def get_subsystem_density_matrix(statevector, trace_systems):
"""
Compute the reduced density matrix of a quantum subsystem.
Args:
statevector (list|array): The state vector of the complete system
trace_systems (list|range): The indices of the qubits to be traced out.
Returns:
numpy.ndarray: The reduced density matrix for the desired subsystem
"""
rho = np.outer(statevector, np.conj(statevector))
rho_sub = partial_trace(rho, trace_systems).data
return rho_sub
def test_density_matrix_partial_trace(self):
"""Test partial_trace function on density matrices"""
rho = DensityMatrix.from_label("10+")
self.assertEqual(partial_trace(rho, [0, 1]),
DensityMatrix.from_label("1"))
self.assertEqual(partial_trace(rho, [0, 2]),
DensityMatrix.from_label("0"))
self.assertEqual(partial_trace(rho, [1, 2]),
DensityMatrix.from_label("+"))
self.assertEqual(partial_trace(rho, [0]),
DensityMatrix.from_label("10"))
self.assertEqual(partial_trace(rho, [1]),
DensityMatrix.from_label("1+"))
self.assertEqual(partial_trace(rho, [2]),
DensityMatrix.from_label("0+"))
self.assertEqual(partial_trace(rho, []), rho)
def test_statevector_partial_trace(self):
"""Test partial_trace function on statevectors"""
psi = Statevector.from_label("10+")
self.assertEqual(partial_trace(psi, [0, 1]),
DensityMatrix.from_label("1"))
self.assertEqual(partial_trace(psi, [0, 2]),
DensityMatrix.from_label("0"))
self.assertEqual(partial_trace(psi, [1, 2]),
DensityMatrix.from_label("+"))
self.assertEqual(partial_trace(psi, [0]),
DensityMatrix.from_label("10"))
self.assertEqual(partial_trace(psi, [1]),
DensityMatrix.from_label("1+"))
self.assertEqual(partial_trace(psi, [2]),
DensityMatrix.from_label("0+"))
self.assertEqual(partial_trace(psi, []), DensityMatrix(psi))
def get_subsystem_fidelity(statevector, trace_systems, subsystem_state):
"""
Compute the fidelity of the quantum subsystem.
Args:
statevector (list|array): The state vector of the complete system
trace_systems (list|range): The indices of the qubits to be traced.
to trace qubits 0 and 4 trace_systems = [0,4]
subsystem_state (list|array): The ground-truth state vector of the subsystem
Returns:
numpy.ndarray: The subsystem fidelity
"""
rho = np.outer(np.conj(statevector), statevector)
rho_sub = partial_trace(rho, trace_systems).data
rho_sub_in = np.outer(np.conj(subsystem_state), subsystem_state)
fidelity = np.trace(
sqrtm(np.dot(np.dot(sqrtm(rho_sub), rho_sub_in), sqrtm(rho_sub))))**2
return fidelity
def test_density_matrix_partial_trace(self):
"""Test partial_trace function on density matrices"""
rho = DensityMatrix.from_label('10+')
self.assertEqual(partial_trace(rho, [0, 1]),
DensityMatrix.from_label('1'))
self.assertEqual(partial_trace(rho, [0, 2]),
DensityMatrix.from_label('0'))
self.assertEqual(partial_trace(rho, [1, 2]),
DensityMatrix.from_label('+'))
self.assertEqual(partial_trace(rho, [0]),
DensityMatrix.from_label('10'))
self.assertEqual(partial_trace(rho, [1]),
DensityMatrix.from_label('1+'))
self.assertEqual(partial_trace(rho, [2]),
DensityMatrix.from_label('0+'))
def test_statevector_partial_trace(self):
"""Test partial_trace function on statevectors"""
psi = Statevector.from_label('10+')
self.assertEqual(partial_trace(psi, [0, 1]),
DensityMatrix.from_label('1'))
self.assertEqual(partial_trace(psi, [0, 2]),
DensityMatrix.from_label('0'))
self.assertEqual(partial_trace(psi, [1, 2]),
DensityMatrix.from_label('+'))
self.assertEqual(partial_trace(psi, [0]),
DensityMatrix.from_label('10'))
self.assertEqual(partial_trace(psi, [1]),
DensityMatrix.from_label('1+'))
self.assertEqual(partial_trace(psi, [2]),
DensityMatrix.from_label('0+'))
