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---
title: ZFeatureMap (v1.2)
description: API reference for qiskit.circuit.library.ZFeatureMap in qiskit v1.2
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.circuit.library.ZFeatureMap
---
# ZFeatureMap
<Class id="qiskit.circuit.library.ZFeatureMap" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/circuit/library/data_preparation/z_feature_map.py#L21-L106" signature="qiskit.circuit.library.ZFeatureMap(feature_dimension, reps=2, data_map_func=None, parameter_prefix='x', insert_barriers=False, name='ZFeatureMap')" modifiers="class">
Bases: [`PauliFeatureMap`](qiskit.circuit.library.PauliFeatureMap "qiskit.circuit.library.data_preparation.pauli_feature_map.PauliFeatureMap")
The first order Pauli Z-evolution circuit.
On 3 qubits and with 2 repetitions the circuit is represented by:
```python
┌───┐┌─────────────┐┌───┐┌─────────────┐
┤ H ├┤ P(2.0*x[0]) ├┤ H ├┤ P(2.0*x[0]) ├
├───┤├─────────────┤├───┤├─────────────┤
┤ H ├┤ P(2.0*x[1]) ├┤ H ├┤ P(2.0*x[1]) ├
├───┤├─────────────┤├───┤├─────────────┤
┤ H ├┤ P(2.0*x[2]) ├┤ H ├┤ P(2.0*x[2]) ├
└───┘└─────────────┘└───┘└─────────────┘
```
This is a sub-class of [`PauliFeatureMap`](qiskit.circuit.library.PauliFeatureMap "qiskit.circuit.library.PauliFeatureMap") where the Pauli strings are fixed as \[‘Z’]. As a result the first order expansion will be a circuit without entangling gates.
**Examples**
```python
>>> from qiskit.circuit.library import ZFeatureMap
>>> prep = ZFeatureMap(3, reps=3, insert_barriers=True)
>>> print(prep.decompose())
┌───┐ ░ ┌─────────────┐ ░ ┌───┐ ░ ┌─────────────┐ ░ ┌───┐ ░ ┌─────────────┐
q_0: ┤ H ├─░─┤ P(2.0*x[0]) ├─░─┤ H ├─░─┤ P(2.0*x[0]) ├─░─┤ H ├─░─┤ P(2.0*x[0]) ├
├───┤ ░ ├─────────────┤ ░ ├───┤ ░ ├─────────────┤ ░ ├───┤ ░ ├─────────────┤
q_1: ┤ H ├─░─┤ P(2.0*x[1]) ├─░─┤ H ├─░─┤ P(2.0*x[1]) ├─░─┤ H ├─░─┤ P(2.0*x[1]) ├
├───┤ ░ ├─────────────┤ ░ ├───┤ ░ ├─────────────┤ ░ ├───┤ ░ ├─────────────┤
q_2: ┤ H ├─░─┤ P(2.0*x[2]) ├─░─┤ H ├─░─┤ P(2.0*x[2]) ├─░─┤ H ├─░─┤ P(2.0*x[2]) ├
└───┘ ░ └─────────────┘ ░ └───┘ ░ └─────────────┘ ░ └───┘ ░ └─────────────┘
```
```python
>>> data_map = lambda x: x[0]*x[0] + 1 # note: input is an array
>>> prep = ZFeatureMap(3, reps=1, data_map_func=data_map)
>>> print(prep.decompose())
┌───┐┌──────────────────────┐
q_0: ┤ H ├┤ P(2.0*x[0]**2 + 2.0) ├
├───┤├──────────────────────┤
q_1: ┤ H ├┤ P(2.0*x[1]**2 + 2.0) ├
├───┤├──────────────────────┤
q_2: ┤ H ├┤ P(2.0*x[2]**2 + 2.0) ├
└───┘└──────────────────────┘
```
```python
>>> from qiskit.circuit.library import RealAmplitudes
>>> classifier = ZFeatureMap(3, reps=1).compose(RealAmplitudes(3, reps=1))
>>> print(classifier.decompose())
┌───┐┌─────────────┐┌──────────┐ ┌──────────┐
q_0: ┤ H ├┤ P(2.0*x[0]) ├┤ RY(θ[0]) ├─■──■─┤ RY(θ[3]) ├────────────
├───┤├─────────────┤├──────────┤ │ │ └──────────┘┌──────────┐
q_1: ┤ H ├┤ P(2.0*x[1]) ├┤ RY(θ[1]) ├─■──┼──────■──────┤ RY(θ[4]) ├
├───┤├─────────────┤├──────────┤ │ │ ├──────────┤
q_2: ┤ H ├┤ P(2.0*x[2]) ├┤ RY(θ[2]) ├────■──────■──────┤ RY(θ[5]) ├
└───┘└─────────────┘└──────────┘ └──────────┘
```
Create a new first-order Pauli-Z expansion circuit.
**Parameters**
* **feature\_dimension** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")) – The number of features
* **reps** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")) – The number of repeated circuits. Defaults to 2, has a minimum value of 1.
* **data\_map\_func** ([*Callable*](https://docs.python.org/3/library/typing.html#typing.Callable "(in Python v3.13)")*\[\[*[*ndarray*](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.1)")*],* [*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")*] | None*) – 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 "(in Python v3.13)")) – The prefix used if default parameters are generated.
* **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – If True, barriers are inserted in between the evolution instructions and hadamard layers.
## Attributes
### alpha
<Attribute id="qiskit.circuit.library.ZFeatureMap.alpha">
The Pauli rotation factor (alpha).
**Returns**
The Pauli rotation factor.
</Attribute>
### ancillas
<Attribute id="qiskit.circuit.library.ZFeatureMap.ancillas">
A list of `AncillaQubit`s in the order that they were added. You should not mutate this.
</Attribute>
### calibrations
<Attribute id="qiskit.circuit.library.ZFeatureMap.calibrations">
Return calibration dictionary.
The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`
</Attribute>
### clbits
<Attribute id="qiskit.circuit.library.ZFeatureMap.clbits">
A list of `Clbit`s in the order that they were added. You should not mutate this.
</Attribute>
### data
<Attribute id="qiskit.circuit.library.ZFeatureMap.data">
The circuit data (instructions and context).
**Returns**
a list-like object containing the [`CircuitInstruction`](qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s for each instruction.
**Return type**
QuantumCircuitData
</Attribute>
### entanglement
<Attribute id="qiskit.circuit.library.ZFeatureMap.entanglement">
Get the entanglement strategy.
**Returns**
The entanglement strategy, see `get_entangler_map()` for more detail on how the format is interpreted.
</Attribute>
### entanglement\_blocks
<Attribute id="qiskit.circuit.library.ZFeatureMap.entanglement_blocks">
The blocks in the entanglement layers.
**Returns**
The blocks in the entanglement layers.
</Attribute>
### feature\_dimension
<Attribute id="qiskit.circuit.library.ZFeatureMap.feature_dimension">
Returns the feature dimension (which is equal to the number of qubits).
**Returns**
The feature dimension of this feature map.
</Attribute>
### flatten
<Attribute id="qiskit.circuit.library.ZFeatureMap.flatten">
Returns whether the circuit is wrapped in nested gates/instructions or flattened.
</Attribute>
### global\_phase
<Attribute id="qiskit.circuit.library.ZFeatureMap.global_phase">
The global phase of the current circuit scope in radians.
</Attribute>
### initial\_state
<Attribute id="qiskit.circuit.library.ZFeatureMap.initial_state">
Return the initial state that is added in front of the n-local circuit.
**Returns**
The initial state.
</Attribute>
### insert\_barriers
<Attribute id="qiskit.circuit.library.ZFeatureMap.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.
</Attribute>
### instances
<Attribute id="qiskit.circuit.library.ZFeatureMap.instances" attributeValue="164" />
### layout
<Attribute id="qiskit.circuit.library.ZFeatureMap.layout">
Return any associated layout information about the circuit
This attribute contains an optional [`TranspileLayout`](qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](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()`](compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function, an initial layout which permutes the qubits based on the selected physical qubits on the [`Target`](qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.
</Attribute>
### metadata
<Attribute id="qiskit.circuit.library.ZFeatureMap.metadata">
Arbitrary user-defined 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.
</Attribute>
### num\_ancillas
<Attribute id="qiskit.circuit.library.ZFeatureMap.num_ancillas">
Return the number of ancilla qubits.
</Attribute>
### num\_captured\_vars
<Attribute id="qiskit.circuit.library.ZFeatureMap.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.ZFeatureMap.num_input_vars "qiskit.circuit.library.ZFeatureMap.num_input_vars") must be zero.
</Attribute>
### num\_clbits
<Attribute id="qiskit.circuit.library.ZFeatureMap.num_clbits">
Return number of classical bits.
</Attribute>
### num\_declared\_vars
<Attribute id="qiskit.circuit.library.ZFeatureMap.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.
</Attribute>
### num\_input\_vars
<Attribute id="qiskit.circuit.library.ZFeatureMap.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.ZFeatureMap.num_captured_vars "qiskit.circuit.library.ZFeatureMap.num_captured_vars") must be zero.
</Attribute>
### num\_layers
<Attribute id="qiskit.circuit.library.ZFeatureMap.num_layers">
Return the number of layers in the n-local circuit.
**Returns**
The number of layers in the circuit.
</Attribute>
### num\_parameters
<Attribute id="qiskit.circuit.library.ZFeatureMap.num_parameters">
The number of parameter objects in the circuit.
</Attribute>
### num\_parameters\_settable
<Attribute id="qiskit.circuit.library.ZFeatureMap.num_parameters_settable">
The number of distinct parameters.
</Attribute>
### num\_qubits
<Attribute id="qiskit.circuit.library.ZFeatureMap.num_qubits">
Returns the number of qubits in this circuit.
**Returns**
The number of qubits.
</Attribute>
### num\_vars
<Attribute id="qiskit.circuit.library.ZFeatureMap.num_vars">
The number of real-time classical variables in the circuit.
This is the length of the `iter_vars()` iterable.
</Attribute>
### op\_start\_times
<Attribute id="qiskit.circuit.library.ZFeatureMap.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 "(in Python v3.13)") – When circuit is not scheduled.
</Attribute>
### ordered\_parameters
<Attribute id="qiskit.circuit.library.ZFeatureMap.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.
</Attribute>
### parameter\_bounds
<Attribute id="qiskit.circuit.library.ZFeatureMap.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.
</Attribute>
### parameters
<Attribute id="qiskit.circuit.library.ZFeatureMap.parameters">
The parameters defined in the circuit.
This attribute returns the [`Parameter`](qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](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`](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`](qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit.
</Attribute>
### paulis
<Attribute id="qiskit.circuit.library.ZFeatureMap.paulis">
The Pauli strings used in the entanglement of the qubits.
**Returns**
The Pauli strings as list.
</Attribute>
### preferred\_init\_points
<Attribute id="qiskit.circuit.library.ZFeatureMap.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.
</Attribute>
### prefix
<Attribute id="qiskit.circuit.library.ZFeatureMap.prefix" attributeValue="'circuit'" />
### qregs
<Attribute id="qiskit.circuit.library.ZFeatureMap.qregs" attributeTypeHint="list[QuantumRegister]">
A list of the `QuantumRegister`s in this circuit. You should not mutate this.
</Attribute>
### qubits
<Attribute id="qiskit.circuit.library.ZFeatureMap.qubits">
A list of `Qubit`s in the order that they were added. You should not mutate this.
</Attribute>
### reps
<Attribute id="qiskit.circuit.library.ZFeatureMap.reps">
The number of times rotation and entanglement block are repeated.
**Returns**
The number of repetitions.
</Attribute>
### rotation\_blocks
<Attribute id="qiskit.circuit.library.ZFeatureMap.rotation_blocks">
The blocks in the rotation layers.
**Returns**
The blocks in the rotation layers.
</Attribute>
### name
<Attribute id="qiskit.circuit.library.ZFeatureMap.name" attributeTypeHint="str">
A human-readable name for the circuit.
</Attribute>
### cregs
<Attribute id="qiskit.circuit.library.ZFeatureMap.cregs" attributeTypeHint="list[ClassicalRegister]">
A list of the `ClassicalRegister`s in this circuit. You should not mutate this.
</Attribute>
### duration
<Attribute id="qiskit.circuit.library.ZFeatureMap.duration" attributeTypeHint="int | float | None">
The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by [`unit`](#qiskit.circuit.library.ZFeatureMap.unit "qiskit.circuit.library.ZFeatureMap.unit").
</Attribute>
### unit
<Attribute id="qiskit.circuit.library.ZFeatureMap.unit">
The unit that [`duration`](#qiskit.circuit.library.ZFeatureMap.duration "qiskit.circuit.library.ZFeatureMap.duration") is specified in.
</Attribute>
</Class>
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