qiskit.quantum_info.Statevector

__init__(data, dims=None)

Initialize a statevector object.

Parameters

• **(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).

Raises

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.

Default absolute tolerance parameter for float comparisons.

conjugate()

Return the conjugate of the operator.

copy()

Make a copy of current operator.

Return data.

Return total state dimension.

dims(qargs=None)

Return tuple of input dimension for specified subsystems.

draw(output=None, **drawer_args)

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().

Parameters

• 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.

Returns

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

Raises

ValueError – when an invalid output method is selected.

equiv(other, rtol=None, atol=None)

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

Parameters

• 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.

Returns

True if statevectors are equivalent up to global phase.

Return type

bool

evolve(other, qargs=None)

Evolve a quantum state by the operator.

Parameters

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

Returns

the output quantum state.

Return type

Statevector

Raises

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

expand(other)

Return the tensor product state other ⊗ self.

Parameters

other (Statevector) – a quantum state object.

Returns

the tensor product state other ⊗ self.

Return type

Statevector

Raises

QiskitError – if other is not a quantum state.

expectation_value(oper, qargs=None)

Compute the expectation value of an operator.

Parameters

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

Returns

the expectation value.

Return type

complex

classmethod from_instruction(instruction)

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.

Parameters

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

Returns

The final statevector.

Return type

Statevector

Raises

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

static from_int(i, dims)

Return a computational basis statevector.

Parameters

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

Returns

The computational basis state $|i\rangle$.

Return type

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)

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

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

Parameters

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

Returns

The N-qubit basis state density matrix.

Return type

Statevector

Raises

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)

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.

Parameters

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

Returns

the pair (outcome, state) where outcome is the

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

Return type

tuple

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

probabilities(qargs=None, decimals=None)

Return the subsystem measurement probability vector.

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

Parameters

• 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

The Numpy vector array of probabilities.

Return type

np.array

Examples

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.

Parameters

• 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

The measurement probabilities in dict (ket) form.

Return type

dict

purity()

Return the purity of the quantum state.

reset(qargs=None)

Reset state or subsystems to the 0-state.

Parameters

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

Returns

the reset state.

Return type

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()

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

Returns

the Statevector with reversed subsystem order.

Return type

Statevector

Default relative tolerance parameter for float comparisons.

sample_counts(shots, qargs=None)

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

Parameters

• 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).

Returns

sampled counts dictionary.

Return type

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.

Parameters

• 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).

Returns

list of sampled counts if the order sampled.

Return type

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.

Return settings.

Return type

Dict

tensor(other)

Return the tensor product state self ⊗ other.

Parameters

other (Statevector) – a quantum state object.

Returns

the tensor product operator self ⊗ other.

Return type

Statevector

Raises

QiskitError – if other is not a quantum state.

to_dict(decimals=None)

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.

Parameters

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

Returns

the dictionary form of the Statevector.

Return type

dict

Example

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()

Convert state to a rank-1 projector operator

trace()

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