PauliTwoDesign
class qiskit.circuit.library.PauliTwoDesign(num_qubits=None, reps=3, seed=None, insert_barriers=False, name='PauliTwoDesign')
Bases: TwoLocal
The Pauli Two-Design ansatz.
This class implements a particular form of a 2-design circuit [1], which is frequently studied in quantum machine learning literature, such as e.g. the investigating of Barren plateaus in variational algorithms [2].
The circuit consists of alternating rotation and entanglement layers with an initial layer of gates. The rotation layers contain single qubit Pauli rotations, where the axis is chosen uniformly at random to be X, Y or Z. The entanglement layers is compromised of pairwise CZ gates with a total depth of 2.
For instance, the circuit could look like this (but note that choosing a different seed yields different Pauli rotations).
┌─────────┐┌──────────┐ ░ ┌──────────┐ ░ ┌──────────┐
q_0: ┤ RY(π/4) ├┤ RZ(θ[0]) ├─■─────░─┤ RY(θ[4]) ├─■─────░──┤ RZ(θ[8]) ├
├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ├──────────┤
q_1: ┤ RY(π/4) ├┤ RZ(θ[1]) ├─■──■──░─┤ RY(θ[5]) ├─■──■──░──┤ RX(θ[9]) ├
├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ┌┴──────────┤
q_2: ┤ RY(π/4) ├┤ RX(θ[2]) ├─■──■──░─┤ RY(θ[6]) ├─■──■──░─┤ RX(θ[10]) ├
├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ├───────────┤
q_3: ┤ RY(π/4) ├┤ RZ(θ[3]) ├─■─────░─┤ RX(θ[7]) ├─■─────░─┤ RY(θ[11]) ├
└─────────┘└──────────┘ ░ └──────────┘ ░ └───────────┘Examples
from qiskit.circuit.library import PauliTwoDesign
circuit = PauliTwoDesign(4, reps=2, seed=5, insert_barriers=True)
circuit.draw('mpl')
References
[1]: Nakata et al., Unitary 2-designs from random X- and Z-diagonal unitaries.
[2]: McClean et al., Barren plateaus in quantum neural network training landscapes.
Parameters
- num_qubits (int | None) – The number of qubits of the Pauli Two-Design circuit.
- reps (int) – Specifies how often a block consisting of a rotation layer and entanglement layer is repeated.
- seed (int | None) – The seed for randomly choosing the axes of the Pauli rotations.
- insert_barriers (bool) – If
True, barriers are inserted in between each layer. IfFalse, no barriers are inserted. Defaults toFalse.
Attributes
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}}
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
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.
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: 189
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
Return the number of settable parameters.
Returns
The number of possibly 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.
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.
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.
duration
Type: int | float | None
The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by unit.
unit
The unit that duration is specified in.