# qiskit.quantum_info.Statevector¶

class Statevector(data, dims=None)[source]

Statevector class

Initialize a statevector object.

Paramètres
• (np.array or list or Statevector or Operator or QuantumCircuit or (data) – 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).

Lève

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.

__init__(data, dims=None)[source]

Initialize a statevector object.

Paramètres
• (np.array or list or Statevector or Operator or QuantumCircuit or (data) – 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).

Lève

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.

Methods

 __init__(data[, dims]) Initialize a statevector object. Return the conjugate of the operator. Make a copy of current operator. dims([qargs]) Return tuple of input dimension for specified subsystems. draw([output]) Return a visualization of the Statevector. equiv(other[, rtol, atol]) Return True if other is equivalent as a statevector up to global phase. evolve(other[, qargs]) Evolve a quantum state by the operator. expand(other) Return the tensor product state other ⊗ self. expectation_value(oper[, qargs]) Compute the expectation value of an operator. from_instruction(instruction) Return the output statevector of an instruction. from_int(i, dims) Return a computational basis statevector. from_label(label) Return a tensor product of Pauli X,Y,Z eigenstates. is_valid([atol, rtol]) Return True if a Statevector has norm 1. measure([qargs]) Measure subsystems and return outcome and post-measure state. probabilities([qargs, decimals]) Return the subsystem measurement probability vector. probabilities_dict([qargs, decimals]) Return the subsystem measurement probability dictionary. Return the purity of the quantum state. reset([qargs]) Reset state or subsystems to the 0-state. Return a Statevector with reversed subsystem ordering. sample_counts(shots[, qargs]) Sample a dict of qubit measurement outcomes in the computational basis. sample_memory(shots[, qargs]) Sample a list of qubit measurement outcomes in the computational basis. seed([value]) Set the seed for the quantum state RNG. tensor(other) Return the tensor product state self ⊗ other. to_dict([decimals]) Convert the statevector to dictionary form. Convert state to a rank-1 projector operator Return the trace of the quantum state as a density matrix.

Attributes

 atol Default absolute tolerance parameter for float comparisons. data Return data. dim Return total state dimension. num_qubits Return the number of qubits if a N-qubit state or None otherwise. rtol Default relative tolerance parameter for float comparisons.
property atol

Default absolute tolerance parameter for float comparisons.

conjugate()[source]

Return the conjugate of the operator.

copy()

Make a copy of current operator.

property data

Return data.

property dim

dims(qargs=None)

Return tuple of input dimension for specified subsystems.

draw(output=None, **drawer_args)[source]

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().

Paramètres
• output (str) – Select the output method to use for drawing the state. Valid choices are repr, text, latex, latex_source, qsphere, hinton, or bloch. 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.

Renvoie

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

Lève

ValueError – when an invalid output method is selected.

equiv(other, rtol=None, atol=None)[source]

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

Note

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.

Paramètres
• 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.

Renvoie

True if statevectors are equivalent up to global phase.

Type renvoyé

bool

evolve(other, qargs=None)[source]

Evolve a quantum state by the operator.

Paramètres
• other (Operator) – The operator to evolve by.

• qargs (list) – a list of Statevector subsystem positions to apply the operator on.

Renvoie

the output quantum state.

Type renvoyé

Statevector

Lève

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

expand(other)[source]

Return the tensor product state other ⊗ self.

Paramètres

other (Statevector) – a quantum state object.

Renvoie

the tensor product state other ⊗ self.

Type renvoyé

Statevector

Lève

QiskitError – if other is not a quantum state.

expectation_value(oper, qargs=None)[source]

Compute the expectation value of an operator.

Paramètres
• oper (Operator) – an operator to evaluate expval of.

• qargs (None or list) – subsystems to apply operator on.

Renvoie

the expectation value.

Type renvoyé

complex

classmethod from_instruction(instruction)[source]

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.

Paramètres

instruction (qiskit.circuit.Instruction or QuantumCircuit) – instruction or circuit

Renvoie

The final statevector.

Type renvoyé

Statevector

Lève

QiskitError – if the instruction contains invalid instructions for the statevector simulation.

static from_int(i, dims)[source]

Return a computational basis statevector.

Paramètres
• i (int) – the basis state element.

• dims (int or tuple or list) – The subsystem dimensions of the statevector (See additional information).

Renvoie

The computational basis state $$|i\rangle$$.

Type renvoyé

Statevector

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)[source]

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

Table 15 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"

$$[1 / \sqrt{2}, -i / \sqrt{2}]$$

Paramètres

label (string) – a eigenstate string ket label (see table for allowed values).

Renvoie

The N-qubit basis state density matrix.

Type renvoyé

Statevector

Lève

QiskitError – if the label contains invalid characters, or the length of the label is larger than an explicitly specified num_qubits.

is_valid(atol=None, rtol=None)[source]

Return True if a Statevector has norm 1.

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.

Paramètres

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

Renvoie

the pair (outcome, state) where outcome is the

measurement outcome string label, and state is the collapsed post-measurement state for the corresponding outcome.

Type renvoyé

tuple

property num_qubits

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

probabilities(qargs=None, decimals=None)[source]

Return the subsystem measurement probability vector.

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

Paramètres
• 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).

Renvoie

The Numpy vector array of probabilities.

Type renvoyé

np.array

Exemples

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.

Paramètres
• 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).

Renvoie

The measurement probabilities in dict (ket) form.

Type renvoyé

dict

purity()[source]

Return the purity of the quantum state.

reset(qargs=None)[source]

Reset state or subsystems to the 0-state.

Paramètres

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

Renvoie

the reset state.

Type renvoyé

Statevector

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()[source]

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 $$|\psi_{0} \rangle \otimes ... \otimes |\psi_{n-1} \rangle$$.

Renvoie

the Statevector with reversed subsystem order.

Type renvoyé

Statevector

property rtol

Default relative tolerance parameter for float comparisons.

sample_counts(shots, qargs=None)

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

Paramètres
• 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).

Renvoie

sampled counts dictionary.

Type renvoyé

Counts

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.

Paramètres
• 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).

Renvoie

list of sampled counts if the order sampled.

Type renvoyé

np.array

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)[source]

Return the tensor product state self ⊗ other.

Paramètres

other (Statevector) – a quantum state object.

Renvoie

the tensor product operator self ⊗ other.

Type renvoyé

Statevector

Lève

QiskitError – if other is not a quantum state.

to_dict(decimals=None)[source]

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.

Paramètres

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

Renvoie

the dictionary form of the Statevector.

Type renvoyé

dict

Exemple

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()[source]

Convert state to a rank-1 projector operator

trace()[source]

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