def to_statevector(self, atol=None, rtol=None):
"""Return a statevector from a pure density matrix.
Args:
atol (float): Absolute tolerance for checking operation validity.
rtol (float): Relative tolerance for checking operation validity.
Returns:
Statevector: The pure density matrix's corresponding statevector.
Corresponds to the eigenvector of the only non-zero eigenvalue.
Raises:
QiskitError: if the state is not pure.
"""
from qiskit.quantum_info.states.statevector import Statevector
if atol is None:
atol = self.atol
if rtol is None:
rtol = self.rtol
if not is_hermitian_matrix(self._data, atol=atol, rtol=rtol):
raise QiskitError("Not a valid density matrix (non-hermitian).")
evals, evecs = np.linalg.eig(self._data)
nonzero_evals = evals[abs(evals) > atol]
if len(nonzero_evals) != 1 or not np.isclose(nonzero_evals[0], 1, atol=atol, rtol=rtol):
raise QiskitError("Density matrix is not a pure state")
psi = evecs[:, np.argmax(evals)] # eigenvectors returned in columns.
return Statevector(psi)
def from_label(cls, label):
r"""Return a tensor product of Pauli X,Y,Z eigenstates.
.. list-table:: Single-qubit state labels
:header-rows: 1
* - Label
- Statevector
* - ``"0"``
- :math:`\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}`
* - ``"1"``
- :math:`\begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}`
* - ``"+"``
- :math:`\frac{1}{2}\begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}`
* - ``"-"``
- :math:`\frac{1}{2}\begin{pmatrix} 1 & -1 \\ -1 & 1 \end{pmatrix}`
* - ``"r"``
- :math:`\frac{1}{2}\begin{pmatrix} 1 & -i \\ i & 1 \end{pmatrix}`
* - ``"l"``
- :math:`\frac{1}{2}\begin{pmatrix} 1 & i \\ -i & 1 \end{pmatrix}`
Args:
label (string): a eigenstate string ket label (see table for
allowed values).
Returns:
Statevector: The N-qubit basis state density matrix.
Raises:
QiskitError: if the label contains invalid characters, or the length
of the label is larger than an explicitly specified num_qubits.
"""
from qiskit.quantum_info.states.statevector import Statevector
return DensityMatrix(Statevector.from_label(label))
def format_statevector(vec, decimals=None):
"""Format statevector coming from the backend to present to the Qiskit user.
Args:
vec (list): a list of [re, im] complex numbers.
decimals (int): the number of decimals in the statevector.
If None, no rounding is done.
Returns:
list[complex]: a list of python complex numbers.
"""
# pylint: disable=cyclic-import
from qiskit.quantum_info.states.statevector import Statevector
if isinstance(vec, Statevector):
if decimals:
return Statevector(np.around(vec.data, decimals=decimals),
dims=vec.dims())
return vec
if isinstance(vec, np.ndarray):
if decimals:
return np.around(vec, decimals=decimals)
return vec
num_basis = len(vec)
if vec and isinstance(vec[0], complex):
vec_complex = np.array(vec, dtype=complex)
else:
vec_complex = np.zeros(num_basis, dtype=complex)
for i in range(num_basis):
vec_complex[i] = vec[i][0] + 1j * vec[i][1]
if decimals:
vec_complex = np.around(vec_complex, decimals=decimals)
return vec_complex
def test_from_labels(self):
"""Initialize from labels."""
desired_sv = Statevector.from_label('01+-lr')
qc = QuantumCircuit(6)
qc.initialize('01+-lr', range(6))
job = execute(qc, BasicAer.get_backend('statevector_simulator'))
result = job.result()
statevector = result.get_statevector()
fidelity = state_fidelity(statevector, desired_sv)
self.assertGreater(
fidelity, self._desired_fidelity,
"Initializer has low fidelity {:.2g}.".format(fidelity))
def from_label(cls, label):
"""Return a tensor product of Pauli X,Y,Z eigenstates.
Args:
label (string): a eigenstate string ket label 0,1,+,-,r,l.
Returns:
Statevector: The N-qubit basis state density matrix.
Raises:
QiskitError: if the label contains invalid characters, or the length
of the label is larger than an explicitly specified num_qubits.
Additional Information:
The labels correspond to the single-qubit states:
'0': [[1, 0], [0, 0]]
'1': [[0, 0], [0, 1]]
'+': [[0.5, 0.5], [0.5 , 0.5]]
'-': [[0.5, -0.5], [-0.5 , 0.5]]
'r': [[0.5, -0.5j], [0.5j , 0.5]]
'l': [[0.5, 0.5j], [-0.5j , 0.5]]
"""
return DensityMatrix(Statevector.from_label(label))
def _format_state(state, validate=True):
"""Format input state into class object"""
if isinstance(state, list):
state = np.array(state, dtype=complex)
if isinstance(state, np.ndarray):
ndim = state.ndim
if ndim == 1:
state = Statevector(state)
elif ndim == 2:
dim1, dim2 = state.shape
if dim2 == 1:
state = Statevector(state)
elif dim1 == dim2:
state = DensityMatrix(state)
if not isinstance(state, (Statevector, DensityMatrix)):
raise QiskitError("Input is not a quantum state")
if validate and not state.is_valid():
raise QiskitError("Input quantum state is not a valid")
return state
