---
title: PauliFeatureMap (v2.0)
description: API reference for qiskit.circuit.library.PauliFeatureMap in qiskit v2.0
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.0/qiskit.circuit.library.PauliFeatureMap
---

# PauliFeatureMap

*class* `qiskit.circuit.library.PauliFeatureMap(feature_dimension=None, reps=2, entanglement='full', alpha=2.0, paulis=None, data_map_func=None, parameter_prefix='x', insert_barriers=False, name='PauliFeatureMap')`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/data_preparation/pauli_feature_map.py#L324-L642)

Bases: [`NLocal`](/docs/api/qiskit/2.0/qiskit.circuit.library.NLocal "qiskit.circuit.library.n_local.n_local.NLocal")

The Pauli Expansion circuit.

The Pauli Expansion circuit is a data encoding circuit that transforms input data $\vec{x} \in \mathbb{R}^n$, where n is the `feature_dimension`, as

$$
U_{\Phi(\vec{x})}=\exp\left(i\sum_{S \in \mathcal{I}}
\phi_S(\vec{x})\prod_{i\in S} P_i\right).
$$

Here, $S$ is a set of qubit indices that describes the connections in the feature map, $\mathcal{I}$ is a set containing all these index sets, and $P_i \in \{I, X, Y, Z\}$. Per default the data-mapping $\phi_S$ is

$$
\phi_S(\vec{x}) = \begin{cases}
x_i \text{ if } S = \{i\} \\
\prod_{j \in S} (\pi - x_j) \text{ if } |S| > 1
\end{cases}.
$$

The possible connections can be set using the `entanglement` and `paulis` arguments. For example, for single-qubit $Z$ rotations and two-qubit $YY$ interactions between all qubit pairs, we can set:

```python
feature_map = PauliFeatureMap(..., paulis=["Z", "YY"], entanglement="full")
```

which will produce blocks of the form

```text
┌───┐┌─────────────┐┌──────────┐                                            ┌───────────┐
┤ H ├┤ P(2.0*x[0]) ├┤ RX(pi/2) ├──■──────────────────────────────────────■──┤ RX(-pi/2) ├
├───┤├─────────────┤├──────────┤┌─┴─┐┌────────────────────────────────┐┌─┴─┐├───────────┤
┤ H ├┤ P(2.0*x[1]) ├┤ RX(pi/2) ├┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├┤ RX(-pi/2) ├
└───┘└─────────────┘└──────────┘└───┘└────────────────────────────────┘└───┘└───────────┘
```

The circuit contains `reps` repetitions of this transformation.

Please refer to [`ZFeatureMap`](/docs/api/qiskit/2.0/qiskit.circuit.library.ZFeatureMap "qiskit.circuit.library.ZFeatureMap") for the case of single-qubit Pauli-$Z$ rotations and to [`ZZFeatureMap`](/docs/api/qiskit/2.0/qiskit.circuit.library.ZZFeatureMap "qiskit.circuit.library.ZZFeatureMap") for the single- and two-qubit Pauli-$Z$ rotations.

**Examples**

```python
>>> prep = PauliFeatureMap(2, reps=1, paulis=['ZZ'])
>>> print(prep.decompose())
     ┌───┐
q_0: ┤ H ├──■──────────────────────────────────────■──
     ├───┤┌─┴─┐┌────────────────────────────────┐┌─┴─┐
q_1: ┤ H ├┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├
     └───┘└───┘└────────────────────────────────┘└───┘
```

```python
>>> prep = PauliFeatureMap(2, reps=1, paulis=['Z', 'XX'])
>>> print(prep.decompose())
     ┌───┐┌─────────────┐┌───┐                                            ┌───┐
q_0: ┤ H ├┤ P(2.0*x[0]) ├┤ H ├──■──────────────────────────────────────■──┤ H ├
     ├───┤├─────────────┤├───┤┌─┴─┐┌────────────────────────────────┐┌─┴─┐├───┤
q_1: ┤ H ├┤ P(2.0*x[1]) ├┤ H ├┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├┤ H ├
     └───┘└─────────────┘└───┘└───┘└────────────────────────────────┘└───┘└───┘
```

```python
>>> prep = PauliFeatureMap(2, reps=1, paulis=['ZY'])
>>> print(prep.decompose())
     ┌───┐┌──────────┐                                            ┌───────────┐
q_0: ┤ H ├┤ RX(pi/2) ├──■──────────────────────────────────────■──┤ RX(-pi/2) ├
     ├───┤└──────────┘┌─┴─┐┌────────────────────────────────┐┌─┴─┐└───────────┘
q_1: ┤ H ├────────────┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├─────────────
     └───┘            └───┘└────────────────────────────────┘└───┘
```

```python
>>> from qiskit.circuit.library import EfficientSU2
>>> prep = PauliFeatureMap(3, reps=3, paulis=['Z', 'YY', 'ZXZ'])
>>> wavefunction = EfficientSU2(3)
>>> classifier = prep.compose(wavefunction)
>>> classifier.num_parameters
27
>>> classifier.count_ops()
OrderedDict([('cx', 39), ('rx', 36), ('u1', 21), ('h', 15), ('ry', 12), ('rz', 12)])
```

References:

\[1] Havlicek et al. Supervised learning with quantum enhanced feature spaces, [Nature 567, 209-212 (2019)](https://www.nature.com/articles/s41586-019-0980-2).

Create a new Pauli expansion circuit.

> **Deprecated since version 1.3\_pending**
>
> The class `qiskit.circuit.library.data_preparation.pauli_feature_map.PauliFeatureMap` is pending deprecation as of Qiskit 1.3. It will be marked deprecated in a future release, and then removed no earlier than 3 months after the release date. Use the pauli\_feature\_map function as a replacement. Note that this will no longer return a BlueprintCircuit, but just a plain QuantumCircuit.

**Parameters**

- **feature\_dimension** (*Optional\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]*) – Number of qubits in the circuit.
- **reps** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The number of repeated circuits.
- **entanglement** (*Union\[*[*str*](https://docs.python.org/3/library/stdtypes.html#str)*, Dict\[*[*int*](https://docs.python.org/3/library/functions.html#int)*, List\[Tuple\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]]], Callable\[\[*[*int*](https://docs.python.org/3/library/functions.html#int)*], Union\[*[*str*](https://docs.python.org/3/library/stdtypes.html#str)*, Dict\[*[*int*](https://docs.python.org/3/library/functions.html#int)*, List\[Tuple\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]]]]]]*) – Specifies the entanglement structure. Can be a string (`'full'`, `'linear'`, `'reverse_linear'`, `'circular'` or `'sca'`) or can be a dictionary where the keys represent the number of qubits and the values are list of integer-pairs specifying the indices of qubits that are entangled with one another, for example: `{1: [(0,), (2,)], 2: [(0,1), (2,0)]}` or can be a `Callable[[int], Union[str | Dict[...]]]` to return an entanglement specific for a repetition
- **alpha** ([*float*](https://docs.python.org/3/library/functions.html#float)) – The Pauli rotation factor, multiplicative to the pauli rotations
- **paulis** (*Optional\[List\[*[*str*](https://docs.python.org/3/library/stdtypes.html#str)*]]*) – A list of strings for to-be-used paulis. If None are provided, `['Z', 'ZZ']` will be used.
- **data\_map\_func** (*Optional\[Callable\[\[np.ndarray],* [*float*](https://docs.python.org/3/library/functions.html#float)*]]*) – A mapping function for data x which can be supplied to override the default mapping from `self_product()`.
- **parameter\_prefix** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The prefix used if default parameters are generated.
- **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If True, barriers are inserted in between the evolution instructions and hadamard layers.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) –

## Attributes

### alpha

The Pauli rotation factor (alpha).

**Returns**

The Pauli rotation factor.

### ancillas

A list of `AncillaQubit`s in the order that they were added. You should not mutate this.

### clbits

A list of `Clbit`s in the order that they were added. You should not mutate this.

**Example**

```python
from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit

qr1 = QuantumRegister(2)
qr2 = QuantumRegister(1)
cr1 = ClassicalRegister(2)
cr2 = ClassicalRegister(1)
qc = QuantumCircuit(qr1, qr2, cr1, cr2)

print("List the qubits in this circuit:", qc.qubits)
print("List the classical bits in this circuit:", qc.clbits)
```

```text
List the qubits in this circuit: [Qubit(QuantumRegister(2, 'q0'), 0),
Qubit(QuantumRegister(2, 'q0'), 1), Qubit(QuantumRegister(1, 'q1'), 0)]
List the classical bits in this circuit: [Clbit(ClassicalRegister(2, 'c0'), 0),
Clbit(ClassicalRegister(2, 'c0'), 1), Clbit(ClassicalRegister(1, 'c1'), 0)]
```

### cregs

A list of `Clbit`s in the order that they were added. You should not mutate this.

### data

The circuit data (instructions and context).

**Returns**

a list-like object containing the [`CircuitInstruction`](/docs/api/qiskit/2.0/qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s for each instruction.

**Return type**

QuantumCircuitData

### duration

The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by [`unit`](#qiskit.circuit.library.PauliFeatureMap.unit "qiskit.circuit.library.PauliFeatureMap.unit").

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.duration` is deprecated as of Qiskit 1.3.0. It will be removed in Qiskit 3.0.0.

### entanglement

Get the entanglement strategy.

**Returns**

The entanglement strategy, see [`get_entangler_map()`](#qiskit.circuit.library.PauliFeatureMap.get_entangler_map "qiskit.circuit.library.PauliFeatureMap.get_entangler_map") for more detail on how the format is interpreted.

### entanglement\_blocks

The blocks in the entanglement layers.

**Returns**

The blocks in the entanglement layers.

### feature\_dimension

Returns the feature dimension (which is equal to the number of qubits).

**Returns**

The feature dimension of this feature map.

### flatten

Returns whether the circuit is wrapped in nested gates/instructions or flattened.

### global\_phase

The global phase of the current circuit scope in radians.

**Example**

```python
from qiskit import QuantumCircuit

circuit = QuantumCircuit(2)
circuit.h(0)
circuit.cx(0, 1)
print(circuit.global_phase)
```

```text
0.0
```

```python
from numpy import pi

circuit.global_phase = pi/4
print(circuit.global_phase)
```

```text
0.7853981633974483
```

### initial\_state

Return the initial state that is added in front of the n-local circuit.

**Returns**

The initial state.

### insert\_barriers

If barriers are inserted in between the layers or not.

**Returns**

`True`, if barriers are inserted in between the layers, `False` if not.

### instances

Default value: `160`

### layout

Return any associated layout information about the circuit.

This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/2.0/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/2.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/2.0/qiskit.transpiler.PassManager#run "qiskit.transpiler.PassManager.run") to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the [`transpile()`](/docs/api/qiskit/2.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function: an initial layout that permutes the qubits based on the selected physical qubits on the [`Target`](/docs/api/qiskit/2.0/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout, which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/2.0/qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.

**Example**

```python
from qiskit import QuantumCircuit
from qiskit.providers.fake_provider import GenericBackendV2
from qiskit.transpiler import generate_preset_pass_manager

# Create circuit to test transpiler on
qc = QuantumCircuit(3, 3)
qc.h(0)
qc.cx(0, 1)
qc.swap(1, 2)
qc.cx(0, 1)

# Add measurements to the circuit
qc.measure([0, 1, 2], [0, 1, 2])

# Specify the QPU to target
backend = GenericBackendV2(3)

# Transpile the circuit
pass_manager = generate_preset_pass_manager(
optimization_level=1, backend=backend
)
transpiled = pass_manager.run(qc)

# Print the layout after transpilation
print(transpiled.layout.routing_permutation())
```

```text
[0, 1, 2]
```

### metadata

Arbitrary user-defined dictionary of metadata for the circuit.

Qiskit will not examine the content of this mapping, but it will pass it through the transpiler and reattach it to the output, so you can track your own metadata.

**Example**

```python
from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2, metadata={'experiment_type': 'Bell state experiment'})

print(qc.metadata)
```

```text
{'experiment_type': 'Bell state experiment'}
```

### num\_ancillas

Return the number of ancilla qubits.

**Example**

```python
from qiskit import QuantumCircuit, QuantumRegister, AncillaRegister

# Create a 2-qubit quantum circuit
reg = QuantumRegister(2)
qc = QuantumCircuit(reg)

# Create an ancilla register with 1 qubit
anc = AncillaRegister(1)
qc.add_register(anc)  # Add the ancilla register to the circuit

print("Number of ancilla qubits:", qc.num_ancillas)
```

```text
Number of ancilla qubits: 1
```

### num\_captured\_stretches

The number of stretches in the circuit marked as captured from an enclosing scope.

This is the length of the `iter_captured_stretches()` iterable. If this is non-zero, [`num_input_vars`](#qiskit.circuit.library.PauliFeatureMap.num_input_vars "qiskit.circuit.library.PauliFeatureMap.num_input_vars") must be zero.

### num\_captured\_vars

The number of real-time classical variables in the circuit marked as captured from an enclosing scope.

This is the length of the `iter_captured_vars()` iterable. If this is non-zero, [`num_input_vars`](#qiskit.circuit.library.PauliFeatureMap.num_input_vars "qiskit.circuit.library.PauliFeatureMap.num_input_vars") must be zero.

### num\_clbits

Return number of classical bits.

**Example**

```python
from qiskit import QuantumCircuit

# Create a new circuit with two qubits and one classical bit
qc = QuantumCircuit(2, 1)
print("Number of classical bits:", qc.num_clbits)
```

```text
Number of classical bits: 1
```

### num\_declared\_stretches

The number of stretches in the circuit that are declared by this circuit scope, excluding captures.

This is the length of the `iter_declared_stretches()` iterable.

### num\_declared\_vars

The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.

This is the length of the `iter_declared_vars()` iterable.

### num\_identifiers

The number of real-time classical variables and stretches in the circuit.

This is equal to [`num_vars()`](#qiskit.circuit.library.PauliFeatureMap.num_vars "qiskit.circuit.library.PauliFeatureMap.num_vars") + [`num_stretches()`](#qiskit.circuit.library.PauliFeatureMap.num_stretches "qiskit.circuit.library.PauliFeatureMap.num_stretches").

### num\_input\_vars

The number of real-time classical variables in the circuit marked as circuit inputs.

This is the length of the `iter_input_vars()` iterable. If this is non-zero, [`num_captured_vars`](#qiskit.circuit.library.PauliFeatureMap.num_captured_vars "qiskit.circuit.library.PauliFeatureMap.num_captured_vars") must be zero.

### num\_layers

Return the number of layers in the n-local circuit.

**Returns**

The number of layers in the circuit.

### num\_parameters

The number of parameter objects in the circuit.

### num\_parameters\_settable

The number of distinct parameters.

### num\_qubits

Returns the number of qubits in this circuit.

**Returns**

The number of qubits.

### num\_stretches

The number of stretches in the circuit.

This is the length of the `iter_stretches()` iterable.

### num\_vars

The number of real-time classical variables in the circuit.

This is the length of the `iter_vars()` iterable.

### op\_start\_times

Return a list of operation start times.

> **Note**
>
> This attribute computes the estimate starting time of the operations in the scheduled circuit and only works for simple circuits that have no control flow or other classical feed-forward operations.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

**Example**

```python
from qiskit import QuantumCircuit
from qiskit.providers.fake_provider import GenericBackendV2
from qiskit.transpiler import generate_preset_pass_manager

qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
qc.measure_all()

# Print the original circuit
print("Original circuit:")
print(qc)

# Transpile the circuit with a specific basis gates list and print the resulting circuit
backend = GenericBackendV2(2, basis_gates=['u1', 'u2', 'u3', 'cx'])
pm = generate_preset_pass_manager(
    optimization_level=1, backend=backend, scheduling_method="alap"
)
transpiled_qc = pm.run(qc)
print("Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']:")
print(transpiled_qc)

# Print the start times of each instruction in the transpiled circuit
print("Start times of instructions in the transpiled circuit:")
for instruction, start_time in zip(transpiled_qc.data, transpiled_qc.op_start_times):
    print(f"{instruction.operation.name}: {start_time}")
```

```text
Original circuit:
        ┌───┐      ░ ┌─┐
q_0: ┤ H ├──■───░─┤M├───
        └───┘┌─┴─┐ ░ └╥┘┌─┐
q_1: ─────┤ X ├─░──╫─┤M├
            └───┘ ░  ║ └╥┘
meas: 2/══════════════╩══╩═
                    0  1

Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']:
            ┌─────────┐          ░ ┌─────────────────┐┌─┐
q_0 -> 0 ───┤ U2(0,π) ├──────■───░─┤ Delay(1255[dt]) ├┤M├
        ┌──┴─────────┴───┐┌─┴─┐ ░ └───────┬─┬───────┘└╥┘
q_1 -> 1 ┤ Delay(196[dt]) ├┤ X ├─░─────────┤M├─────────╫─
        └────────────────┘└───┘ ░         └╥┘         ║
meas: 2/═══════════════════════════════════╩══════════╩═
                                            1          0

Start times of instructions in the transpiled circuit:
u2: 0
delay: 0
cx: 196
barrier: 2098
delay: 2098
measure: 3353
measure: 2098
```

**Returns**

List of integers representing instruction estimated start times. The index corresponds to the index of instruction in `QuantumCircuit.data`.

**Raises**

[**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError) – When circuit is not scheduled.

### ordered\_parameters

The parameters used in the underlying circuit.

This includes float values and duplicates.

**Examples**

```python
>>> # prepare circuit ...
>>> print(nlocal)
     ┌───────┐┌──────────┐┌──────────┐┌──────────┐
q_0: ┤ Ry(1) ├┤ Ry(θ[1]) ├┤ Ry(θ[1]) ├┤ Ry(θ[3]) ├
     └───────┘└──────────┘└──────────┘└──────────┘
>>> nlocal.parameters
{Parameter(θ[1]), Parameter(θ[3])}
>>> nlocal.ordered_parameters
[1, Parameter(θ[1]), Parameter(θ[1]), Parameter(θ[3])]
```

**Returns**

The parameters objects used in the circuit.

### parameter\_bounds

The parameter bounds for the unbound parameters in the circuit.

**Returns**

A list of pairs indicating the bounds, as (lower, upper). None indicates an unbounded parameter in the corresponding direction. If `None` is returned, problem is fully unbounded.

### parameters

The parameters defined in the circuit.

This attribute returns the [`Parameter`](/docs/api/qiskit/2.0/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](/docs/api/qiskit/2.0/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically.

**Examples**

The snippet below shows that insertion order of parameters does not matter.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])
```

Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
   ┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
   └─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])
```

To respect numerical sorting, a [`ParameterVector`](/docs/api/qiskit/2.0/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])
])
```

**Returns**

The sorted [`Parameter`](/docs/api/qiskit/2.0/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit.

### paulis

The Pauli strings used in the entanglement of the qubits.

**Returns**

The Pauli strings as list.

### preferred\_init\_points

The initial points for the parameters. Can be stored as initial guess in optimization.

**Returns**

The initial values for the parameters, or None, if none have been set.

### prefix

Default value: `'circuit'`

### qregs

A list of the quantum registers associated with the circuit.

### qubits

A list of `Qubit`s in the order that they were added. You should not mutate this.

### reps

The number of times rotation and entanglement block are repeated.

**Returns**

The number of repetitions.

### rotation\_blocks

The blocks in the rotation layers.

**Returns**

The blocks in the rotation layers.

### unit

The unit that [`duration`](#qiskit.circuit.library.PauliFeatureMap.duration "qiskit.circuit.library.PauliFeatureMap.duration") is specified in.

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.unit` is deprecated as of Qiskit 1.3.0. It will be removed in Qiskit 3.0.0.

### name

Type: `str`

A human-readable name for the circuit.

**Example**

```python
from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)
```

```text
my_circuit
```

## Methods

### get\_entangler\_map

`get_entangler_map(rep_num, block_num, num_block_qubits)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/data_preparation/pauli_feature_map.py#L605-L642)

Get the entangler map for in the repetition `rep_num` and the block `block_num`.

The entangler map for the current block is derived from the value of `self.entanglement`. Below the different cases are listed, where `i` and `j` denote the repetition number and the block number, respectively, and `n` the number of qubits in the block.

| entanglement type                | entangler map                                      |
| -------------------------------- | -------------------------------------------------- |
| `None`                           | `[[0, ..., n - 1]]`                                |
| `str` (e.g `'full'`)             | the specified connectivity on `n` qubits           |
| `List[int]`                      | \[`entanglement`]                                  |
| `List[List[int]]`                | `entanglement`                                     |
| `List[List[List[int]]]`          | `entanglement[i]`                                  |
| `List[List[List[List[int]]]]`    | `entanglement[i][j]`                               |
| `List[str]`                      | the connectivity specified in `entanglement[i]`    |
| `List[List[str]]`                | the connectivity specified in `entanglement[i][j]` |
| `Callable[int, str]`             | same as `List[str]`                                |
| `Callable[int, List[List[int]]]` | same as `List[List[List[int]]]`                    |

Note that all indices are to be taken modulo the length of the array they act on, i.e. no out-of-bounds index error will be raised but we re-iterate from the beginning of the list.

**Parameters**

- **rep\_num** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The current repetition we are in.
- **block\_num** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The block number within the entanglement layers.
- **num\_block\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The number of qubits in the block.

**Returns**

The entangler map for the current block in the current repetition.

**Raises**

[**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError) – If the value of `entanglement` could not be cast to a corresponding entangler map.

**Return type**

[*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)\[[*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)\[[int](https://docs.python.org/3/library/functions.html#int)]]

### pauli\_block

`pauli_block(pauli_string)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/data_preparation/pauli_feature_map.py#L559-L563)

Get the Pauli block for the feature map circuit.

### pauli\_evolution

`pauli_evolution(pauli_string, time)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/data_preparation/pauli_feature_map.py#L565-L603)

Get the evolution block for the given pauli string.