---
title: ZZFeatureMap (v2.0)
description: API reference for qiskit.circuit.library.ZZFeatureMap in qiskit v2.0
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.0/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/2.0/qiskit/circuit/library/data_preparation/_zz_feature_map.py#L21-L150)

Bases: [`PauliFeatureMap`](/docs/api/qiskit/2.0/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:

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

```text
     ┌───┐┌─────────────┐
q_0: ┤ H ├┤ P(2.0*x[0]) ├──■──────────────────────────────────────■──
     ├───┤├─────────────┤┌─┴─┐┌────────────────────────────────┐┌─┴─┐
q_1: ┤ H ├┤ P(2.0*x[1]) ├┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├
     └───┘└─────────────┘└───┘└────────────────────────────────┘└───┘
```

```python
from qiskit.circuit.library import EfficientSU2
classifier = ZZFeatureMap(3).compose(EfficientSU2(3))
classifier.num_parameters
```

```text
27
```

```python
classifier.parameters  # 'x' for the data preparation, 'θ' for the SU2 parameters
```

```text
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])
])
```

```python
classifier.count_ops()
```

```text
OrderedDict([('ZZFeatureMap', 1), ('EfficientSU2', 1)])
```

Create a new second-order Pauli-Z expansion.

> **Deprecated since version 1.3\_pending**
>
> The class `qiskit.circuit.library.data_preparation._zz_feature_map.ZZFeatureMap` 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 z\_feature\_map function as a replacement. Note that this will no longer return a BlueprintCircuit, but just a plain QuantumCircuit.

**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)  *|*[*Dict*](https://docs.python.org/3/library/typing.html#typing.Dict)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*,* [*List*](https://docs.python.org/3/library/typing.html#typing.List)*\[*[*Tuple*](https://docs.python.org/3/library/typing.html#typing.Tuple)*\[*[*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)*],* [*str*](https://docs.python.org/3/library/stdtypes.html#str)  *|*[*Dict*](https://docs.python.org/3/library/typing.html#typing.Dict)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*,* [*List*](https://docs.python.org/3/library/typing.html#typing.List)*\[*[*Tuple*](https://docs.python.org/3/library/typing.html#typing.Tuple)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]]]]*) – Specifies the entanglement structure. Refer to [`PauliFeatureMap`](/docs/api/qiskit/2.0/qiskit.circuit.library.PauliFeatureMap "qiskit.circuit.library.PauliFeatureMap") 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.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) –

**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

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.ZZFeatureMap.unit "qiskit.circuit.library.ZZFeatureMap.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()` 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: `251`

### 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.ZZFeatureMap.num_input_vars "qiskit.circuit.library.ZZFeatureMap.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.ZZFeatureMap.num_input_vars "qiskit.circuit.library.ZZFeatureMap.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.ZZFeatureMap.num_vars "qiskit.circuit.library.ZZFeatureMap.num_vars") + [`num_stretches()`](#qiskit.circuit.library.ZZFeatureMap.num_stretches "qiskit.circuit.library.ZZFeatureMap.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.ZZFeatureMap.num_captured_vars "qiskit.circuit.library.ZZFeatureMap.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.ZZFeatureMap.duration "qiskit.circuit.library.ZZFeatureMap.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
```