qiskit.quantum_info.Statevector¶

class
Statevector
(data, dims=None)[source]¶ Statevector class
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
orInstruction
. 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
orNone
– 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 Nqubit state. If it is not a power of two the state will have a single ddimensional subsystem.

__init__
(data, dims=None)[source]¶ 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
orInstruction
. 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
orNone
– 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 Nqubit state. If it is not a power of two the state will have a single ddimensional subsystem.
Methods
__init__
(data[, dims])Initialize a statevector object.
Return the conjugate of the operator.
copy
()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 postmeasure state.
probabilities
([qargs, decimals])Return the subsystem measurement probability vector.
probabilities_dict
([qargs, decimals])Return the subsystem measurement probability dictionary.
purity
()Return the purity of the quantum state.
reset
([qargs])Reset state or subsystems to the 0state.
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 rank1 projector operator
trace
()Return the trace of the quantum state as a density matrix.
Attributes
Default absolute tolerance parameter for float comparisons.
Return data.
Return total state dimension.
Return the number of qubits if a Nqubit state or None otherwise.
Default relative tolerance parameter for float comparisons.

property
atol
¶ Default absolute tolerance parameter for float comparisons.

copy
()¶ Make a copy of current operator.

property
data
¶ Return data.

property
dim
¶ Return total state dimension.

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().
 Parameters
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.
 Returns
matplotlib.Figure
orstr
orTextMatrix
orIPython.display.Latex
: Drawing of the Statevector. Raises
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.
 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)[source]¶ 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
 Raises
QiskitError – if the operator dimension does not match the specified Statevector subsystem dimensions.

expand
(other)[source]¶ Return the tensor product state other ⊗ self.
 Parameters
other (Statevector) – a quantum state object.
 Returns
the tensor product state other ⊗ self.
 Return type
 Raises
QiskitError – if other is not a quantum state.

expectation_value
(oper, qargs=None)[source]¶ 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)[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.
 Parameters
instruction (qiskit.circuit.Instruction or QuantumCircuit) – instruction or circuit
 Returns
The final statevector.
 Return type
 Raises
QiskitError – if the instruction contains invalid instructions for the statevector simulation.

static
from_int
(i, dims)[source]¶ 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
 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 Nqubit state. If it is not a power of two the state will have a single ddimensional subsystem.

classmethod
from_label
(label)[source]¶ Return a tensor product of Pauli X,Y,Z eigenstates.
¶ 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"
\([1 / \sqrt{2}, i / \sqrt{2}]\)
 Parameters
label (string) – a eigenstate string ket label (see table for allowed values).
 Returns
The Nqubit basis state density matrix.
 Return type
 Raises
QiskitError – if the label contains invalid characters, or the length of the label is larger than an explicitly specified num_qubits.

measure
(qargs=None)¶ Measure subsystems and return outcome and postmeasure 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)
whereoutcome
is the measurement outcome string label, and
state
is the collapsed postmeasurement state for the corresponding outcome.
 the pair
 Return type
tuple

property
num_qubits
¶ Return the number of qubits if a Nqubit 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.
 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 2qubit product state \(\psi\rangle=+\rangle\otimes0\rangle\).
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 qubit0 probs_qubit_0 = psi.probabilities([0]) print('Qubit0 probs: {}'.format(probs_qubit_0)) # Probabilities for measuring only qubit1 probs_qubit_1 = psi.probabilities([1]) print('Qubit1 probs: {}'.format(probs_qubit_1))
probs: [0.5 0. 0.5 0. ] Qubit0 probs: [1. 0.] Qubit1 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 outputfrom 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 Ketlike 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

reset
(qargs=None)[source]¶ Reset state or subsystems to the 0state.
 Parameters
qargs (list or None) – subsystems to reset, if None all subsystems will be reset to their 0state (Default: None).
 Returns
the reset state.
 Return type
 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 postmeasurement states are rotated to the 0state. 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 \(\psi \rangle = \psi_{n1} \rangle \otimes ... \otimes \psi_0 \rangle\) the returned statevector will be \(\psi_{0} \rangle \otimes ... \otimes \psi_{n1} \rangle\).
 Returns
the Statevector with reversed subsystem order.
 Return type

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.
 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
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.

tensor
(other)[source]¶ Return the tensor product state self ⊗ other.
 Parameters
other (Statevector) – a quantum state object.
 Returns
the tensor product operator self ⊗ other.
 Return type
 Raises
QiskitError – if other is not a quantum state.

to_dict
(decimals=None)[source]¶ Convert the statevector to dictionary form.
This dictionary representation uses a Ketlike 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 ketform of a 2qubit 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 nonqubit 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 20dimensional system consisting of a qubit and 10dimensional 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)}