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# ZFeatureMap¶

class ZFeatureMap(feature_dimension, reps=2, data_map_func=None, parameter_prefix='x', insert_barriers=False, name='ZFeatureMap')[source]

The first order Pauli Z-evolution circuit.

On 3 qubits and with 2 repetitions the circuit is represented by:

```┌───┐┌──────────────┐┌───┐┌──────────────┐
┤ H ├┤ U1(2.0*x[0]) ├┤ H ├┤ U1(2.0*x[0]) ├
├───┤├──────────────┤├───┤├──────────────┤
┤ H ├┤ U1(2.0*x[1]) ├┤ H ├┤ U1(2.0*x[1]) ├
├───┤├──────────────┤├───┤├──────────────┤
┤ H ├┤ U1(2.0*x[2]) ├┤ H ├┤ U1(2.0*x[2]) ├
└───┘└──────────────┘└───┘└──────────────┘
```

This is a sub-class of `PauliFeatureMap` where the Pauli strings are fixed as [‘Z’]. As a result the first order expansion will be a circuit without entangling gates.

Examples

```>>> prep = ZFeatureMap(3, reps=3, insert_barriers=True)
>>> print(prep)
┌───┐ ░ ┌──────────────┐ ░ ┌───┐ ░ ┌──────────────┐ ░ ┌───┐ ░ ┌──────────────┐
q_0: ┤ H ├─░─┤ U1(2.0*x[0]) ├─░─┤ H ├─░─┤ U1(2.0*x[0]) ├─░─┤ H ├─░─┤ U1(2.0*x[0]) ├
├───┤ ░ ├──────────────┤ ░ ├───┤ ░ ├──────────────┤ ░ ├───┤ ░ ├──────────────┤
q_1: ┤ H ├─░─┤ U1(2.0*x[1]) ├─░─┤ H ├─░─┤ U1(2.0*x[1]) ├─░─┤ H ├─░─┤ U1(2.0*x[1]) ├
├───┤ ░ ├──────────────┤ ░ ├───┤ ░ ├──────────────┤ ░ ├───┤ ░ ├──────────────┤
q_2: ┤ H ├─░─┤ U1(2.0*x[2]) ├─░─┤ H ├─░─┤ U1(2.0*x[2]) ├─░─┤ H ├─░─┤ U1(2.0*x[2]) ├
└───┘ ░ └──────────────┘ ░ └───┘ ░ └──────────────┘ ░ └───┘ ░ └──────────────┘
```
```>>> 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)
┌───┐┌───────────────────────┐
q_0: ┤ H ├┤ U1(2.0*x[0]**2 + 2.0) ├
├───┤├───────────────────────┤
q_1: ┤ H ├┤ U1(2.0*x[1]**2 + 2.0) ├
├───┤├───────────────────────┤
q_2: ┤ H ├┤ U1(2.0*x[2]**2 + 2.0) ├
└───┘└───────────────────────┘
```
```>>> classifier = ZFeatureMap(3, reps=1) + RY(3, reps=1)
>>> print(classifier)
┌───┐┌──────────────┐┌──────────┐      ┌──────────┐
q_0: ┤ H ├┤ U1(2.0*x[0]) ├┤ RY(θ[0]) ├─■──■─┤ RY(θ[3]) ├────────────
├───┤├──────────────┤├──────────┤ │  │ └──────────┘┌──────────┐
q_1: ┤ H ├┤ U1(2.0*x[1]) ├┤ RY(θ[1]) ├─■──┼──────■──────┤ RY(θ[4]) ├
├───┤├──────────────┤├──────────┤    │      │      ├──────────┤
q_2: ┤ H ├┤ U1(2.0*x[2]) ├┤ RY(θ[2]) ├────■──────■──────┤ RY(θ[5]) ├
└───┘└──────────────┘└──────────┘                  └──────────┘
```

Create a new first-order Pauli-Z expansion circuit.

Parameters
• feature_dimension (`int`) – The number of features

• reps (`int`) – The number of repeated circuits. Defaults to 2, has a minimum value of 1.

• data_map_func (`Optional`[`Callable`[[`ndarray`], `float`]]) – A mapping function for data x which can be supplied to override the default mapping from `self_product()`.

• parameter_prefix (`str`) – The prefix used if default parameters are generated.

• insert_barriers (`bool`) – If True, barriers are inserted in between the evolution instructions and hadamard layers.

Attributes

alpha

The Pauli rotation factor (alpha).

Return type

`float`

Returns

The Pauli rotation factor.

ancillas

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

Return type

`List`[`AncillaQubit`]

calibrations

Return calibration dictionary.

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

Return type

`dict`

clbits

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

Return type

`List`[`Clbit`]

data
entanglement

Get the entanglement strategy.

Return type

`Union`[`str`, `List`[`str`], `List`[`List`[`str`]], `List`[`int`], `List`[`List`[`int`]], `List`[`List`[`List`[`int`]]], `List`[`List`[`List`[`List`[`int`]]]], `Callable`[[`int`], `str`], `Callable`[[`int`], `List`[`List`[`int`]]]]

Returns

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

entanglement_blocks
extension_lib = 'include "qelib1.inc";'
feature_dimension

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

Return type

`int`

Returns

The feature dimension of this feature map.

global_phase

Return the global phase of the circuit in radians.

Return type

`Union`[`ParameterExpression`, `float`]

initial_state

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

Return type

`QuantumCircuit`

Returns

The initial state.

insert_barriers

If barriers are inserted in between the layers or not.

Return type

`bool`

Returns

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

instances = 2741

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.

Return type

`dict`

num_ancillas

Return the number of ancilla qubits.

Return type

`int`

num_clbits

Return number of classical bits.

Return type

`int`

num_layers

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

Return type

`int`

Returns

The number of layers in the circuit.

num_parameters
Return type

`int`

num_parameters_settable

The number of distinct parameters.

num_qubits

Returns the number of qubits in this circuit.

Return type

`int`

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.

Return type

`List`[`int`]

Returns

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

Raises

AttributeError – When circuit is not scheduled.

ordered_parameters

The parameters used in the underlying circuit.

This includes float values and duplicates.

Examples

```>>> # 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])]
```
Return type

`List`[`Parameter`]

Returns

The parameters objects used in the circuit.

parameter_bounds

The parameter bounds for the unbound parameters in the circuit.

Return type

`Optional`[`List`[`Tuple`[`float`, `float`]]]

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
Return type

`ParameterView`

paulis

The Pauli strings used in the entanglement of the qubits.

Return type

`List`[`str`]

Returns

The Pauli strings as list.

preferred_init_points

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

Return type

`Optional`[`List`[`float`]]

Returns

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

prefix = 'circuit'
qregs

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.

Return type

`List`[`Qubit`]

reps

The number of times rotation and entanglement block are repeated.

Return type

`int`

Returns

The number of repetitions.

rotation_blocks

The blocks in the rotation layers.

Return type

`List`[`Instruction`]

Returns

The blocks in the rotation layers.