# Statevector

*class *`qiskit.quantum_info.Statevector(data, dims=None)`

Bases: `QuantumState`

, `TolerancesMixin`

Statevector class

Initialize a statevector object.

**Parameters**

**or**(*data (np.array or**list*(opens in a new tab)*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*(opens in a new tab)*or**tuple*(opens in a new tab)*or**list*(opens in a new tab)) – 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.

## Attributes

### atol

Default value: `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

Default value: `1e-05`

### settings

Return settings.

## Methods

### conjugate

### copy

### dims

### draw

`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*(opens in a new tab)) – 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`

(opens in a new tab) or `TextMatrix`

or `IPython.display.Latex`

: Drawing of the Statevector.

**Raises**

**ValueError**(opens in a new tab) – when an invalid output method is selected.

**Examples**

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')
```

### equiv

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

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

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*(opens in a new tab)) – relative tolerance value for comparison.**atol**(*float*(opens in a new tab)) – absolute tolerance value for comparison.

**Returns**

True if statevectors are equivalent up to global phase.

**Return type**

### evolve

`evolve(other, qargs=None)`

Evolve a quantum state by the operator.

**Parameters**

**other**(*Operator**|**QuantumCircuit**|**circuit.Instruction*) – The operator to evolve by.**qargs**(*list*(opens in a new tab)) – 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

`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**

**Raises**

**QiskitError** – if other is not a quantum state.

### expectation_value

`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*(opens in a new tab)) – subsystems to apply operator on.

**Returns**

the expectation value.

**Return type**

### from_instruction

*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* *or**QuantumCircuit*) – instruction or circuit

**Returns**

The final statevector.

**Return type**

**Raises**

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

### from_int

*static *`from_int(i, dims)`

Return a computational basis statevector.

**Parameters**

**i**(*int*(opens in a new tab)) – the basis state element.**dims**(*int*(opens in a new tab)*or**tuple*(opens in a new tab)*or**list*(opens in a new tab)) – 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 N-qubit state. If it is not a power of two the state will have a single d-dimensional subsystem.

### from_label

*classmethod *`from_label(label)`

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**

**Raises**

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

### inner

`inner(other)`

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

**Parameters**

**other** (*Statevector*) – a quantum state object.

**Returns**

the inner product of self and other, $\langle self| other \rangle$.

**Return type**

np.complex128

**Raises**

**QiskitError** – if other is not a quantum state or has different dimension.

### is_valid

`is_valid(atol=None, rtol=None)`

Return True if a Statevector has norm 1.

**Return type**

### measure

`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*(opens in a new tab) *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**

### probabilities

`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*(opens in a new tab)) – subsystems to return probabilities for, if None return for all subsystems (Default: None).**decimals**(*None or**int*(opens in a new tab)) – 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

`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*(opens in a new tab)) – subsystems to return probabilities for, if None return for all subsystems (Default: None).**decimals**(*None or**int*(opens in a new tab)) – 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**

### purity

### reset

`reset(qargs=None)`

Reset state or subsystems to the 0-state.

**Parameters**

**qargs** (*list*(opens in a new tab) *or None*) – subsystems to reset, if None all subsystems will be reset to their 0-state (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 post-measurement states are rotated to the 0-state. The RNG seed for this sampling can be set using the `seed()`

method.

### reverse_qargs

`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**

### sample_counts

`sample_counts(shots, qargs=None)`

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

**Parameters**

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

**Returns**

sampled counts dictionary.

**Return type**

Additional Information:

This function

samplesmeasurement 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

`sample_memory(shots, qargs=None)`

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

**Parameters**

**shots**(*int*(opens in a new tab)) – number of samples to generate.**qargs**(*None or**list*(opens in a new tab)) – 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

samplesmeasurement 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

### tensor

`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**

**Raises**

**QiskitError** – if other is not a quantum state.

### to_dict

`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*(opens in a new tab)) – 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**

**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

### trace

`trace()`

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

**Return type**

*float64*