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')
Bases: NLocal
The Pauli Expansion circuit.
The Pauli Expansion circuit is a data encoding circuit that transforms input data , where n is the feature_dimension, as
Here, is a set of qubit indices that describes the connections in the feature map, is a set containing all these index sets, and . Per default the data-mapping is
The possible connections can be set using the entanglement and paulis arguments. For example, for single-qubit rotations and two-qubit interactions between all qubit pairs, we can set:
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.
Please refer to ZFeatureMap for the case of single-qubit Pauli- rotations and to ZZFeatureMap for the single- and two-qubit Pauli- rotations.
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.
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 aCallable[[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 AncillaQubits 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}}
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 Clbits 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 CircuitInstructions 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.
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: 214
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 SwapGates 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 QuantumRegisters in this circuit. You should not mutate this.
qubits
A list of Qubits 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.
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 ClassicalRegisters in this circuit. You should not mutate this.
Methods
get_entangler_map
get_entangler_map(rep_num, block_num, num_block_qubits)
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