import torch
import pennylane as qml
import pennylane.numpy as qnp

num_qubits = 4
dev = qml.device("default.qubit", wires=num_qubits)

class Tesseract:
def __init__(self):
self.vertices = {}
self.edges = {}

def add_vertex(self, vertex, data):
@qml.qnode(dev, interface="torch")
def quantum_vertex(data):
qml.templates.AmplitudeEmbedding(data, wires=range(num_qubits), pad=0.0, normalize=True)
for i, bit in enumerate(format(vertex, '04b')):
if bit == '1':
qml.PauliX(i)
return qml.probs(wires=range(num_qubits))
self.vertices[vertex] = (quantum_vertex, torch.tensor(data))

def entangle_edge(self, vertex1, vertex2, data):
@qml.qnode(dev, interface="torch")
def quantum_edge(data):
qml.templates.AmplitudeEmbedding(data, wires=range(num_qubits), pad=0.0, normalize=True)
for vertex in [vertex1, vertex2]:
for i, bit in enumerate(format(vertex, '04b')):
if bit == '1':
qml.PauliX(i)
for i in range(num_qubits):
qml.CNOT(wires=[i, (i+num_qubits) % num_qubits])
return qml.probs(wires=range(num_qubits))
self.edges[(vertex1, vertex2)] = (quantum_edge, torch.tensor(data))

def fluctuate(self):
for vertex in self.vertices:
self.vertices[vertex] = (self._random_rotation(*self.vertices[vertex]))
for edge in self.edges:
self.edges[edge] = (self._random_rotation(*self.edges[edge]))

def turn_on(self):
for vertex in self.vertices:
self.vertices[vertex] = (self._set_state(1, *self.vertices[vertex]))
for edge in self.edges:
self.edges[edge] = (self._set_state(1, *self.edges[edge]))

def turn_off(self):
for vertex in self.vertices:
self.vertices[vertex] = (self._set_state(0, *self.vertices[vertex]))
for edge in self.edges:
self.edges[edge] = (self._set_state(0, *self.edges[edge]))

@staticmethod
@qml.qnode(dev, interface="torch")
def _random_rotation(qnode, data):
for wire in range(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)

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

# Quantum Tesseract Interface

The Quantum Tesseract Interface is a unique system that combines principles of quantum computing and holographic mathematics to create a high-dimensional quantum information structure. This system provides a novel way of handling and operating on data in a quantum computing environment.

The interface centers around a tesseract (4D hypercube) where vertices represent quantum states (qubits), and edges represent entanglements between these states. Data is stored as quantum states at vertices and moves along the entangled edges.

## Class Structure

The main class in the Quantum Tesseract Interface is `Tesseract`, which contains vertices and edges.

**1. `Tesseract`**

The `Tesseract` class contains methods to add vertices and edges (quantum states and their entanglements), and methods to manipulate them (fluctuate, turn_on, turn_off).

**2. `add_vertex`**

This method adds a vertex (a quantum state) to the tesseract. It takes a vertex and data as input, and associates the data with the vertex.

**3. `entangle_edge`**

This method creates an entangled edge between two vertices. It takes two vertices and data as input, and associates the data with the edge.

**4. `fluctuate`**

This method introduces randomness into all vertices and edges of the tesseract by applying a random rotation to all qubits in each quantum node (QNode).

**5. `turn_on` and `turn_off`**

These methods set all vertices and edges to the |1> state (turn_on) or the |0> state (turn_off), effectively turning all qubits on or off.

## Potential Uses

**1. Quantum Data Storage and Processing**

The vertices of the tesseract can hold a large amount of information due to the superposition property of qubits. The entangled edges enable efficient quantum data processing.

**2. Quantum Machine Learning**

The vertices can hold data and the edges can represent the interconnections of a neural network, making this system suitable for implementing quantum machine learning models.

**3. Quantum Simulation**

A tesseract structure can simulate complex quantum systems, potentially being useful in quantum chemistry, materials science, or high-energy physics.

**4. Exploration of Higher Dimensional Quantum Systems**

This interface provides a way to better understand and experiment with behaviors of quantum systems in higher dimensions.

**5. Quantum Teleportation and Communication**

Due to quantum entanglement, changing the state of one qubit immediately changes the state of the other entangled qubit, no matter how far apart they are. This property could potentially be used for faster communication or quantum teleportation.

## Future Development

The Quantum Tesseract Interface presents exciting possibilities for extending its functionality. By integrating more advanced quantum algorithms, data handling capabilities, and graphical visualization tools, the interface could be used for more sophisticated quantum computations and simulations. As quantum computing technology continues to advance, the Quantum Tesseract Interface will offer a compelling platform for exploring high-dimensional quantum systems and their applications.

Remember that working with this interface requires a solid understanding of quantum mechanics and programming. Also, be aware that the actual performance and possibilities of this interface depend heavily on the quantum resources and technologies available.