import numpy as np

def quantum_error_correction_hamming(num_qubits, error_rate):
    """
    Implement error correction using the Hamming code.

    Parameters:
    - num_qubits: Number of qubits in the quantum state.
    - error_rate: Probability of error in the quantum state.

    Returns:
    - original_states: Original random quantum state.
    - received_states: Quantum states with errors.
    - corrected_states: Corrected quantum states after error correction using Hamming code.
    """
    original_states = np.random.choice([0, 1], size=num_qubits)
    error = np.random.choice([0, 1], size=num_qubits, p=[1-error_rate, error_rate])

    received_states = (original_states + error) % 2

    # Placeholder for actual Hamming code error correction
    corrected_states = received_states

    return original_states, received_states, corrected_states