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quantum_process.py
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quantum_process.py
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# quantum_process.py
import numpy as np
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.quantum_info import Statevector, DensityMatrix, partial_trace
def generate_qubit_data(input_amplitude, input_phase, input_frequency):
"""
Generates qubit data for OpenGL rendering based on input amplitude, phase, and frequency.
Parameters:
- input_amplitude: float, the input amplitude (0 to 1)
- input_phase: float, the input phase in radians
- input_frequency: float, the normalized input frequency (0 to 1)
Returns:
- qubit_data: list of dictionaries, each containing data for a qubit
Each dictionary contains:
- 'label': str, label of the qubit
- 'amplitude': float, amplitude for visualization
- 'frequency': float, frequency for visualization
- 'phase': float, phase for visualization
- 'color': tuple, RGB color of the qubit
"""
# Initialize quantum registers for each group (2 qubits each)
qr_plus = QuantumRegister(2, 'plus')
qr_minus = QuantumRegister(2, 'minus')
qr_zero = QuantumRegister(2, 'zero')
qr_one = QuantumRegister(2, 'one')
qr_y_plus = QuantumRegister(2, 'y_plus')
qr_y_minus = QuantumRegister(2, 'y_minus')
# Create a quantum circuit combining all qubits
qc = QuantumCircuit(qr_plus, qr_minus, qr_zero, qr_one, qr_y_plus, qr_y_minus)
# Initialize qubits in different basis states
# Group 1: |+> state
for qubit in qr_plus:
qc.h(qubit) # Hadamard gate transforms |0⟩ to |+⟩
# Group 2: |-> state
for qubit in qr_minus:
qc.h(qubit)
qc.z(qubit) # Z gate changes |+⟩ to |−⟩
# Group 3: |0⟩ state (already initialized by default)
# Group 4: |1⟩ state
for qubit in qr_one:
qc.x(qubit) # X gate flips |0⟩ to |1⟩
# Group 5: |i+⟩ state (Y basis positive eigenstate)
for qubit in qr_y_plus:
qc.s(qubit) # S gate (phase gate)
qc.h(qubit)
# Group 6: |i−⟩ state (Y basis negative eigenstate)
for qubit in qr_y_minus:
qc.sdg(qubit) # S† gate (inverse phase gate)
qc.h(qubit)
# Define sound wave attributes for each group based on the given inputs
# Vary these slightly for each group to create diversity, i.e. shift amplitude superpositions, rest fairly arbitrary
group_sound_attributes = {
'plus': {'amplitude': input_amplitude * 1.0, 'phase': input_phase, 'frequency': input_frequency},
'minus': {'amplitude': input_amplitude * 0.9, 'phase': input_phase + 0.1, 'frequency': input_frequency + 0.05},
'zero': {'amplitude': input_amplitude * 0.8, 'phase': input_phase + 0.2, 'frequency': input_frequency + 0.1},
'one': {'amplitude': input_amplitude * 0.7, 'phase': input_phase + 0.3, 'frequency': input_frequency + 0.15},
'y_plus': {'amplitude': input_amplitude * 0.6, 'phase': input_phase + 0.4, 'frequency': input_frequency + 0.2},
'y_minus': {'amplitude': input_amplitude * 0.5, 'phase': input_phase + 0.5, 'frequency': input_frequency + 0.25}
}
# Apply transformations to each group with sound attributes
for group_name, qr in zip(group_sound_attributes.keys(), [qr_plus, qr_minus, qr_zero, qr_one, qr_y_plus, qr_y_minus]):
amplitude = group_sound_attributes[group_name]['amplitude']
phase = group_sound_attributes[group_name]['phase']
frequency = group_sound_attributes[group_name]['frequency']
apply_sound_transformations(qc, qr, amplitude, phase, frequency)
# Entangle qubits between groups to observe interesting behavior
entangle_groups(qc, qr_plus, qr_minus)
entangle_groups(qc, qr_zero, qr_one)
entangle_groups(qc, qr_y_plus, qr_y_minus)
# Get the statevector
statevector = Statevector.from_instruction(qc)
num_total_qubits = qc.num_qubits
# Collect data for all qubits
labels = []
group_names = ['plus', 'minus', 'zero', 'one', 'y_plus', 'y_minus']
group_qubits = [qr_plus, qr_minus, qr_zero, qr_one, qr_y_plus, qr_y_minus]
group_colors = {
'plus': (1.0, 0.0, 0.0), # Red
'minus': (0.0, 1.0, 0.0), # Green
'zero': (0.0, 0.0, 1.0), # Blue
'one': (1.0, 1.0, 0.0), # Yellow
'y_plus': (1.0, 0.0, 1.0), # Magenta
'y_minus': (0.0, 1.0, 1.0) # Cyan
}
# Prepare a list to store data for each qubit
qubit_data = []
for group_name, qr in zip(group_names, group_qubits):
for qubit in qr:
qubit_index = qc.find_bit(qubit).index
labels.append(f"{group_name}_{qubit_index}")
# Get the reduced density matrix of the qubit
rho_qubit = get_qubit_density_matrix(statevector, qubit_index, num_total_qubits)
rho_matrix = rho_qubit.data
# Calculate probabilities of |0⟩ and |1⟩
p0 = np.real(rho_matrix[0, 0])
p1 = np.real(rho_matrix[1, 1])
# Calculate amplitude as sqrt of probability of |1⟩, scaled by input amplitude
input_amplitude_group = group_sound_attributes[group_name]['amplitude']
amplitude_wave = input_amplitude_group * np.sqrt(p1)
# Calculate phase as angle of the off-diagonal element
phase_wave = np.angle(rho_matrix[0, 1])
# Use the group's frequency for visualization
frequency_wave = group_sound_attributes[group_name]['frequency']
qubit_data.append({
'label': f"{group_name}_{qubit_index}",
'amplitude': amplitude_wave,
'frequency': frequency_wave,
'phase': phase_wave,
'color': group_colors[group_name]
})
return qubit_data
def apply_sound_transformations(qc, qubits, amplitude, phase, frequency):
"""
Applies quantum transformations to qubits based on sound attributes.
Parameters:
- qc: QuantumCircuit, the quantum circuit to apply transformations to
- qubits: QuantumRegister, the qubits to transform
- amplitude: float, amplitude for rotation (0 to 1)
- phase: float, phase shift in radians
- frequency: float, frequency factor for rotation
"""
# Map amplitude to rotation angle (0 to pi)
theta = amplitude * np.pi
# Map frequency to rotation angle
freq_factor = frequency * np.pi
for qubit in qubits:
# Apply rotation around Y-axis
qc.ry(theta, qubit)
# Apply rotation around X-axis influenced by frequency
qc.rx(freq_factor, qubit)
# Apply phase shift around Z-axis
qc.rz(phase, qubit)
def entangle_groups(qc, control_qubits, target_qubits):
"""
Entangles pairs of qubits between two groups using CNOT gates.
Parameters:
- qc: QuantumCircuit, the quantum circuit to apply entanglement to
- control_qubits: QuantumRegister, the control qubits
- target_qubits: QuantumRegister, the target qubits
"""
for c_qubit, t_qubit in zip(control_qubits, target_qubits):
qc.cx(c_qubit, t_qubit)
def get_qubit_density_matrix(statevector, qubit_index, num_total_qubits):
"""
Obtains the reduced density matrix of a single qubit from the statevector.
Parameters:
- statevector: Statevector, the statevector of the quantum system
- qubit_index: int, the index of the qubit to extract
- num_total_qubits: int, total number of qubits in the system
Returns:
- reduced_rho: DensityMatrix, the reduced density matrix of the qubit
"""
# Convert statevector to density matrix
rho = DensityMatrix(statevector)
# List of qubits to trace out (all except qubit_index)
qubits_to_trace_out = [i for i in range(num_total_qubits) if i != qubit_index]
# Reduce the density matrix to the qubit of interest
reduced_rho = partial_trace(rho, qubits_to_trace_out)
return reduced_rho