Statevector#

class qiskit.quantum_info.Statevector(data, dims=None)[ソース]#

ベースクラス: QuantumState, TolerancesMixin

Statevector class

Initialize a statevector object.

パラメータ:

or (data (np.array or list or Statevector or Operator or QuantumCircuit) – qiskit.circuit.Instruction): Data from which the statevector can be constructed. This can be either a complex vector, another statevector, a Operator with only one column or a QuantumCircuit or Instruction. If the data is a circuit or instruction, the statevector is constructed by assuming that all qubits are initialized to the zero state.
dims (int or tuple or list) – Optional. The subsystem dimension of the state (See additional information).

例外:

QiskitError – if input data is not valid.

Additional Information:

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.

Attributes

atol = 1e-08#

data#: Return data.

dim#: Return total state dimension.

num_qubits#: Return the number of qubits if a N-qubit state or None otherwise.

rtol = 1e-05#

settings#: Return settings.

Methods

conjugate()[ソース]#

Return the conjugate of the operator.

戻り値の型:: Statevector

copy()#: Make a copy of current operator.

dims(qargs=None)#: Return tuple of input dimension for specified subsystems.

draw(output=None, **drawer_args)[ソース]#

Return a visualization of the Statevector.

repr: ASCII TextMatrix of the state’s __repr__.

text: ASCII TextMatrix that can be printed in the console.

latex: An IPython Latex object for displaying in Jupyter Notebooks.

latex_source: Raw, uncompiled ASCII source to generate array using LaTeX.

qsphere: Matplotlib figure, rendering of statevector using plot_state_qsphere().

hinton: Matplotlib figure, rendering of statevector using plot_state_hinton().

bloch: Matplotlib figure, rendering of statevector using plot_bloch_multivector().

city: Matplotlib figure, rendering of statevector using plot_state_city().

paulivec: Matplotlib figure, rendering of statevector using plot_state_paulivec().

パラメータ:

output (str) – Select the output method to use for drawing the state. Valid choices are repr, text, latex, latex_source, qsphere, hinton, bloch, city, or paulivec. Default is repr. Default can be changed by adding the line state_drawer = <default> to ~/.qiskit/settings.conf under [default].
drawer_args – Arguments to be passed directly to the relevant drawing function or constructor (TextMatrix(), array_to_latex(), plot_state_qsphere(), plot_state_hinton() or plot_bloch_multivector()). See the relevant function under qiskit.visualization for that function’s documentation.

戻り値:

matplotlib.Figure or str or TextMatrix or IPython.display.Latex: Drawing of the Statevector.

例外:

ValueError – when an invalid output method is selected.

サンプル

Plot one of the Bell states

from numpy import sqrt
from qiskit.quantum_info import Statevector
sv=Statevector([1/sqrt(2), 0, 0, -1/sqrt(2)])
sv.draw(output='hinton')

(Source code)

../_images/qiskit-quantum_info-Statevector-1.png

equiv(other, rtol=None, atol=None)[ソース]#

Return True if other is equivalent as a statevector up to global phase.

注釈

If other is not a Statevector, but can be used to initialize a statevector object, this will check that Statevector(other) is equivalent to the current statevector up to global phase.

パラメータ:

other (Statevector) – an object from which a Statevector can be constructed.
rtol (float) – relative tolerance value for comparison.
atol (float) – absolute tolerance value for comparison.

戻り値:

True if statevectors are equivalent up to global phase.

戻り値の型:

bool

evolve(other, qargs=None)[ソース]#

Evolve a quantum state by the operator.

パラメータ:

other (Operator | QuantumCircuit | circuit.Instruction) – The operator to evolve by.
qargs (list) – a list of Statevector subsystem positions to apply the operator on.

戻り値:

the output quantum state.

戻り値の型:

Statevector

例外:

QiskitError – if the operator dimension does not match the specified Statevector subsystem dimensions.

expand(other)[ソース]#

Return the tensor product state other ⊗ self.

パラメータ:: other (Statevector) – a quantum state object.
戻り値:: the tensor product state other ⊗ self.
戻り値の型:: Statevector
例外:: QiskitError – if other is not a quantum state.

expectation_value(oper, qargs=None)[ソース]#

Compute the expectation value of an operator.

パラメータ:

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

戻り値:

the expectation value.

戻り値の型:

complex

classmethod from_instruction(instruction)[ソース]#

Return the output statevector of an instruction.

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

パラメータ:: instruction (qiskit.circuit.Instruction or QuantumCircuit) – instruction or circuit
戻り値:: The final statevector.
戻り値の型:: Statevector
例外:: QiskitError – if the instruction contains invalid instructions for the statevector simulation.

static from_int(i, dims)[ソース]#

Return a computational basis statevector.

パラメータ:

i (int) – the basis state element.
dims (int or tuple or list) – The subsystem dimensions of the statevector (See additional information).

戻り値:

The computational basis state \(|i\rangle\).

戻り値の型:

Statevector

Additional Information:

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.

classmethod from_label(label)[ソース]#

Return a tensor product of Pauli X,Y,Z eigenstates.

Table 12 Single-qubit state labels#
Label	Statevector
`"0"`	\([1, 0]\)
`"1"`	\([0, 1]\)
`"+"`	\([1 / \sqrt{2}, 1 / \sqrt{2}]\)
`"-"`	\([1 / \sqrt{2}, -1 / \sqrt{2}]\)
`"r"`	\([1 / \sqrt{2}, i / \sqrt{2}]\)
`"l"`	\([1 / \sqrt{2}, -i / \sqrt{2}]\)

パラメータ:: label (string) – a eigenstate string ket label (see table for allowed values).
戻り値:: The N-qubit basis state density matrix.
戻り値の型:: Statevector
例外:: QiskitError – if the label contains invalid characters, or the length of the label is larger than an explicitly specified num_qubits.

inner(other)[ソース]#

Return the inner product of self and other as \(\langle self| other \rangle\).

パラメータ:: other (Statevector) – a quantum state object.
戻り値:: the inner product of self and other, \(\langle self| other \rangle\).
戻り値の型:: np.complex128
例外:: QiskitError – if other is not a quantum state or has different dimension.

is_valid(atol=None, rtol=None)[ソース]#

Return True if a Statevector has norm 1.

戻り値の型:: bool

measure(qargs=None)#

Measure subsystems and return outcome and post-measure state.

Note that this function uses the QuantumStates internal random number generator for sampling the measurement outcome. The RNG seed can be set using the seed() method.

パラメータ:

qargs (list or None) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

戻り値:

the pair (outcome, state) where outcome is the: measurement outcome string label, and state is the collapsed post-measurement state for the corresponding outcome.

戻り値の型:

tuple

probabilities(qargs=None, decimals=None)[ソース]#

Return the subsystem measurement probability vector.

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

パラメータ:

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).

戻り値:

The Numpy vector array of probabilities.

戻り値の型:

np.array

サンプル

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

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([0])
print('Qubit-0 probs: {}'.format(probs_qubit_0))

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

probs: [0.5 0.  0.5 0. ]
Qubit-0 probs: [1. 0.]
Qubit-1 probs: [0.5 0.5]

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

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: [0.5 0.  0.5 0. ]
Swapped probs: [0.5 0.5 0.  0. ]

probabilities_dict(qargs=None, decimals=None)#

Return the subsystem measurement probability dictionary.

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

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.

パラメータ:

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).

戻り値:

The measurement probabilities in dict (ket) form.

戻り値の型:

dict

purity()[ソース]#

Return the purity of the quantum state.

戻り値の型:: float64

reset(qargs=None)[ソース]#

Reset state or subsystems to the 0-state.

パラメータ:: qargs (list or None) – subsystems to reset, if None all subsystems will be reset to their 0-state (Default: None).
戻り値:: the reset state.
戻り値の型:: Statevector

Additional Information:: 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 seed() method.

reverse_qargs()[ソース]#

Return a Statevector with reversed subsystem ordering.

For a tensor product state this is equivalent to reversing the order of tensor product subsystems. For a statevector \(|\psi \rangle = |\psi_{n-1} \rangle \otimes ... \otimes |\psi_0 \rangle\) the returned statevector will be \(|\psi_{0} \rangle \otimes ... \otimes |\psi_{n-1} \rangle\).

戻り値:: the Statevector with reversed subsystem order.
戻り値の型:: Statevector

sample_counts(shots, qargs=None)#

Sample a dict of qubit measurement outcomes in the computational basis.

パラメータ:

shots (int) – number of samples to generate.
qargs (None or list) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

戻り値:

sampled counts dictionary.

戻り値の型:

Counts

Additional Information:

This function samples measurement outcomes using the measure probabilities() for the current state and qargs. It does not actually implement the measurement so the current state is not modified.

The seed for random number generator used for sampling can be set to a fixed value by using the stats seed() method.

sample_memory(shots, qargs=None)#

Sample a list of qubit measurement outcomes in the computational basis.

パラメータ:

shots (int) – number of samples to generate.
qargs (None or list) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

戻り値:

list of sampled counts if the order sampled.

戻り値の型:

np.array

Additional Information:

This function samples measurement outcomes using the measure probabilities() for the current state and qargs. It does not actually implement the measurement so the current state is not modified.

The seed for random number generator used for sampling can be set to a fixed value by using the stats seed() method.

seed(value=None)#: Set the seed for the quantum state RNG.

tensor(other)[ソース]#

Return the tensor product state self ⊗ other.

パラメータ:: other (Statevector) – a quantum state object.
戻り値:: the tensor product operator self ⊗ other.
戻り値の型:: Statevector
例外:: QiskitError – if other is not a quantum state.

to_dict(decimals=None)[ソース]#

Convert the statevector to dictionary form.

パラメータ:: decimals (None or int) – the number of decimal places to round values. If None no rounding is done (Default: None).
戻り値:: the dictionary form of the Statevector.
戻り値の型:: dict

サンプル

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

from qiskit.quantum_info import Statevector

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

{'00': (0.7071067811865475+0j), '10': (-0.7071067811865475+0j)}

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

import numpy as np
from qiskit.quantum_info import Statevector

vec = np.zeros(9)
vec[0] = 1 / np.sqrt(2)
vec[-1] = 1 / np.sqrt(2)
psi = Statevector(vec, dims=(3, 3))
print(psi.to_dict())

{'00': (0.7071067811865475+0j), '22': (0.7071067811865475+0j)}

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

import numpy as np
from qiskit.quantum_info import Statevector

vec = np.zeros(2 * 10)
vec[0] = 1 / np.sqrt(2)
vec[-1] = 1 / np.sqrt(2)
psi = Statevector(vec, dims=(2, 10))
print(psi.to_dict())

{'00': (0.7071067811865475+0j), '91': (0.7071067811865475+0j)}

to_operator()[ソース]#

Convert state to a rank-1 projector operator

戻り値の型:: Operator

trace()[ソース]#

Return the trace of the quantum state as a density matrix.

戻り値の型:: float64