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# ZZFeatureMap¶

class ZZFeatureMap(feature_dimension, reps=2, entanglement='full', data_map_func=None, parameter_prefix='x', insert_barriers=False, name='ZZFeatureMap')[Quellcode]

Second-order Pauli-Z evolution circuit.

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

```┌───┐┌─────────────────┐
┤ 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 `φ` is a classical non-linear function, which defaults to `φ(x) = x` if and `φ(x,y) = (pi - x)(pi - y)`.

Examples

```>>> 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 ├
└───┘└──────────────┘└───┘└─────────────────────────────────┘└───┘
```
```>>> 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.

Parameter
• feature_dimension (int) – Number of features.

• reps (int) – The number of repeated circuits, has a min. value of 1.

• entanglement (Union[str, List[List[int]], Callable[[int], List[int]]]) – Specifies the entanglement structure. Refer to `NLocal` for detail.

• data_map_func (Optional[Callable[[ndarray], float]]) – A mapping function for data x.

• 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.

Verursacht

ValueError – If the feature dimension is smaller than 2.

Attributes

alpha

The Pauli rotation factor (alpha).

Rückgabe

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.

Rückgabe

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).

Rückgabe

The feature dimension of this feature map.

global_phase

Return the global phase of the circuit in radians.

initial_state

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

Rückgabe

The initial state.

insert_barriers

If barriers are inserted in between the layers or not.

Rückgabe

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

instances = 125
layout

Return any associated layout information anout the circuit

This attribute contains an optional `TranspileLayout` object. This is typically set on the output from `transpile()` or `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()` function, an initial layout which permutes the qubits based on the selected physical qubits on the `Target`, and a final layout which is an output permutation caused by `SwapGate`s inserted during routing.

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.

Rückgabe

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.

Rückgabe

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.

Rückgabe

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

Verursacht

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])]
```
Rückgabe

The parameters objects used in the circuit.

parameter_bounds

The parameter bounds for the unbound parameters in the circuit.

Rückgabe

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.

Rückgabe

The Pauli strings as list.

preferred_init_points

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

Rückgabe

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

prefix = 'circuit'
qregs: 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.

Rückgabe

The number of repetitions.

rotation_blocks

The blocks in the rotation layers.

Rückgabe

The blocks in the rotation layers.