import numpy as np
import pandas as pd

# Defining a simplified quantum Hilbert space for representation
# Example dataset structure: Quantum states, entanglements, connections

# Define example quantum states and operators
states = {
    "Q1": [1 / np.sqrt(2), 1 / np.sqrt(2)],  # |+> state (superposition)
    "Q2": [1, 0],                            # |0> state
}

# Define an example entanglement operator (Bell State)
entanglement_operator = np.array([[1, 0, 0, 1],
                                   [0, 1, 1, 0],
                                   [0, 1, -1, 0],
                                   [1, 0, 0, -1]]) / np.sqrt(2)

# Combine into a tensor product to represent the combined state
combined_state = np.kron(states["Q1"], states["Q2"])

# Define connections (as an adjacency matrix for relationships)
connections = np.array([[0, 1],  # Q1 connected to Q2
                        [1, 0]])

# Define Hamiltonian for time evolution (simplified for example)
hamiltonian = np.array([[0, 1],
                        [1, 0]])

# Compute time evolution operator (unitary evolution)
time_step = 1  # Arbitrary time step for example
time_evolution_operator = np.linalg.matrix_power(np.eye(2) - 1j * hamiltonian * time_step, 10)

# Final dataset structure for visualization
dataset = {
    "States": states,
    "Entanglement Operator": entanglement_operator,
    "Combined State": combined_state,
    "Connections (Adjacency Matrix)": connections,
    "Hamiltonian": hamiltonian,
    "Time Evolution Operator": time_evolution_operator
}

# Format for user review as a DataFrame
quantum_data_df = pd.DataFrame({
    "Quantum Element": ["State Q1", "State Q2", "Entanglement Operator", "Combined State", "Hamiltonian", "Time Evolution Operator"],
    "Representation": [
        states["Q1"],
        states["Q2"],
        entanglement_operator,
        combined_state,
        hamiltonian,
        time_evolution_operator
    ]
})

import ace_tools as tools; tools.display_dataframe_to_user(name="Exhaustive Quantum Dataset", dataframe=quantum_data_df)