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---
title: Statevector (v0.26)
description: API reference for qiskit.quantum_info.Statevector in qiskit v0.26
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.quantum_info.Statevector
---
<span id="qiskit-quantum-info-statevector" />
# qiskit.quantum\_info.Statevector
<Class id="qiskit.quantum_info.Statevector" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/quantum_info/states/statevector.py" signature="Statevector(data, dims=None)" modifiers="class">
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``` 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.
### \_\_init\_\_
<Function id="qiskit.quantum_info.Statevector.__init__" signature="__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.
</Function>
## Methods
| | |
| ---------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------- |
| [`__init__`](#qiskit.quantum_info.Statevector.__init__ "qiskit.quantum_info.Statevector.__init__")(data\[, dims]) | Initialize a statevector object. |
| [`conjugate`](#qiskit.quantum_info.Statevector.conjugate "qiskit.quantum_info.Statevector.conjugate")() | Return the conjugate of the operator. |
| [`copy`](#qiskit.quantum_info.Statevector.copy "qiskit.quantum_info.Statevector.copy")() | Make a copy of current operator. |
| [`dims`](#qiskit.quantum_info.Statevector.dims "qiskit.quantum_info.Statevector.dims")(\[qargs]) | Return tuple of input dimension for specified subsystems. |
| [`draw`](#qiskit.quantum_info.Statevector.draw "qiskit.quantum_info.Statevector.draw")(\[output]) | Return a visualization of the Statevector. |
| [`equiv`](#qiskit.quantum_info.Statevector.equiv "qiskit.quantum_info.Statevector.equiv")(other\[, rtol, atol]) | Return True if other is equivalent as a statevector up to global phase. |
| [`evolve`](#qiskit.quantum_info.Statevector.evolve "qiskit.quantum_info.Statevector.evolve")(other\[, qargs]) | Evolve a quantum state by the operator. |
| [`expand`](#qiskit.quantum_info.Statevector.expand "qiskit.quantum_info.Statevector.expand")(other) | Return the tensor product state other ⊗ self. |
| [`expectation_value`](#qiskit.quantum_info.Statevector.expectation_value "qiskit.quantum_info.Statevector.expectation_value")(oper\[, qargs]) | Compute the expectation value of an operator. |
| [`from_instruction`](#qiskit.quantum_info.Statevector.from_instruction "qiskit.quantum_info.Statevector.from_instruction")(instruction) | Return the output statevector of an instruction. |
| [`from_int`](#qiskit.quantum_info.Statevector.from_int "qiskit.quantum_info.Statevector.from_int")(i, dims) | Return a computational basis statevector. |
| [`from_label`](#qiskit.quantum_info.Statevector.from_label "qiskit.quantum_info.Statevector.from_label")(label) | Return a tensor product of Pauli X,Y,Z eigenstates. |
| [`is_valid`](#qiskit.quantum_info.Statevector.is_valid "qiskit.quantum_info.Statevector.is_valid")(\[atol, rtol]) | Return True if a Statevector has norm 1. |
| [`measure`](#qiskit.quantum_info.Statevector.measure "qiskit.quantum_info.Statevector.measure")(\[qargs]) | Measure subsystems and return outcome and post-measure state. |
| [`probabilities`](#qiskit.quantum_info.Statevector.probabilities "qiskit.quantum_info.Statevector.probabilities")(\[qargs, decimals]) | Return the subsystem measurement probability vector. |
| [`probabilities_dict`](#qiskit.quantum_info.Statevector.probabilities_dict "qiskit.quantum_info.Statevector.probabilities_dict")(\[qargs, decimals]) | Return the subsystem measurement probability dictionary. |
| [`purity`](#qiskit.quantum_info.Statevector.purity "qiskit.quantum_info.Statevector.purity")() | Return the purity of the quantum state. |
| [`reset`](#qiskit.quantum_info.Statevector.reset "qiskit.quantum_info.Statevector.reset")(\[qargs]) | Reset state or subsystems to the 0-state. |
| [`reverse_qargs`](#qiskit.quantum_info.Statevector.reverse_qargs "qiskit.quantum_info.Statevector.reverse_qargs")() | Return a Statevector with reversed subsystem ordering. |
| [`sample_counts`](#qiskit.quantum_info.Statevector.sample_counts "qiskit.quantum_info.Statevector.sample_counts")(shots\[, qargs]) | Sample a dict of qubit measurement outcomes in the computational basis. |
| [`sample_memory`](#qiskit.quantum_info.Statevector.sample_memory "qiskit.quantum_info.Statevector.sample_memory")(shots\[, qargs]) | Sample a list of qubit measurement outcomes in the computational basis. |
| [`seed`](#qiskit.quantum_info.Statevector.seed "qiskit.quantum_info.Statevector.seed")(\[value]) | Set the seed for the quantum state RNG. |
| [`tensor`](#qiskit.quantum_info.Statevector.tensor "qiskit.quantum_info.Statevector.tensor")(other) | Return the tensor product state self ⊗ other. |
| [`to_dict`](#qiskit.quantum_info.Statevector.to_dict "qiskit.quantum_info.Statevector.to_dict")(\[decimals]) | Convert the statevector to dictionary form. |
| [`to_operator`](#qiskit.quantum_info.Statevector.to_operator "qiskit.quantum_info.Statevector.to_operator")() | Convert state to a rank-1 projector operator |
| [`trace`](#qiskit.quantum_info.Statevector.trace "qiskit.quantum_info.Statevector.trace")() | Return the trace of the quantum state as a density matrix. |
## Attributes
| | |
| -------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------- |
| [`atol`](#qiskit.quantum_info.Statevector.atol "qiskit.quantum_info.Statevector.atol") | Default absolute tolerance parameter for float comparisons. |
| [`data`](#qiskit.quantum_info.Statevector.data "qiskit.quantum_info.Statevector.data") | Return data. |
| [`dim`](#qiskit.quantum_info.Statevector.dim "qiskit.quantum_info.Statevector.dim") | Return total state dimension. |
| [`num_qubits`](#qiskit.quantum_info.Statevector.num_qubits "qiskit.quantum_info.Statevector.num_qubits") | Return the number of qubits if a N-qubit state or None otherwise. |
| [`rtol`](#qiskit.quantum_info.Statevector.rtol "qiskit.quantum_info.Statevector.rtol") | Default relative tolerance parameter for float comparisons. |
### atol
<Attribute id="qiskit.quantum_info.Statevector.atol">
Default absolute tolerance parameter for float comparisons.
</Attribute>
### conjugate
<Function id="qiskit.quantum_info.Statevector.conjugate" signature="conjugate()">
Return the conjugate of the operator.
</Function>
### copy
<Function id="qiskit.quantum_info.Statevector.copy" signature="copy()">
Make a copy of current operator.
</Function>
### data
<Attribute id="qiskit.quantum_info.Statevector.data">
Return data.
</Attribute>
### dim
<Attribute id="qiskit.quantum_info.Statevector.dim">
Return total state dimension.
</Attribute>
### dims
<Function id="qiskit.quantum_info.Statevector.dims" signature="dims(qargs=None)">
Return tuple of input dimension for specified subsystems.
</Function>
### draw
<Function id="qiskit.quantum_info.Statevector.draw" signature="draw(output=None, **drawer_args)">
Return a visualization of the Statevector.
**repr**: ASCII TextMatrix of the states `__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 functions 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.
</Function>
### equiv
<Function id="qiskit.quantum_info.Statevector.equiv" signature="equiv(other, rtol=None, atol=None)">
Return True if other is equivalent as a statevector up to global phase.
<Admonition title="Note" type="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.
</Admonition>
**Parameters**
* **other** ([*Statevector*](#qiskit.quantum_info.Statevector "qiskit.quantum_info.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
</Function>
### evolve
<Function id="qiskit.quantum_info.Statevector.evolve" signature="evolve(other, qargs=None)">
Evolve a quantum state by the operator.
**Parameters**
* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.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](#qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
**Raises**
**QiskitError** if the operator dimension does not match the specified Statevector subsystem dimensions.
</Function>
### expand
<Function id="qiskit.quantum_info.Statevector.expand" signature="expand(other)">
Return the tensor product state other ⊗ self.
**Parameters**
**other** ([*Statevector*](#qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")) a quantum state object.
**Returns**
the tensor product state other ⊗ self.
**Return type**
[Statevector](#qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
**Raises**
**QiskitError** if other is not a quantum state.
</Function>
### expectation\_value
<Function id="qiskit.quantum_info.Statevector.expectation_value" signature="expectation_value(oper, qargs=None)">
Compute the expectation value of an operator.
**Parameters**
* **oper** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) an operator to evaluate expval of.
* **qargs** (*None or list*) subsystems to apply operator on.
**Returns**
the expectation value.
**Return type**
complex
</Function>
### from\_instruction
<Function id="qiskit.quantum_info.Statevector.from_instruction" signature="from_instruction(instruction)" modifiers="classmethod">
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*](qiskit.circuit.Instruction "qiskit.circuit.Instruction") *or*[*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) instruction or circuit
**Returns**
The final statevector.
**Return type**
[Statevector](#qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
**Raises**
**QiskitError** if the instruction contains invalid instructions for the statevector simulation.
</Function>
### from\_int
<Function id="qiskit.quantum_info.Statevector.from_int" signature="from_int(i, dims)" modifiers="static">
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](#qiskit.quantum_info.Statevector "qiskit.quantum_info.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.
</Function>
### from\_label
<Function id="qiskit.quantum_info.Statevector.from_label" signature="from_label(label)" modifiers="classmethod">
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 N-qubit basis state density matrix.
**Return type**
[Statevector](#qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
**Raises**
**QiskitError** if the label contains invalid characters, or the length of the label is larger than an explicitly specified num\_qubits.
</Function>
### is\_valid
<Function id="qiskit.quantum_info.Statevector.is_valid" signature="is_valid(atol=None, rtol=None)">
Return True if a Statevector has norm 1.
</Function>
### measure
<Function id="qiskit.quantum_info.Statevector.measure" signature="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()`](#qiskit.quantum_info.Statevector.seed "qiskit.quantum_info.Statevector.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
</Function>
### num\_qubits
<Attribute id="qiskit.quantum_info.Statevector.num_qubits">
Return the number of qubits if a N-qubit state or None otherwise.
</Attribute>
### probabilities
<Function id="qiskit.quantum_info.Statevector.probabilities" signature="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 $|\psi\rangle=|+\rangle\otimes|0\rangle$.
```python
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
```python
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. ]
```
</Function>
### probabilities\_dict
<Function id="qiskit.quantum_info.Statevector.probabilities_dict" signature="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
</Function>
### purity
<Function id="qiskit.quantum_info.Statevector.purity" signature="purity()">
Return the purity of the quantum state.
</Function>
### reset
<Function id="qiskit.quantum_info.Statevector.reset" signature="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](#qiskit.quantum_info.Statevector "qiskit.quantum_info.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()`](#qiskit.quantum_info.Statevector.seed "qiskit.quantum_info.Statevector.seed") method.
</Function>
### reverse\_qargs
<Function id="qiskit.quantum_info.Statevector.reverse_qargs" signature="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](#qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
</Function>
### rtol
<Attribute id="qiskit.quantum_info.Statevector.rtol">
Default relative tolerance parameter for float comparisons.
</Attribute>
### sample\_counts
<Function id="qiskit.quantum_info.Statevector.sample_counts" signature="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](qiskit.result.Counts "qiskit.result.Counts")
Additional Information:
> This function *samples* measurement outcomes using the measure [`probabilities()`](#qiskit.quantum_info.Statevector.probabilities "qiskit.quantum_info.Statevector.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()`](#qiskit.quantum_info.Statevector.seed "qiskit.quantum_info.Statevector.seed") method.
</Function>
### sample\_memory
<Function id="qiskit.quantum_info.Statevector.sample_memory" signature="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()`](#qiskit.quantum_info.Statevector.probabilities "qiskit.quantum_info.Statevector.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()`](#qiskit.quantum_info.Statevector.seed "qiskit.quantum_info.Statevector.seed") method.
</Function>
### seed
<Function id="qiskit.quantum_info.Statevector.seed" signature="seed(value=None)">
Set the seed for the quantum state RNG.
</Function>
### tensor
<Function id="qiskit.quantum_info.Statevector.tensor" signature="tensor(other)">
Return the tensor product state self ⊗ other.
**Parameters**
**other** ([*Statevector*](#qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")) a quantum state object.
**Returns**
the tensor product operator self ⊗ other.
**Return type**
[Statevector](#qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")
**Raises**
**QiskitError** if other is not a quantum state.
</Function>
### to\_dict
<Function id="qiskit.quantum_info.Statevector.to_dict" signature="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 $|\psi\rangle = |-\rangle\otimes |0\rangle$
```python
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
```python
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.
```python
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)}
```
</Function>
### to\_operator
<Function id="qiskit.quantum_info.Statevector.to_operator" signature="to_operator()">
Convert state to a rank-1 projector operator
</Function>
### trace
<Function id="qiskit.quantum_info.Statevector.trace" signature="trace()">
Return the trace of the quantum state as a density matrix.
</Function>
</Class>