431 lines
15 KiB
Plaintext
431 lines
15 KiB
Plaintext
---
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title: PauliFeatureMap (v0.31)
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description: API reference for qiskit.circuit.library.PauliFeatureMap in qiskit v0.31
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.circuit.library.PauliFeatureMap
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---
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# PauliFeatureMap
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<Class id="qiskit.circuit.library.PauliFeatureMap" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.18/qiskit/circuit/library/data_preparation/pauli_feature_map.py" signature="PauliFeatureMap(feature_dimension=None, reps=2, entanglement='full', alpha=2.0, paulis=None, data_map_func=None, parameter_prefix='x', insert_barriers=False, name='PauliFeatureMap')" modifiers="class">
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Bases: `qiskit.circuit.library.n_local.n_local.NLocal`
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The Pauli Expansion circuit.
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The Pauli Expansion circuit is a data encoding circuit that transforms input data $\vec{x} \in \mathbb{R}^n$ as
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$$
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U_{\Phi(\vec{x})}=\exp\left(i\sum_{S\subseteq [n]}
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\phi_S(\vec{x})\prod_{i\in S} P_i\right)
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$$
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The circuit contains `reps` repetitions of this transformation. The variable $P_i \in \{ I, X, Y, Z \}$ denotes the Pauli matrices. The index $S$ describes connectivities between different qubits or datapoints: $S \in \{\binom{n}{k}\ combinations,\ k = 1,... n \}$. Per default the data-mapping $\phi_S$ is
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$$
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\begin{split}\phi_S(\vec{x}) = \begin{cases}
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x_0 \text{ if } k = 1 \\
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\prod_{j \in S} (\pi - x_j) \text{ otherwise }
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\end{cases}\end{split}
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$$
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For example, if the Pauli strings are chosen to be $P_0 = Z$ and $P_{0,1} = YY$ on 2 qubits and with 1 repetition using the default data-mapping, the Pauli evolution feature map is represented by:
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```python
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┌───┐┌──────────────┐┌──────────┐ ┌───────────┐
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┤ H ├┤ U1(2.0*x[0]) ├┤ RX(pi/2) ├──■───────────────────────────────────────■──┤ RX(-pi/2) ├
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├───┤├──────────────┤├──────────┤┌─┴─┐┌─────────────────────────────────┐┌─┴─┐├───────────┤
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┤ H ├┤ U1(2.0*x[1]) ├┤ RX(pi/2) ├┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├┤ RX(-pi/2) ├
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└───┘└──────────────┘└──────────┘└───┘└─────────────────────────────────┘└───┘└───────────┘
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```
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Please refer to [`ZFeatureMap`](qiskit.circuit.library.ZFeatureMap "qiskit.circuit.library.ZFeatureMap") for the case $k = 1$, $P_0 = Z$ and to [`ZZFeatureMap`](qiskit.circuit.library.ZZFeatureMap "qiskit.circuit.library.ZZFeatureMap") for the case $k = 2$, $P_0 = Z$ and $P_{0,1} = ZZ$.
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**Examples**
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```python
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>>> prep = PauliFeatureMap(2, reps=1, paulis=['ZZ'])
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>>> print(prep)
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┌───┐
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q_0: ┤ H ├──■───────────────────────────────────────■──
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├───┤┌─┴─┐┌─────────────────────────────────┐┌─┴─┐
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q_1: ┤ H ├┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├
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└───┘└───┘└─────────────────────────────────┘└───┘
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```
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```python
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>>> prep = PauliFeatureMap(2, reps=1, paulis=['Z', 'XX'])
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>>> print(prep)
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┌───┐┌──────────────┐┌───┐ ┌───┐
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q_0: ┤ H ├┤ U1(2.0*x[0]) ├┤ H ├──■───────────────────────────────────────■──┤ H ├
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├───┤├──────────────┤├───┤┌─┴─┐┌─────────────────────────────────┐┌─┴─┐├───┤
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q_1: ┤ H ├┤ U1(2.0*x[1]) ├┤ H ├┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├┤ H ├
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└───┘└──────────────┘└───┘└───┘└─────────────────────────────────┘└───┘└───┘
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```
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```python
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>>> prep = PauliFeatureMap(2, reps=1, paulis=['ZY'])
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>>> print(prep)
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┌───┐┌──────────┐ ┌───────────┐
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q_0: ┤ H ├┤ RX(pi/2) ├──■───────────────────────────────────────■──┤ RX(-pi/2) ├
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├───┤└──────────┘┌─┴─┐┌─────────────────────────────────┐┌─┴─┐└───────────┘
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q_1: ┤ H ├────────────┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├─────────────
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└───┘ └───┘└─────────────────────────────────┘└───┘
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```
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```python
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>>> from qiskit.circuit.library import EfficientSU2
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>>> prep = PauliFeatureMap(3, reps=3, paulis=['Z', 'YY', 'ZXZ'])
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>>> wavefunction = EfficientSU2(3)
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>>> classifier = prep.compose(wavefunction
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>>> classifier.num_parameters
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27
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>>> classifier.count_ops()
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OrderedDict([('cx', 39), ('rx', 36), ('u1', 21), ('h', 15), ('ry', 12), ('rz', 12)])
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```
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**References**
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**\[1]: Havlicek et al. (2018), Supervised learning with quantum enhanced feature spaces.**
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[arXiv:1804.11326](https://arxiv.org/abs/1804.11326)
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Create a new Pauli expansion circuit.
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**Parameters**
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* **feature\_dimension** (`Optional`\[`int`]) – Number of qubits in the circuit.
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* **reps** (`int`) – The number of repeated circuits.
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* **entanglement** (`Union`\[`str`, `List`\[`List`\[`int`]], `Callable`\[\[`int`], `List`\[`int`]]]) – Specifies the entanglement structure. Refer to [`NLocal`](qiskit.circuit.library.NLocal "qiskit.circuit.library.NLocal") for detail.
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* **alpha** (`float`) – The Pauli rotation factor, multiplicative to the pauli rotations
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* **paulis** (`Optional`\[`List`\[`str`]]) – A list of strings for to-be-used paulis. If None are provided, `['Z', 'ZZ']` will be used.
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* **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()`.
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* **parameter\_prefix** (`str`) – The prefix used if default parameters are generated.
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* **insert\_barriers** (`bool`) – If True, barriers are inserted in between the evolution instructions and hadamard layers.
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## Methods Defined Here
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<span id="qiskit-circuit-library-paulifeaturemap-pauli-block" />
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### pauli\_block
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<Function id="qiskit.circuit.library.PauliFeatureMap.pauli_block" signature="PauliFeatureMap.pauli_block(pauli_string)">
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Get the Pauli block for the feature map circuit.
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</Function>
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<span id="qiskit-circuit-library-paulifeaturemap-pauli-evolution" />
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### pauli\_evolution
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<Function id="qiskit.circuit.library.PauliFeatureMap.pauli_evolution" signature="PauliFeatureMap.pauli_evolution(pauli_string, time)">
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Get the evolution block for the given pauli string.
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</Function>
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## Attributes
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### alpha
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.alpha">
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The Pauli rotation factor (alpha).
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**Return type**
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`float`
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**Returns**
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The Pauli rotation factor.
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</Attribute>
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### ancillas
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.ancillas">
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Returns a list of ancilla bits in the order that the registers were added.
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</Attribute>
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### calibrations
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.calibrations">
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Return calibration dictionary.
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**The custom pulse definition of a given gate is of the form**
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\{‘gate\_name’: \{(qubits, params): schedule}}
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</Attribute>
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### clbits
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.clbits">
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Returns a list of classical bits in the order that the registers were added.
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</Attribute>
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### data
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.data" />
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### entanglement
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.entanglement">
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Get the entanglement strategy.
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**Return type**
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`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`]]]]
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**Returns**
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The entanglement strategy, see `get_entangler_map()` for more detail on how the format is interpreted.
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</Attribute>
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### entanglement\_blocks
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.entanglement_blocks" />
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### extension\_lib
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.extension_lib" attributeValue="'include "qelib1.inc";'" />
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### feature\_dimension
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.feature_dimension">
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Returns the feature dimension (which is equal to the number of qubits).
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**Return type**
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`int`
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**Returns**
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The feature dimension of this feature map.
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</Attribute>
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### global\_phase
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.global_phase">
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Return the global phase of the circuit in radians.
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</Attribute>
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### header
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.header" attributeValue="'OPENQASM 2.0;'" />
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### initial\_state
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.initial_state">
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Return the initial state that is added in front of the n-local circuit.
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**Return type**
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`Any`
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**Returns**
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The initial state.
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</Attribute>
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### insert\_barriers
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.insert_barriers">
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If barriers are inserted in between the layers or not.
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**Return type**
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`bool`
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**Returns**
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True, if barriers are inserted in between the layers, False if not.
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</Attribute>
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### instances
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.instances" attributeValue="16" />
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### metadata
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.metadata">
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The user provided metadata associated with the circuit
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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.
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</Attribute>
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### num\_ancillas
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.num_ancillas">
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Return the number of ancilla qubits.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.num_clbits">
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Return number of classical bits.
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</Attribute>
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### num\_layers
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.num_layers">
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Return the number of layers in the n-local circuit.
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**Return type**
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`int`
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**Returns**
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The number of layers in the circuit.
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</Attribute>
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### num\_parameters
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.num_parameters">
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**Return type**
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`int`
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</Attribute>
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### num\_parameters\_settable
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.num_parameters_settable">
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The number of distinct parameters.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.num_qubits">
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Returns the number of qubits in this circuit.
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**Return type**
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`int`
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**Returns**
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The number of qubits.
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</Attribute>
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### ordered\_parameters
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.ordered_parameters">
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The parameters used in the underlying circuit.
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This includes float values and duplicates.
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**Examples**
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```python
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>>> # prepare circuit ...
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>>> print(nlocal)
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┌───────┐┌──────────┐┌──────────┐┌──────────┐
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q_0: ┤ Ry(1) ├┤ Ry(θ[1]) ├┤ Ry(θ[1]) ├┤ Ry(θ[3]) ├
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└───────┘└──────────┘└──────────┘└──────────┘
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>>> nlocal.parameters
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{Parameter(θ[1]), Parameter(θ[3])}
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>>> nlocal.ordered_parameters
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[1, Parameter(θ[1]), Parameter(θ[1]), Parameter(θ[3])]
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```
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**Return type**
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`List`\[`Parameter`]
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**Returns**
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The parameters objects used in the circuit.
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</Attribute>
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### parameter\_bounds
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.parameter_bounds">
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The parameter bounds for the unbound parameters in the circuit.
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**Return type**
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`Optional`\[`List`\[`Tuple`\[`float`, `float`]]]
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**Returns**
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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.
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</Attribute>
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### parameters
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.parameters">
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**Return type**
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`ParameterView`
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</Attribute>
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### paulis
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.paulis">
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The Pauli strings used in the entanglement of the qubits.
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**Return type**
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`List`\[`str`]
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**Returns**
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The Pauli strings as list.
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</Attribute>
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### preferred\_init\_points
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.preferred_init_points">
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The initial points for the parameters. Can be stored as initial guess in optimization.
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**Return type**
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`Optional`\[`List`\[`float`]]
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**Returns**
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The initial values for the parameters, or None, if none have been set.
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</Attribute>
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### prefix
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.prefix" attributeValue="'circuit'" />
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### qregs
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.qregs">
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A list of the quantum registers associated with the circuit.
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</Attribute>
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### qubits
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.qubits">
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Returns a list of quantum bits in the order that the registers were added.
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</Attribute>
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### reps
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.reps">
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The number of times rotation and entanglement block are repeated.
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**Return type**
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`int`
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**Returns**
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The number of repetitions.
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</Attribute>
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### rotation\_blocks
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<Attribute id="qiskit.circuit.library.PauliFeatureMap.rotation_blocks">
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The blocks in the rotation layers.
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**Return type**
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`List`\[`Instruction`]
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**Returns**
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The blocks in the rotation layers.
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</Attribute>
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</Class>
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