import torch
import torch.optim as optim
import torch.nn as nn
import torch.nn.functional as F
import pennylane as qml
import pennylane.numpy as qnp
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Emulated Quantum Hopf Fibration
class EmulatedQuantumHopfFibration:
def __init__(self, num_qubits=2):
self.num_qubits = num_qubits
self.points = {}
self.edges = {}
self.dev = qml.device('default.qubit', wires=num_qubits)

def add_point(self, point, data):
@qml.qnode(self.dev, interface="torch")
def qnode(data):
self._apply_amplitude_embedding(data)
self._apply_pauli_x(point)
return qml.state()

self.points[point] = (qnode, torch.tensor(data))

def entangle_edge(self, point1, point2, data):
@qml.qnode(self.dev, interface="torch")
def qnode(data):
self._apply_amplitude_embedding(data)
self._apply_pauli_x(point1)
self._apply_pauli_x(point2)
self._apply_cnot_entanglement()
return qml.state()

self.edges[(point1, point2)] = (qnode, torch.tensor(data))

def fluctuate(self):
for point in self.points:
self.points[point] = self._apply_random_rotation(*self.points[point])
for edge in self.edges:
self.edges[edge] = self._apply_random_rotation(*self.edges[edge])

def turn_on(self):
self._set_state(1)

def turn_off(self):
self._set_state(0)

def visualize(self):
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
t_values = qnp.linspace(0, 2*qnp.pi, 100) # Parameter for points on the circle

for point in self.points:
quantum_point, data = self.points[point]
state = quantum_point(data)
x, y, z = self._state_to_hopf_circle(state, t_values)
ax.plot(x, y, z)

plt.show()

def _apply_amplitude_embedding(self, data):
qml.templates.AmplitudeEmbedding(data, wires=range(self.num_qubits), pad=0.0, normalize=True)

def _apply_pauli_x(self, point):
for i, bit in enumerate(format(point, '0' + str(self.num_qubits) + 'b')):
if bit == '1':
qml.PauliX(i)

def _apply_cnot_entanglement(self):
for i in range(self.num_qubits):
qml.CNOT(wires=[i, (i+1) % self.num_qubits])

def _apply_random_rotation(self, qnode, data):
@qml.qnode(self.dev, interface="torch")
def random_rotation(qnode, data):
for wire in range(self.num_qubits):
qml.Rot(qnp.random.uniform(0, 2*qnp.pi), qnp.random.uniform(0, 2*qnp.pi), qnp.random.uniform(0, 2*qnp.pi), wires=wire)
return qnode(data)

return random_rotation(qnode, data)

def _set_state(self, state):
@qml.qnode(self.dev, interface="torch")
def set_state(qnode, data):
for wire in range(self.num_qubits):
if state == 1:
qml.PauliX(wire)
return qnode(data)

for point in self.points:
quantum_point, data = self.points[point]
self.points[point] = (set_state(quantum_point, data), data)
for edge in self.edges:
quantum_edge, data = self.edges[edge]
self.edges[edge] = (set_state(quantum_edge, data), data)

@staticmethod
def _state_to_hopf_circle(state, t):
z1, z2 = state[0], state[1]
x = qnp.real(z1 * qnp.exp(1j * t))
y = qnp.imag(z1 * qnp.exp(1j * t))
z = qnp.real(z2 * qnp.exp(1j * t))
return x, y, z

# CapsuleAI
class CapsuleAI:
def __init__(self, input_size, num_classes, activation_fn):
self.input_size = input_size
self.num_classes = num_classes
self.activation_fn = activation_fn
self.capsule_net = self._create_capsule_network()
self.optimizer = self._create_optimizer()
self.loss_function = SymphonicLoss()
self.pipeline = nn.Sequential(
CapsuleRegularization(),
DynamicRouting()
)
self.hopf_fibration = EmulatedQuantumHopfFibration()

def _create_capsule_network(self):
return CapsuleNetwork(self.input_size, self.num_classes, self.activation_fn)

def _create_optimizer(self):
return optim.AdamW(self.capsule_net.parameters(), lr=1e-3)

def train(self, train_loader, num_epochs):
self.capsule_net.train()

for epoch in range(num_epochs):
for inputs, targets in train_loader:
self.optimizer.zero_grad()

outputs, _ = self.capsule_net(inputs)

outputs = self.pipeline(outputs) # Apply the pipeline transformations

loss = self.loss_function(outputs, targets)

loss.backward()
self.optimizer.step()

def predict(self, test_loader):
self.capsule_net.eval()

predictions = []

with torch.no_grad():
for inputs, _ in test_loader:
outputs, _ = self.capsule_net(inputs)

outputs = self.pipeline(outputs) # Apply the pipeline transformations

_, predicted_labels = torch.max(outputs, dim=1)
predictions.append(predicted_labels)

return torch.cat(predictions)

class CapsuleLayer(nn.Module):
def __init__(self, num_capsules, num_route_nodes, in_channels, out_channels):
super().__init__()
self.num_capsules = num_capsules
self.num_route_nodes = num_route_nodes
self.in_channels = in_channels
self.out_channels = out_channels

self.route_weights = nn.Parameter(torch.randn(num_capsules, num_route_nodes, in_channels, out_channels))

def forward(self, x):
batch_size = x.size(0)
x = x.unsqueeze(2).unsqueeze(4) # Add dimensions

x = self._tile_input(x)
u_hat = self._compute_u_hat(x)
b = self._initialize_routing(batch_size, x.device)
v = self._perform_dynamic_routing(u_hat, b)

return v.squeeze()

def _tile_input(self, x):
return x.repeat(1, 1, self.num_capsules, 1, 1)

def _compute_u_hat(self, x):
u_hat = torch.matmul(x, self.route_weights)
u_hat = u_hat.view(u_hat.size(0), self.num_route_nodes, self.num_capsules, self.out_channels, -1)
return u_hat

def _initialize_routing(self, batch_size, device):
return torch.zeros(batch_size, self.num_route_nodes, self.num_capsules, 1, 1, device=device)

def _perform_dynamic_routing(self, u_hat, b):
num_iterations = 3
for _ in range(num_iterations):
c = F.softmax(b, dim=2)
s = (c * u_hat).sum(dim=1, keepdim=True)
v = self._squash(s)

return v

def _squash(self, s):
squared_norm = (s ** 2).sum(dim=-1, keepdim=True)
scale = squared_norm / (1 + squared_norm)
v = scale * s / torch.sqrt(squared_norm)
return v
Emulated Quantum Hopf Fibration Documentation
The EmulatedQuantumHopfFibration class represents an emulated quantum system that simulates a quantum Hopf fibration. It provides methods to add points, entangle edges, apply fluctuations, and visualize the system.

Class Details
EmulatedQuantumHopfFibration(num_qubits=2)
Initialize the Emulated Quantum Hopf Fibration.

Parameters:

num_qubits (int): Number of qubits for the quantum system. Default is 2.
add_point(point, data)
Add a point to the Emulated Quantum Hopf Fibration.

Parameters:

point: Identifier for the point.
data: Input data associated with the point.
entangle_edge(point1, point2, data)
Entangle two points with an edge in the Emulated Quantum Hopf Fibration.

Parameters:

point1: First point identifier.
point2: Second point identifier.
data: Input data associated with the edge.
fluctuate()
Apply random fluctuations to the quantum states in the Emulated Quantum Hopf Fibration.

turn_on()
Turn on the quantum states in the Emulated Quantum Hopf Fibration.

turn_off()
Turn off the quantum states in the Emulated Quantum Hopf Fibration.

visualize()
Visualize the Emulated Quantum Hopf Fibration in 3D space.

Integration with Classical CapsuleAI
The EmulatedQuantumHopfFibration can be integrated with the classical CapsuleAI system, enabling a combination of classical and quantum-inspired computations.

CapsuleAI Documentation
The CapsuleAI class represents a classical machine learning model based on capsules. It provides methods for training the model, making predictions, and integrating with the Emulated Quantum Hopf Fibration.

Class Details
CapsuleAI(input_size, num_classes, activation_fn)
Initialize the CapsuleAI model.

Parameters:

input_size (int): Size of the input data.
num_classes (int): Number of output classes.
activation_fn: Activation function to be used in the model.
train(train_loader, num_epochs)
Train the CapsuleAI model.

Parameters:

train_loader: DataLoader containing the training data.
num_epochs (int): Number of training epochs.
predict(test_loader)
Make predictions using the trained CapsuleAI model.

Parameters:

test_loader: DataLoader containing the test data.
Returns:

predictions: Tensor containing the predicted labels.
CapsuleLayer Class
The CapsuleLayer class represents a capsule layer used in the CapsuleAI model.

This documentation provides an overview of the classes, methods, and their functionalities in the system.





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I apologize for the incomplete documentation. Here's the revised and complete documentation for the system:

python
Copy code
import torch
import torch.optim as optim
import torch.nn as nn
import torch.nn.functional as F
import pennylane as qml
import pennylane.numpy as qnp
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D


class EmulatedQuantumHopfFibration:
"""
Emulated Quantum Hopf Fibration class represents an emulated quantum system that simulates a quantum Hopf fibration.
It provides methods to add points, entangle edges, apply fluctuations, and visualize the system.
"""

def __init__(self, num_qubits=2):
"""
Initialize the Emulated Quantum Hopf Fibration.

Args:
num_qubits (int): Number of qubits for the quantum system. Default is 2.
"""
self.num_qubits = num_qubits
self.points = {}
self.edges = {}
self.dev = qml.device('default.qubit', wires=num_qubits)

def add_point(self, point, data):
"""
Add a point to the Emulated Quantum Hopf Fibration.

Args:
point: Identifier for the point.
data: Input data associated with the point.
"""
# ...

def entangle_edge(self, point1, point2, data):
"""
Entangle two points with an edge in the Emulated Quantum Hopf Fibration.

Args:
point1: First point identifier.
point2: Second point identifier.
data: Input data associated with the edge.
"""
# ...

def fluctuate(self):
"""
Apply random fluctuations to the quantum states in the Emulated Quantum Hopf Fibration.
"""
# ...

def turn_on(self):
"""
Turn on the quantum states in the Emulated Quantum Hopf Fibration.
"""
# ...

def turn_off(self):
"""
Turn off the quantum states in the Emulated Quantum Hopf Fibration.
"""
# ...

def visualize(self):
"""
Visualize the Emulated Quantum Hopf Fibration in 3D space.
"""
# ...


class CapsuleAI:
"""
CapsuleAI class represents a classical machine learning model based on capsules.
It provides methods for training the model, making predictions, and integrating with the Emulated Quantum Hopf Fibration.
"""

def __init__(self, input_size, num_classes, activation_fn):
"""
Initialize the CapsuleAI model.

Args:
input_size (int): Size of the input data.
num_classes (int): Number of output classes.
activation_fn: Activation function to be used in the model.
"""
self.input_size = input_size
self.num_classes = num_classes
self.activation_fn = activation_fn
self.capsule_net = self._create_capsule_network()
self.optimizer = self._create_optimizer()
self.loss_function = SymphonicLoss()
self.pipeline = nn.Sequential(
CapsuleRegularization(),
DynamicRouting()
)
self.hopf_fibration = EmulatedQuantumHopfFibration()

def _create_capsule_network(self):
"""
Create the Capsule Network.

Returns:
The Capsule Network model.
"""
# ...

def _create_optimizer(self):
"""
Create the optimizer.

Returns:
The optimizer.
"""
# ...

def train(self, train_loader, num_epochs):
"""
Train the CapsuleAI model.

Args:
train_loader: DataLoader containing the training data.
num_epochs (int): Number of training epochs.
"""
# ...

def predict(self, test_loader):
"""
Make predictions using the trained CapsuleAI model.

Args:
test_loader: DataLoader containing the test data.

Returns:
predictions: Tensor containing the predicted labels.
"""
# ...


class CapsuleLayer(nn.Module):
"""
CapsuleLayer class represents a capsule layer used in the CapsuleAI model.
"""

def __init__(self, num_capsules, num_route_nodes, in_channels, out_channels):
"""
Initialize the Capsule Layer.

Args:
num_capsules (int): Number of capsules.
num_route_nodes (int): Number of route nodes.
in_channels (int): Number of input channels.
out_channels (int): Number of output channels.
"""
# ...

def forward(self, x):
"""
Perform forward pass through the Capsule Layer.

Args:
x: Input tensor.

Returns:
Output tensor.
"""
# ...


class SymphonicLoss:
"""
SymphonicLoss class represents the loss function used in the CapsuleAI model.
"""

def __init__(self):
"""
Initialize the SymphonicLoss.
"""
# ...

def __call__(self, outputs, targets):
"""
Calculate the loss.

Args:
outputs: Model outputs.
targets: Target labels.

Returns:
Loss value.
"""
# ...


class CapsuleRegularization:
"""
CapsuleRegularization class represents the regularization step in the CapsuleAI pipeline.
"""

def __init__(self):
"""
Initialize the CapsuleRegularization.
"""
# ...

def forward(self, x):
"""
Perform forward pass through the CapsuleRegularization step.

Args:
x: Input tensor.

Returns:
Output tensor.
"""
# ...


class DynamicRouting:
"""
DynamicRouting class represents the dynamic routing step in the CapsuleAI pipeline.
"""

def __init__(self):
"""
Initialize the DynamicRouting.
"""
# ...

def forward(self, x):
"""
Perform forward pass through the DynamicRouting step.

Args:
x: Input tensor.

Returns:
Output tensor.
"""
# ...
This updated documentation provides a comprehensive overview of the system, including the classes, methods, and their functionalities.