---
title: ZZFeatureMap (v0.46)
description: API reference for qiskit.circuit.library.ZZFeatureMap in qiskit v0.46
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/0.46/qiskit.circuit.library.ZZFeatureMap
---

# ZZFeatureMap

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

[GitHub](https://github.com/qiskit/qiskit/tree/stable/0.46/qiskit/circuit/library/data_preparation/zz_feature_map.py)

Bases: [`PauliFeatureMap`](/docs/api/qiskit/0.46/qiskit.circuit.library.PauliFeatureMap "qiskit.circuit.library.data_preparation.pauli_feature_map.PauliFeatureMap")

Second-order Pauli-Z evolution circuit.

For 3 qubits and 1 repetition and linear entanglement the circuit is represented by:

```python
┌───┐┌─────────────────┐
┤ H ├┤ U1(2.0*φ(x[0])) ├──■────────────────────────────■────────────────────────────────────
├───┤├─────────────────┤┌─┴─┐┌──────────────────────┐┌─┴─┐
┤ H ├┤ U1(2.0*φ(x[1])) ├┤ X ├┤ U1(2.0*φ(x[0],x[1])) ├┤ X ├──■────────────────────────────■──
├───┤├─────────────────┤└───┘└──────────────────────┘└───┘┌─┴─┐┌──────────────────────┐┌─┴─┐
┤ H ├┤ U1(2.0*φ(x[2])) ├──────────────────────────────────┤ X ├┤ U1(2.0*φ(x[1],x[2])) ├┤ X ├
└───┘└─────────────────┘                                  └───┘└──────────────────────┘└───┘
```

where $\varphi$ is a classical non-linear function, which defaults to $\varphi(x) = x$ if and $\varphi(x,y) = (\pi - x)(\pi - y)$.

**Examples**

```python
>>> from qiskit.circuit.library import ZZFeatureMap
>>> prep = ZZFeatureMap(2, reps=1)
>>> print(prep)
     ┌───┐┌──────────────┐
q_0: ┤ H ├┤ U1(2.0*x[0]) ├──■───────────────────────────────────────■──
     ├───┤├──────────────┤┌─┴─┐┌─────────────────────────────────┐┌─┴─┐
q_1: ┤ H ├┤ U1(2.0*x[1]) ├┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├
     └───┘└──────────────┘└───┘└─────────────────────────────────┘└───┘
```

```python
>>> from qiskit.circuit.library import EfficientSU2
>>> classifier = ZZFeatureMap(3) + EfficientSU2(3)
>>> classifier.num_parameters
15
>>> classifier.parameters  # 'x' for the data preparation, 'θ' for the SU2 parameters
ParameterView([
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(θ[0]),
    ParameterVectorElement(θ[1]), ParameterVectorElement(θ[2]),
    ParameterVectorElement(θ[3]), ParameterVectorElement(θ[4]),
    ParameterVectorElement(θ[5]), ParameterVectorElement(θ[6]),
    ParameterVectorElement(θ[7]), ParameterVectorElement(θ[8]),
    ParameterVectorElement(θ[9]), ParameterVectorElement(θ[10]),
    ParameterVectorElement(θ[11]), ParameterVectorElement(θ[12]),
    ParameterVectorElement(θ[13]), ParameterVectorElement(θ[14]),
    ParameterVectorElement(θ[15]), ParameterVectorElement(θ[16]),
    ParameterVectorElement(θ[17]), ParameterVectorElement(θ[18]),
    ParameterVectorElement(θ[19]), ParameterVectorElement(θ[20]),
    ParameterVectorElement(θ[21]), ParameterVectorElement(θ[22]),
    ParameterVectorElement(θ[23])
])
>>> classifier.count_ops()
OrderedDict([('ZZFeatureMap', 1), ('EfficientSU2', 1)])
```

Create a new second-order Pauli-Z expansion.

**Parameters**

- **feature\_dimension** ([*int*](https://docs.python.org/3/library/functions.html#int)) – Number of features.
- **reps** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The number of repeated circuits, has a min. value of 1.
- **entanglement** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)  *|*[*List*](https://docs.python.org/3/library/typing.html#typing.List)*\[*[*List*](https://docs.python.org/3/library/typing.html#typing.List)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]] |* [*Callable*](https://docs.python.org/3/library/typing.html#typing.Callable)*\[\[*[*int*](https://docs.python.org/3/library/functions.html#int)*],* [*List*](https://docs.python.org/3/library/typing.html#typing.List)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]]*) – Specifies the entanglement structure. Refer to [`NLocal`](/docs/api/qiskit/0.46/qiskit.circuit.library.NLocal "qiskit.circuit.library.NLocal") for detail.
- **data\_map\_func** ([*Callable*](https://docs.python.org/3/library/typing.html#typing.Callable)*\[\[*[*ndarray*](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray)*],* [*float*](https://docs.python.org/3/library/functions.html#float)*] | None*) – A mapping function for data x.
- **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.

**Raises**

[**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError) – If the feature dimension is smaller than 2.

## Attributes

### alpha

The Pauli rotation factor (alpha).

**Returns**

The Pauli rotation factor.

### ancillas

Returns a list of ancilla bits in the order that the registers were added.

### calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`

### clbits

Returns a list of classical bits in the order that the registers were added.

### data

### entanglement

Get the entanglement strategy.

**Returns**

The entanglement strategy, see `get_entangler_map()` for more detail on how the format is interpreted.

### entanglement\_blocks

### extension\_lib

Default value: `'include "qelib1.inc";'`

### 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

Return the global phase of the current circuit scope in radians.

### header

Default value: `'OPENQASM 2.0;'`

### 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: `163`

### layout

Return any associated layout information about the circuit

This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/0.46/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/0.46/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/0.46/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/0.46/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function, an initial layout which permutes the qubits based on the selected physical qubits on the [`Target`](/docs/api/qiskit/0.46/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/0.46/qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.

### metadata

The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided `dict` of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

### num\_ancillas

Return the number of ancilla qubits.

### num\_clbits

Return number of classical bits.

### num\_layers

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

**Returns**

The number of layers in the circuit.

### num\_parameters

### num\_parameters\_settable

The number of distinct parameters.

### num\_qubits

Returns the number of qubits in this circuit.

**Returns**

The number of qubits.

### op\_start\_times

Return a list of operation start times.

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

**Returns**

List of integers representing instruction 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

### 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

Type: `list[QuantumRegister]`

A list of the quantum registers associated with the circuit.

### qubits

Returns a list of quantum bits in the order that the registers were added.

### 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.