==============================] - 1s 99ms/step - loss: 0.5673 - custom_accuracy: 0.8482 - val_loss: 0.7076 - val_custom_accuracy: 0.7292
Epoch 19/25
7/7 [==============================] - 1s 102ms/step - loss: 0.5629 - custom_accuracy: 0.8661 - val_loss: 0.7252 - val_custom_accuracy: 0.7292
Epoch 20/25
7/7 [==============================] - 1s 100ms/step - loss: 0.5693 - custom_accuracy: 0.8125 - val_loss: 0.7171 - val_custom_accuracy: 0.7292
Epoch 21/25
7/7 [==============================] - 1s 100ms/step - loss: 0.5686 - custom_accuracy: 0.8393 - val_loss: 0.7164 - val_custom_accuracy: 0.7292
Epoch 22/25
7/7 [==============================] - 1s 100ms/step - loss: 0.5561 - custom_accuracy: 0.8214 - val_loss: 0.7175 - val_custom_accuracy: 0.7292
Epoch 23/25
7/7 [==============================] - 1s 100ms/step - loss: 0.5549 - custom_accuracy: 0.8393 - val_loss: 0.7078 - val_custom_accuracy: 0.7292
Epoch 24/25
7/7 [==============================] - 1s 99ms/step - loss: 0.5527 - custom_accuracy: 0.8214 - val_loss: 0.7096 - val_custom_accuracy: 0.7292
Epoch 25/25
7/7 [==============================] - 1s 99ms/step - loss: 0.5480 - custom_accuracy: 0.8393 - val_loss: 0.7232 - val_custom_accuracy: 0.7500

plt.plot(history.history['loss'][1:], label='Training')
plt.plot(history.history['val_loss'][1:], label='Validation')
plt.title('Training a Quantum CNN to Detect Excited Cluster States')
plt.xlabel('Epochs')
plt.ylabel('Loss')
plt.legend()
plt.show()

png

2. 混合模型

您不必使用量子卷积从八个量子比特变为一个量子比特——您可以进行一到两轮量子卷积，并将结果馈送到经典神经网络。本节探讨量子-经典混合模型。

2.1 具有单个量子滤波器的混合模型

应用一层量子卷积，读取所有比特上的\(\langle \hat{Z}_n \rangle\)，然后是一个密集连接的神经网络。

2.1.1 模型定义

# 1-local operators to read out
readouts = [cirq.Z(bit) for bit in cluster_state_bits[4:]]


def multi_readout_model_circuit(qubits):
    """Make a model circuit with less quantum pool and conv operations."""
    model_circuit = cirq.Circuit()
    symbols = sympy.symbols('qconv0:21')
    model_circuit += quantum_conv_circuit(qubits, symbols[0:15])
    model_circuit += quantum_pool_circuit(qubits[:4], qubits[4:],
                                          symbols[15:21])
    return model_circuit


# Build a model enacting the logic in 2.1 of this notebook.
excitation_input_dual = tf.keras.Input(shape=(), dtype=tf.dtypes.string)

cluster_state_dual = tfq.layers.AddCircuit()(
    excitation_input_dual, prepend=cluster_state_circuit(cluster_state_bits))

quantum_model_dual = tfq.layers.PQC(
    multi_readout_model_circuit(cluster_state_bits),
    readouts)(cluster_state_dual)

d1_dual = tf.keras.layers.Dense(8)(quantum_model_dual)

d2_dual = tf.keras.layers.Dense(1)(d1_dual)

hybrid_model = tf.keras.Model(inputs=[excitation_input_dual], outputs=[d2_dual])

# Display the model architecture
tf.keras.utils.plot_model(hybrid_model,
                          show_shapes=True,
                          show_layer_names=False,
                          dpi=70)

/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/keras/src/initializers/initializers.py:120: UserWarning: The initializer RandomUniform is unseeded and being called multiple times, which will return identical values each time (even if the initializer is unseeded). Please update your code to provide a seed to the initializer, or avoid using the same initializer instance more than once.
  warnings.warn(

png

2.1.2 训练模型

hybrid_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.02),
                     loss=tf.losses.mse,
                     metrics=[custom_accuracy])

hybrid_history = hybrid_model.fit(x=train_excitations,
                                  y=train_labels,
                                  batch_size=16,
                                  epochs=25,
                                  verbose=1,
                                  validation_data=(test_excitations,
                                                   test_labels))

Epoch 1/25
7/7 [==============================] - 1s 100ms/step - loss: 0.6982 - custom_accuracy: 0.7589 - val_loss: 0.5877 - val_custom_accuracy: 0.7708
Epoch 2/25
7/7 [==============================] - 0s 68ms/step - loss: 0.2746 - custom_accuracy: 0.9554 - val_loss: 0.3261 - val_custom_accuracy: 0.9167
Epoch 3/25
7/7 [==============================] - 0s 66ms/step - loss: 0.2351 - custom_accuracy: 0.9464 - val_loss: 0.3478 - val_custom_accuracy: 0.9375
Epoch 4/25
7/7 [==============================] - 0s 67ms/step - loss: 0.2033 - custom_accuracy: 0.9554 - val_loss: 0.2885 - val_custom_accuracy: 0.9375
Epoch 5/25
7/7 [==============================] - 0s 65ms/step - loss: 0.2024 - custom_accuracy: 0.9554 - val_loss: 0.3089 - val_custom_accuracy: 0.9792
Epoch 6/25
7/7 [==============================] - 0s 64ms/step - loss: 0.1904 - custom_accuracy: 0.9911 - val_loss: 0.2340 - val_custom_accuracy: 1.0000
Epoch 7/25
7/7 [==============================] - 0s 64ms/step - loss: 0.1717 - custom_accuracy: 0.9732 - val_loss: 0.2339 - val_custom_accuracy: 1.0000
Epoch 8/25
7/7 [==============================] - 0s 64ms/step - loss: 0.1827 - custom_accuracy: 0.9821 - val_loss: 0.2440 - val_custom_accuracy: 1.0000
Epoch 9/25
7/7 [==============================] - 0s 64ms/step - loss: 0.1881 - custom_accuracy: 0.9821 - val_loss: 0.2371 - val_custom_accuracy: 1.0000
Epoch 10/25
7/7 [==============================] - 0s 64ms/step - loss: 0.1814 - custom_accuracy: 0.9911 - val_loss: 0.2549 - val_custom_accuracy: 1.0000
Epoch 11/25
7/7 [==============================] - 0s 64ms/step - loss: 0.1745 - custom_accuracy: 0.9911 - val_loss: 0.2521 - val_custom_accuracy: 0.9583
Epoch 12/25
7/7 [==============================] - 0s 64ms/step - loss: 0.1726 - custom_accuracy: 0.9911 - val_loss: 0.2241 - val_custom_accuracy: 1.0000
Epoch 13/25
7/7 [==============================] - 0s 65ms/step - loss: 0.1775 - custom_accuracy: 0.9911 - val_loss: 0.2386 - val_custom_accuracy: 0.9792
Epoch 14/25
7/7 [==============================] - 0s 63ms/step - loss: 0.2061 - custom_accuracy: 0.9643 - val_loss: 0.2496 - val_custom_accuracy: 1.0000
Epoch 15/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1840 - custom_accuracy: 0.9821 - val_loss: 0.3156 - val_custom_accuracy: 0.9375
Epoch 16/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1860 - custom_accuracy: 0.9821 - val_loss: 0.2323 - val_custom_accuracy: 0.9792
Epoch 17/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1755 - custom_accuracy: 0.9911 - val_loss: 0.2253 - val_custom_accuracy: 1.0000
Epoch 18/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1917 - custom_accuracy: 0.9732 - val_loss: 0.2386 - val_custom_accuracy: 1.0000
Epoch 19/25
7/7 [==============================] - 0s 62ms/step - loss: 0.1814 - custom_accuracy: 0.9911 - val_loss: 0.2515 - val_custom_accuracy: 0.9792
Epoch 20/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1899 - custom_accuracy: 0.9643 - val_loss: 0.2307 - val_custom_accuracy: 0.9792
Epoch 21/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1722 - custom_accuracy: 0.9911 - val_loss: 0.2353 - val_custom_accuracy: 1.0000
Epoch 22/25
7/7 [==============================] - 0s 64ms/step - loss: 0.1755 - custom_accuracy: 0.9732 - val_loss: 0.2237 - val_custom_accuracy: 1.0000
Epoch 23/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1973 - custom_accuracy: 0.9821 - val_loss: 0.2977 - val_custom_accuracy: 0.9792
Epoch 24/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1862 - custom_accuracy: 0.9821 - val_loss: 0.2310 - val_custom_accuracy: 0.9792
Epoch 25/25
7/7 [==============================] - 0s 63ms/step - loss: 0.1853 - custom_accuracy: 0.9821 - val_loss: 0.2680 - val_custom_accuracy: 0.9792

plt.plot(history.history['val_custom_accuracy'], label='QCNN')
plt.plot(hybrid_history.history['val_custom_accuracy'], label='Hybrid CNN')
plt.title('Quantum vs Hybrid CNN performance')
plt.xlabel('Epochs')
plt.legend()
plt.ylabel('Validation Accuracy')
plt.show()

png

正如您所见，在非常适度的经典帮助下，混合模型通常会比纯量子版本更快地收敛。

2.2 具有多个量子滤波器的混合卷积

现在让我们尝试一种使用多个量子卷积和一个经典神经网络来组合它们的架构。

2.2.1 模型定义

excitation_input_multi = tf.keras.Input(shape=(), dtype=tf.dtypes.string)

cluster_state_multi = tfq.layers.AddCircuit()(
    excitation_input_multi, prepend=cluster_state_circuit(cluster_state_bits))

# apply 3 different filters and measure expectation values

quantum_model_multi1 = tfq.layers.PQC(
    multi_readout_model_circuit(cluster_state_bits),
    readouts)(cluster_state_multi)

quantum_model_multi2 = tfq.layers.PQC(
    multi_readout_model_circuit(cluster_state_bits),
    readouts)(cluster_state_multi)

quantum_model_multi3 = tfq.layers.PQC(
    multi_readout_model_circuit(cluster_state_bits),
    readouts)(cluster_state_multi)

# concatenate outputs and feed into a small classical NN
concat_out = tf.keras.layers.concatenate(
    [quantum_model_multi1, quantum_model_multi2, quantum_model_multi3])

dense_1 = tf.keras.layers.Dense(8)(concat_out)

dense_2 = tf.keras.layers.Dense(1)(dense_1)

multi_qconv_model = tf.keras.Model(inputs=[excitation_input_multi],
                                   outputs=[dense_2])

# Display the model architecture
tf.keras.utils.plot_model(multi_qconv_model,
                          show_shapes=True,
                          show_layer_names=True,
                          dpi=70)

/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/keras/src/initializers/initializers.py:120: UserWarning: The initializer RandomUniform is unseeded and being called multiple times, which will return identical values each time (even if the initializer is unseeded). Please update your code to provide a seed to the initializer, or avoid using the same initializer instance more than once.
  warnings.warn(
/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/keras/src/initializers/initializers.py:120: UserWarning: The initializer RandomUniform is unseeded and being called multiple times, which will return identical values each time (even if the initializer is unseeded). Please update your code to provide a seed to the initializer, or avoid using the same initializer instance more than once.
  warnings.warn(
/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/keras/src/initializers/initializers.py:120: UserWarning: The initializer RandomUniform is unseeded and being called multiple times, which will return identical values each time (even if the initializer is unseeded). Please update your code to provide a seed to the initializer, or avoid using the same initializer instance more than once.
  warnings.warn(

png

2.2.2 训练模型

multi_qconv_model.compile(
    optimizer=tf.keras.optimizers.Adam(learning_rate=0.02),
    loss=tf.losses.mse,
    metrics=[custom_accuracy])

multi_qconv_history = multi_qconv_model.fit(x=train_excitations,
                                            y=train_labels,
                                            batch_size=16,
                                            epochs=25,
                                            verbose=1,
                                            validation_data=(test_excitations,
                                                             test_labels))

Epoch 1/25
7/7 [==============================] - 2s 116ms/step - loss: 0.6554 - custom_accuracy: 0.7857 - val_loss: 0.4377 - val_custom_accuracy: 0.8958
Epoch 2/25
7/7 [==============================] - 0s 74ms/step - loss: 0.2390 - custom_accuracy: 0.9375 - val_loss: 0.2941 - val_custom_accuracy: 0.9375
Epoch 3/25
7/7 [==============================] - 1s 79ms/step - loss: 0.2300 - custom_accuracy: 0.9643 - val_loss: 0.2889 - val_custom_accuracy: 0.9583
Epoch 4/25
7/7 [==============================] - 0s 72ms/step - loss: 0.1848 - custom_accuracy: 0.9821 - val_loss: 0.2479 - val_custom_accuracy: 0.9792
Epoch 5/25
7/7 [==============================] - 0s 72ms/step - loss: 0.1928 - custom_accuracy: 0.9821 - val_loss: 0.2408 - val_custom_accuracy: 0.9792
Epoch 6/25
7/7 [==============================] - 1s 77ms/step - loss: 0.1789 - custom_accuracy: 0.9821 - val_loss: 0.2372 - val_custom_accuracy: 1.0000
Epoch 7/25
7/7 [==============================] - 0s 69ms/step - loss: 0.1675 - custom_accuracy: 0.9821 - val_loss: 0.2517 - val_custom_accuracy: 1.0000
Epoch 8/25
7/7 [==============================] - 0s 71ms/step - loss: 0.1608 - custom_accuracy: 0.9911 - val_loss: 0.2438 - val_custom_accuracy: 1.0000
Epoch 9/25
7/7 [==============================] - 0s 70ms/step - loss: 0.1718 - custom_accuracy: 0.9821 - val_loss: 0.2568 - val_custom_accuracy: 0.9792
Epoch 10/25
7/7 [==============================] - 0s 73ms/step - loss: 0.1780 - custom_accuracy: 0.9821 - val_loss: 0.2741 - val_custom_accuracy: 0.9792
Epoch 11/25
7/7 [==============================] - 0s 70ms/step - loss: 0.1794 - custom_accuracy: 0.9911 - val_loss: 0.2458 - val_custom_accuracy: 0.9792
Epoch 12/25
7/7 [==============================] - 0s 70ms/step - loss: 0.1843 - custom_accuracy: 0.9821 - val_loss: 0.2515 - val_custom_accuracy: 0.9792
Epoch 13/25
7/7 [==============================] - 1s 71ms/step - loss: 0.1775 - custom_accuracy: 0.9911 - val_loss: 0.2820 - val_custom_accuracy: 0.9792
Epoch 14/25
7/7 [==============================] - 0s 72ms/step - loss: 0.1771 - custom_accuracy: 0.9911 - val_loss: 0.2586 - val_custom_accuracy: 1.0000
Epoch 15/25
7/7 [==============================] - 1s 79ms/step - loss: 0.1665 - custom_accuracy: 0.9732 - val_loss: 0.2348 - val_custom_accuracy: 1.0000
Epoch 16/25
7/7 [==============================] - 0s 73ms/step - loss: 0.1962 - custom_accuracy: 0.9732 - val_loss: 0.2533 - val_custom_accuracy: 0.9792
Epoch 17/25
7/7 [==============================] - 1s 79ms/step - loss: 0.1769 - custom_accuracy: 0.9911 - val_loss: 0.2565 - val_custom_accuracy: 0.9792
Epoch 18/25
7/7 [==============================] - 1s 74ms/step - loss: 0.1648 - custom_accuracy: 0.9911 - val_loss: 0.2618 - val_custom_accuracy: 0.9583
Epoch 19/25
7/7 [==============================] - 0s 71ms/step - loss: 0.1722 - custom_accuracy: 0.9732 - val_loss: 0.2442 - val_custom_accuracy: 0.9792
Epoch 20/25
7/7 [==============================] - 1s 78ms/step - loss: 0.1646 - custom_accuracy: 0.9732 - val_loss: 0.2327 - val_custom_accuracy: 0.9792
Epoch 21/25
7/7 [==============================] - 0s 70ms/step - loss: 0.1632 - custom_accuracy: 0.9732 - val_loss: 0.2418 - val_custom_accuracy: 0.9792
Epoch 22/25
7/7 [==============================] - 0s 71ms/step - loss: 0.1560 - custom_accuracy: 0.9911 - val_loss: 0.2440 - val_custom_accuracy: 1.0000
Epoch 23/25
7/7 [==============================] - 0s 72ms/step - loss: 0.1594 - custom_accuracy: 0.9821 - val_loss: 0.2495 - val_custom_accuracy: 0.9375
Epoch 24/25
7/7 [==============================] - 1s 80ms/step - loss: 0.1669 - custom_accuracy: 0.9821 - val_loss: 0.3298 - val_custom_accuracy: 0.9583
Epoch 25/25
7/7 [==============================] - 0s 68ms/step - loss: 0.1758 - custom_accuracy: 0.9821 - val_loss: 0.2492 - val_custom_accuracy: 0.9792

plt.plot(history.history['val_custom_accuracy'][:25], label='QCNN')
plt.plot(hybrid_history.history['val_custom_accuracy'][:25], label='Hybrid CNN')
plt.plot(multi_qconv_history.history['val_custom_accuracy'][:25],
         label='Hybrid CNN \n Multiple Quantum Filters')
plt.title('Quantum vs Hybrid CNN performance')
plt.xlabel('Epochs')
plt.legend()
plt.ylabel('Validation Accuracy')
plt.show()

png