PauliFeatureMap

class qiskit.circuit.library.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')

GitHub

Bases: NLocal

The Pauli Expansion circuit.

\vec{x} \in \mathbb{R}^n

U_{\Phi(\vec{x})}=\exp\left(i\sum_{S \in \mathcal{I}} \phi_S(\vec{x})\prod_{i\in S} P_i\right).

S

\phi_S(\vec{x}) = \begin{cases} x_i \text{ if } S = \{i\} \\ \prod_{j \in S} (\pi - x_j) \text{ if } |S| > 1 \end{cases}.

Z

feature_map = PauliFeatureMap(..., paulis=["Z", "YY"], entanglement="full")

which will produce blocks of the form

┌───┐┌─────────────┐┌──────────┐                                            ┌───────────┐
┤ H ├┤ P(2.0*x[0]) ├┤ RX(pi/2) ├──■──────────────────────────────────────■──┤ RX(-pi/2) ├
├───┤├─────────────┤├──────────┤┌─┴─┐┌────────────────────────────────┐┌─┴─┐├───────────┤
┤ H ├┤ P(2.0*x[1]) ├┤ RX(pi/2) ├┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├┤ RX(-pi/2) ├
└───┘└─────────────┘└──────────┘└───┘└────────────────────────────────┘└───┘└───────────┘

The circuit contains reps repetitions of this transformation.

Z

Examples

>>> prep = PauliFeatureMap(2, reps=1, paulis=['ZZ'])
>>> print(prep.decompose())
     ┌───┐
q_0: ┤ H ├──■──────────────────────────────────────■──
     ├───┤┌─┴─┐┌────────────────────────────────┐┌─┴─┐
q_1: ┤ H ├┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├
     └───┘└───┘└────────────────────────────────┘└───┘

>>> prep = PauliFeatureMap(2, reps=1, paulis=['Z', 'XX'])
>>> print(prep.decompose())
     ┌───┐┌─────────────┐┌───┐                                            ┌───┐
q_0: ┤ H ├┤ P(2.0*x[0]) ├┤ H ├──■──────────────────────────────────────■──┤ H ├
     ├───┤├─────────────┤├───┤┌─┴─┐┌────────────────────────────────┐┌─┴─┐├───┤
q_1: ┤ H ├┤ P(2.0*x[1]) ├┤ H ├┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├┤ H ├
     └───┘└─────────────┘└───┘└───┘└────────────────────────────────┘└───┘└───┘

>>> prep = PauliFeatureMap(2, reps=1, paulis=['ZY'])
>>> print(prep.decompose())
     ┌───┐┌──────────┐                                            ┌───────────┐
q_0: ┤ H ├┤ RX(pi/2) ├──■──────────────────────────────────────■──┤ RX(-pi/2) ├
     ├───┤└──────────┘┌─┴─┐┌────────────────────────────────┐┌─┴─┐└───────────┘
q_1: ┤ H ├────────────┤ X ├┤ P(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├─────────────
     └───┘            └───┘└────────────────────────────────┘└───┘

>>> from qiskit.circuit.library import EfficientSU2
>>> prep = PauliFeatureMap(3, reps=3, paulis=['Z', 'YY', 'ZXZ'])
>>> wavefunction = EfficientSU2(3)
>>> classifier = prep.compose(wavefunction)
>>> classifier.num_parameters
27
>>> classifier.count_ops()
OrderedDict([('cx', 39), ('rx', 36), ('u1', 21), ('h', 15), ('ry', 12), ('rz', 12)])

References:

[1] Havlicek et al. Supervised learning with quantum enhanced feature spaces, Nature 567, 209-212 (2019) .

Create a new Pauli expansion circuit.

Deprecated since version 1.3_pending

The class qiskit.circuit.library.data_preparation.pauli_feature_map.PauliFeatureMap 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 pauli_feature_map function as a replacement. Note that this will no longer return a BlueprintCircuit, but just a plain QuantumCircuit.

Parameters

feature_dimension (Optional[int]) – Number of qubits in the circuit.
reps (int) – The number of repeated circuits.
entanglement (Union[str, Dict[int, List[Tuple[int]]], Callable[[int], Union[str, Dict[int, List[Tuple[int]]]]]]) – Specifies the entanglement structure. Can be a string ('full', 'linear', 'reverse_linear', 'circular' or 'sca') or can be a dictionary where the keys represent the number of qubits and the values are list of integer-pairs specifying the indices of qubits that are entangled with one another, for example: {1: [(0,), (2,)], 2: [(0,1), (2,0)]} or can be a Callable[[int], Union[str | Dict[...]]] to return an entanglement specific for a repetition
alpha (float) – The Pauli rotation factor, multiplicative to the pauli rotations
paulis (Optional[List[str]]) – A list of strings for to-be-used paulis. If None are provided, ['Z', 'ZZ'] will be used.
data_map_func (Optional[Callable[[np.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.
name (str) –

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.

calibrations

Return calibration dictionary.

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

Deprecated since version 1.3

The property qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations is deprecated as of Qiskit 1.3. It will be removed in Qiskit 2.0. The entire Qiskit Pulse package is being deprecated and will be moved to the Qiskit Dynamics repository: https://github.com/qiskit-community/qiskit-dynamics . Note that once removed, qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations will have no alternative in Qiskit.

clbits

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 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 .

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 2.0.0.

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.

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: 195

layout

Return any associated layout information about 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.

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.

num_ancillas

Return the number of ancilla qubits.

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 must be zero.

num_clbits

Return number of classical bits.

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_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 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_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.

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 - 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])]

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 objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.

Examples

The snippet below shows that insertion order of parameters does not matter.

>>> 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.

>>> 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 can be used.

>>> 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 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

Type: list[QuantumRegister]

A list of the QuantumRegister s in this circuit. You should not mutate this.

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 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 2.0.0.

name

Type: str

A human-readable name for the circuit.

cregs

Type: list[ClassicalRegister]

A list of the ClassicalRegister s in this circuit. You should not mutate this.

Methods

get_entangler_map

get_entangler_map(rep_num, block_num, num_block_qubits)

GitHub

Get the entangler map for in the repetition rep_num and the block block_num .

The entangler map for the current block is derived from the value of self.entanglement . Below the different cases are listed, where i and j denote the repetition number and the block number, respectively, and n the number of qubits in the block.

entanglement type	entangler map

| None | [[0, ..., n - 1]] | | str (e.g'full') | the specified connectivity on n qubits | | List[int] | [entanglement] | | List[List[int]] | entanglement | | List[List[List[int]]] | entanglement[i] | | List[List[List[List[int]]]] | entanglement[i][j] | | List[str] | the connectivity specified in entanglement[i] | | List[List[str]] | the connectivity specified in entanglement[i][j] | | Callable[int, str] | same as List[str] | | Callable[int, List[List[int]]] | same as List[List[List[int]]] |

Note that all indices are to be taken modulo the length of the array they act on, i.e. no out-of-bounds index error will be raised but we re-iterate from the beginning of the list.

Parameters

rep_num (int) – The current repetition we are in.
block_num (int) – The block number within the entanglement layers.
num_block_qubits (int) – The number of qubits in the block.

Returns

The entangler map for the current block in the current repetition.

Raises

ValueError - If the value of entanglement could not be cast to a corresponding entangler map.

Return type

Sequence [Sequence [int]]

pauli_block

pauli_block(pauli_string)

GitHub

Get the Pauli block for the feature map circuit.

pauli_evolution

pauli_evolution(pauli_string, time)

GitHub

Get the evolution block for the given pauli string.

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