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# qiskit.quantum_info.states.statevector의 소스 코드

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2019.
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""
Statevector quantum state class.
"""

import copy
import re
import warnings
from numbers import Number

import numpy as np

from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.instruction import Instruction
from qiskit.exceptions import QiskitError
from qiskit.quantum_info.states.quantum_state import QuantumState
from qiskit.quantum_info.operators.operator import Operator
from qiskit.quantum_info.operators.predicates import matrix_equal

[문서]class Statevector(QuantumState):
"""Statevector class"""

[문서]    def __init__(self, data, dims=None):
"""Initialize a statevector object.

Args:
data (vector_like): a complex statevector.
dims (int or tuple or list): Optional. The subsystem dimension of

Raises:
QiskitError: if input data is not valid.

The dims kwarg can be None, an integer, or an iterable of
integers.

* Iterable -- the subsystem dimensions are the values in the list
with the total number of subsystems given by the length of the list.

* Int or None -- the length of the input vector
specifies the total dimension of the density matrix. If it is a
power of two the state will be initialized as an N-qubit state.
If it is not a power of two the state will have a single
d-dimensional subsystem.
"""
if isinstance(data, (list, np.ndarray)):
# Finally we check if the input is a raw vector in either a
# python list or numpy array format.
self._data = np.asarray(data, dtype=complex)
elif isinstance(data, Statevector):
self._data = data._data
if dims is None:
dims = data._dims
elif isinstance(data, Operator):
# We allow conversion of column-vector operators to Statevectors
input_dim, _ = data.dim
if input_dim != 1:
raise QiskitError("Input Operator is not a column-vector.")
self._data = np.ravel(data.data)
else:
raise QiskitError("Invalid input data format for Statevector")
# Check that the input is a numpy vector or column-vector numpy
# matrix. If it is a column-vector matrix reshape to a vector.
ndim = self._data.ndim
shape = self._data.shape
if ndim != 1:
if ndim == 2 and shape == 1:
self._data = np.reshape(self._data, shape)
elif ndim != 2 or shape != 1:
raise QiskitError("Invalid input: not a vector or column-vector.")
super().__init__(self._automatic_dims(dims, shape))

def __eq__(self, other):
return super().__eq__(other) and np.allclose(
self._data, other._data, rtol=self.rtol, atol=self.atol)

def __repr__(self):
prefix = 'Statevector('
pad = len(prefix) * ' '
return '{}{},\n{}dims={})'.format(
prefix, np.array2string(
self.data, separator=', ', prefix=prefix),

@property
def data(self):
"""Return data."""
return self._data

[문서]    def is_valid(self, atol=None, rtol=None):
"""Return True if a Statevector has norm 1."""
if atol is None:
atol = self.atol
if rtol is None:
rtol = self.rtol
norm = np.linalg.norm(self.data)
return np.allclose(norm, 1, rtol=rtol, atol=atol)

[문서]    def to_operator(self):
"""Convert state to a rank-1 projector operator"""
mat = np.outer(self.data, np.conj(self.data))
return Operator(mat, input_dims=self.dims(), output_dims=self.dims())

[문서]    def conjugate(self):
"""Return the conjugate of the operator."""
return Statevector(np.conj(self.data), dims=self.dims())

[문서]    def trace(self):
"""Return the trace of the quantum state as a density matrix."""
return np.sum(np.abs(self.data) ** 2)

[문서]    def purity(self):
"""Return the purity of the quantum state."""
# For a valid statevector the purity is always 1, however if we simply
# have an arbitrary vector (not correctly normalized) then the
# purity is equivalent to the trace squared:
# P(|psi>) = Tr[|psi><psi|psi><psi|] = |<psi|psi>|^2
return self.trace() ** 2

[문서]    def tensor(self, other):
"""Return the tensor product state self ⊗ other.

Args:
other (Statevector): a quantum state object.

Returns:
Statevector: the tensor product operator self ⊗ other.

Raises:
QiskitError: if other is not a quantum state.
"""
if not isinstance(other, Statevector):
other = Statevector(other)
dims = other.dims() + self.dims()
data = np.kron(self._data, other._data)
return Statevector(data, dims)

[문서]    def expand(self, other):
"""Return the tensor product state other ⊗ self.

Args:
other (Statevector): a quantum state object.

Returns:
Statevector: the tensor product state other ⊗ self.

Raises:
QiskitError: if other is not a quantum state.
"""
if not isinstance(other, Statevector):
other = Statevector(other)
dims = self.dims() + other.dims()
data = np.kron(other._data, self._data)
return Statevector(data, dims)

"""Return the linear combination self + other.

Args:
other (Statevector): a quantum state object.

Returns:
Statevector: the linear combination self + other.

Raises:
QiskitError: if other is not a quantum state, or has
incompatible dimensions.
"""
if not isinstance(other, Statevector):
other = Statevector(other)
if self.dim != other.dim:
raise QiskitError("other Statevector has different dimensions.")
return Statevector(self.data + other.data, self.dims())

def _multiply(self, other):
"""Return the scalar multiplied state self * other.

Args:
other (complex): a complex number.

Returns:
Statevector: the scalar multiplied state other * self.

Raises:
QiskitError: if other is not a valid complex number.
"""
if not isinstance(other, Number):
raise QiskitError("other is not a number")
return Statevector(other * self.data, self.dims())

[문서]    def evolve(self, other, qargs=None):
"""Evolve a quantum state by the operator.

Args:
other (Operator): The operator to evolve by.
qargs (list): a list of Statevector subsystem positions to apply
the operator on.

Returns:
Statevector: the output quantum state.

Raises:
QiskitError: if the operator dimension does not match the
specified Statevector subsystem dimensions.
"""
if qargs is None:
qargs = getattr(other, 'qargs', None)

# Get return vector
ret = copy.copy(self)

# Evolution by a circuit or instruction
if isinstance(other, QuantumCircuit):
other = other.to_instruction()
if isinstance(other, Instruction):
if self.num_qubits is None:
raise QiskitError("Cannot apply QuantumCircuit to non-qubit Statevector.")
return self._evolve_instruction(ret, other, qargs=qargs)

# Evolution by an Operator
if not isinstance(other, Operator):
other = Operator(other)

# check dimension
if self.dims(qargs) != other.input_dims():
raise QiskitError(
"Operator input dimensions are not equal to statevector subsystem dimensions."
)
return Statevector._evolve_operator(ret, other, qargs=qargs)

[문서]    def equiv(self, other, rtol=None, atol=None):
"""Return True if statevectors are equivalent up to global phase.

Args:
other (Statevector): a statevector object.
rtol (float): relative tolerance value for comparison.
atol (float): absolute tolerance value for comparison.

Returns:
bool: True if statevectors are equivalent up to global phase.
"""
if not isinstance(other, Statevector):
try:
other = Statevector(other)
except QiskitError:
return False
if self.dim != other.dim:
return False
if atol is None:
atol = self.atol
if rtol is None:
rtol = self.rtol
return matrix_equal(self.data, other.data, ignore_phase=True,
rtol=rtol, atol=atol)

[문서]    def expectation_value(self, oper, qargs=None):
"""Compute the expectation value of an operator.

Args:
oper (Operator): an operator to evaluate expval of.
qargs (None or list): subsystems to apply operator on.

Returns:
complex: the expectation value.
"""
val = self.evolve(oper, qargs=qargs)
conj = self.conjugate()
return np.dot(conj.data, val.data)

[문서]    def probabilities(self, qargs=None, decimals=None):
"""Return the subsystem measurement probability vector.

Measurement probabilities are with respect to measurement in the
computation (diagonal) basis.

Args:
qargs (None or list): subsystems to return probabilities for,
if None return for all subsystems (Default: None).
decimals (None or int): the number of decimal places to round
values. If None no rounding is done (Default: None).

Returns:
np.array: The Numpy vector array of probabilities.

Examples:

Consider a 2-qubit product state
:math:|\\psi\\rangle=|+\\rangle\\otimes|0\\rangle.

.. jupyter-execute::

from qiskit.quantum_info import Statevector

psi = Statevector.from_label('+0')

# Probabilities for measuring both qubits
probs = psi.probabilities()
print('probs: {}'.format(probs))

# Probabilities for measuring only qubit-0
probs_qubit_0 = psi.probabilities()
print('Qubit-0 probs: {}'.format(probs_qubit_0))

# Probabilities for measuring only qubit-1
probs_qubit_1 = psi.probabilities()
print('Qubit-1 probs: {}'.format(probs_qubit_1))

We can also permute the order of qubits in the qargs list
to change the qubit position in the probabilities output

.. jupyter-execute::

from qiskit.quantum_info import Statevector

psi = Statevector.from_label('+0')

# Probabilities for measuring both qubits
probs = psi.probabilities([0, 1])
print('probs: {}'.format(probs))

# Probabilities for measuring both qubits
# but swapping qubits 0 and 1 in output
probs_swapped = psi.probabilities([1, 0])
print('Swapped probs: {}'.format(probs_swapped))
"""
probs = self._subsystem_probabilities(
np.abs(self.data) ** 2, self._dims, qargs=qargs)
if decimals is not None:
probs = probs.round(decimals=decimals)
return probs

[문서]    def reset(self, qargs=None):
"""Reset state or subsystems to the 0-state.

Args:
qargs (list or None): subsystems to reset, if None all
subsystems will be reset to their 0-state
(Default: None).

Returns:
Statevector: the reset state.

If all subsystems are reset this will return the ground state
on all subsystems. If only a some subsystems are reset this
function will perform a measurement on those subsystems and
evolve the subsystems so that the collapsed post-measurement
states are rotated to the 0-state. The RNG seed for this
sampling can be set using the :meth:seed method.
"""
if qargs is None:
# Resetting all qubits does not require sampling or RNG
state = np.zeros(self._dim, dtype=complex)
state = 1
return Statevector(state, dims=self._dims)

# Sample a single measurement outcome
dims = self.dims(qargs)
probs = self.probabilities(qargs)
sample = self._rng.choice(len(probs), p=probs, size=1)

# Convert to projector for state update
proj = np.zeros(len(probs), dtype=complex)
proj[sample] = 1 / np.sqrt(probs[sample])

# Rotate outcome to 0
reset = np.eye(len(probs))
reset[0, 0] = 0
reset[sample, sample] = 0
reset[0, sample] = 1

# compose with reset projection
reset = np.dot(reset, np.diag(proj))
return self.evolve(
Operator(reset, input_dims=dims, output_dims=dims),
qargs=qargs)

[문서]    def to_counts(self):
"""Returns the statevector as a counts dict
of probabilities.

DEPRECATED: use :meth:probabilities_dict instead.

Returns:
dict: Counts of probabilities.
"""
warnings.warn(
'The Statevector.to_counts method is deprecated as of 0.13.0,'
' and will be removed no earlier than 3 months after that '
'release date. You should use the Statevector.probabilities_dict'
return self.probabilities_dict()

[문서]    @classmethod
def from_label(cls, label):
"""Return a tensor product of Pauli X,Y,Z eigenstates.

.. list-table:: Single-qubit state labels

* - Label
- Statevector
* - "0"
- :math:[1, 0]
* - "1"
- :math:[0, 1]
* - "+"
- :math:[1 / \\sqrt{2},  1 / \\sqrt{2}]
* - "-"
- :math:[1 / \\sqrt{2},  -1 / \\sqrt{2}]
* - "r"
- :math:[1 / \\sqrt{2},  i / \\sqrt{2}]
* - "l"
- :math:[1 / \\sqrt{2},  -i / \\sqrt{2}]

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.
"""
# Check label is valid
if re.match(r'^[01rl\-+]+$', label) is None: raise QiskitError('Label contains invalid characters.') # We can prepare Z-eigenstates by converting the computational # basis bit-string to an integer and preparing that unit vector # However, for X-basis states, we will prepare a Z-eigenstate first # then apply Hadamard gates to rotate 0 and 1s to + and -. z_label = label xy_states = False if re.match('^+$', label) is None:
# We have X or Y eigenstates so replace +,r with 0 and
# -,l with 1 and prepare the corresponding Z state
xy_states = True
z_label = z_label.replace('+', '0')
z_label = z_label.replace('r', '0')
z_label = z_label.replace('-', '1')
z_label = z_label.replace('l', '1')
# Initialize Z eigenstate vector
num_qubits = len(label)
data = np.zeros(1 << num_qubits, dtype=complex)
pos = int(z_label, 2)
data[pos] = 1
state = Statevector(data)
if xy_states:
# Apply hadamards to all qubits in X eigenstates
x_mat = np.array([[1, 1], [1, -1]], dtype=complex) / np.sqrt(2)
# Apply S.H to qubits in Y eigenstates
y_mat = np.dot(np.diag([1, 1j]), x_mat)
for qubit, char in enumerate(reversed(label)):
if char in ['+', '-']:
state = state.evolve(x_mat, qargs=[qubit])
elif char in ['r', 'l']:
state = state.evolve(y_mat, qargs=[qubit])
return state

[문서]    @staticmethod
def from_int(i, dims):
"""Return a computational basis statevector.

Args:
i (int): the basis state element.
dims (int or tuple or list): The subsystem dimensions of the statevector

Returns:
Statevector: The computational basis state :math:|i\\rangle.

The dims kwarg can be an integer or an iterable of integers.

* Iterable -- the subsystem dimensions are the values in the list
with the total number of subsystems given by the length of the list.

* Int -- the integer specifies the total dimension of the
state. If it is a power of two the state will be initialized
as an N-qubit state. If it is not a power of  two the state
will have a single d-dimensional subsystem.
"""
size = np.product(dims)
state = np.zeros(size, dtype=complex)
state[i] = 1.0
return Statevector(state, dims=dims)

[문서]    @classmethod
def from_instruction(cls, instruction):
"""Return the output statevector of an instruction.

The statevector is initialized in the state :math:|{0,\\ldots,0}\\rangle of the
same number of qubits as the input instruction or circuit, evolved
by the input instruction, and the output statevector returned.

Args:
instruction (qiskit.circuit.Instruction or QuantumCircuit): instruction or circuit

Returns:
Statevector: The final statevector.

Raises:
QiskitError: if the instruction contains invalid instructions for
the statevector simulation.
"""
# Convert circuit to an instruction
if isinstance(instruction, QuantumCircuit):
instruction = instruction.to_instruction()
# Initialize an the statevector in the all |0> state
init = np.zeros(2 ** instruction.num_qubits, dtype=complex)
init = 1.0
vec = Statevector(init, dims=instruction.num_qubits * (2,))
return Statevector._evolve_instruction(vec, instruction)

[문서]    def to_dict(self, decimals=None):
r"""Convert the statevector to dictionary form.

This dictionary representation uses a Ket-like notation where the
dictionary keys are qudit strings for the subsystem basis vectors.
If any subsystem has a dimension greater than 10 comma delimiters are
inserted between integers so that subsystems can be distinguished.

Args:
decimals (None or int): the number of decimal places to round
values. If None no rounding is done
(Default: None).

Returns:
dict: the dictionary form of the Statevector.

Example:

The ket-form of a 2-qubit statevector
:math:|\psi\rangle = |-\rangle\otimes |0\rangle

.. jupyter-execute::

from qiskit.quantum_info import Statevector

psi = Statevector.from_label('-0')
print(psi.to_dict())

For non-qubit subsystems the integer range can go from 0 to 9. For
example in a qutrit system

.. jupyter-execute::

import numpy as np
from qiskit.quantum_info import Statevector

vec = np.zeros(9)
vec = 1 / np.sqrt(2)
vec[-1] = 1 / np.sqrt(2)
psi = Statevector(vec, dims=(3, 3))
print(psi.to_dict())

For large subsystem dimensions delimeters are required. The
following example is for a 20-dimensional system consisting of
a qubit and 10-dimensional qudit.

.. jupyter-execute::

import numpy as np
from qiskit.quantum_info import Statevector

vec = np.zeros(2 * 10)
vec = 1 / np.sqrt(2)
vec[-1] = 1 / np.sqrt(2)
psi = Statevector(vec, dims=(2, 10))
print(psi.to_dict())
"""
return self._vector_to_dict(self.data,
self._dims,
decimals=decimals,
string_labels=True)

@property
def _shape(self):
"""Return the tensor shape of the matrix operator"""
return tuple(reversed(self.dims()))

@staticmethod
def _evolve_operator(statevec, oper, qargs=None):
"""Evolve a qudit statevector"""
is_qubit = bool(statevec.num_qubits and oper.num_qubits)

if qargs is None:
# Full system evolution
statevec._data = np.dot(oper._data, statevec._data)
if not is_qubit:
statevec._set_dims(oper._output_dims)
return statevec

# Calculate contraction dimensions
if is_qubit:
# Qubit contraction
new_dim = statevec._dim
num_qargs = statevec.num_qubits
else:
# Qudit contraction
new_dims = list(statevec._dims)
for i, qubit in enumerate(qargs):
new_dims[qubit] = oper._output_dims[i]
new_dim = np.product(new_dims)
num_qargs = len(new_dims)

# Get transpose axes
indices = [num_qargs - 1 - i for i in reversed(qargs)]
axes = indices + [i for i in range(num_qargs) if i not in indices]
axes_inv = np.argsort(axes).tolist()

# Calculate contraction dimensions
if is_qubit:
pre_tensor_shape = num_qargs * (2,)
post_tensor_shape = pre_tensor_shape
contract_shape = (1 << oper.num_qubits, 1 << (num_qargs - oper.num_qubits))
else:
contract_dim = np.product(oper._input_dims)
pre_tensor_shape = statevec._shape
contract_shape = (contract_dim, statevec._dim // contract_dim)
post_tensor_shape = list(reversed(oper._output_dims)) + [
pre_tensor_shape[i] for i in range(num_qargs) if i not in indices]

# reshape input for contraction
statevec._data = np.reshape(np.transpose(
np.reshape(statevec.data, pre_tensor_shape), axes), contract_shape)
statevec._data = np.reshape(np.dot(oper.data, statevec._data), post_tensor_shape)
statevec._data = np.reshape(np.transpose(statevec._data, axes_inv), new_dim)

# Update dimension
if not is_qubit:
statevec._set_dims(new_dims)
return statevec

@staticmethod
def _evolve_instruction(statevec, obj, qargs=None):
"""Update the current Statevector by applying an instruction."""
from qiskit.circuit.reset import Reset
from qiskit.circuit.barrier import Barrier

mat = Operator._instruction_to_matrix(obj)
if mat is not None:
# Perform the composition and inplace update the current state
# of the operator
return Statevector._evolve_operator(statevec, Operator(mat), qargs=qargs)

# Special instruction types
if isinstance(obj, Reset):
statevec._data = statevec.reset(qargs)._data
return statevec
if isinstance(obj, Barrier):
return statevec

# If the instruction doesn't have a matrix defined we use its
# circuit decomposition definition if it exists, otherwise we
# cannot compose this gate and raise an error.
if obj.definition is None:
raise QiskitError('Cannot apply Instruction: {}'.format(obj.name))
if not isinstance(obj.definition, QuantumCircuit):
raise QiskitError('{} instruction definition is {}; expected QuantumCircuit'.format(
obj.name, type(obj.definition)))
if obj.definition.global_phase:
statevec._data *= np.exp(1j * float(obj.definition.global_phase))
qubits = {qubit: i for i, qubit in enumerate(obj.definition.qubits)}
for instr, qregs, cregs in obj.definition:
if cregs:
raise QiskitError(
'Cannot apply instruction with classical registers: {}'.format(
instr.name))
# Get the integer position of the flat register
if qargs is None:
new_qargs = [qubits[tup] for tup in qregs]
else:
new_qargs = [qargs[qubits[tup]] for tup in qregs]
Statevector._evolve_instruction(statevec, instr, qargs=new_qargs)
return statevec