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 \(\sqrt{H} = RY(\pi/4)\) 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')

(Source code)

References

[1]: Nakata et al., Unitary 2-designs from random X- and Z-diagonal unitaries.

arXiv:1502.07514

[2]: McClean et al., Barren plateaus in quantum neural network training landscapes.

arXiv:1803.11173

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. If False, no barriers are inserted. Defaults to False.

Attributes

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.

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.

extension_lib = 'include "qelib1.inc";'

flatten

Returns whether the circuit is wrapped in nested gates/instructions or flattened.

global_phase

Return the global phase of the current circuit scope in radians.

header = 'OPENQASM 2.0;'

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 = 192

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

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.

Returns:

The number of layers in the circuit.

num_parameters

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.

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

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 = '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.

Returns:

The number of repetitions.

rotation_blocks

The blocks in the rotation layers.

Returns:

The blocks in the rotation layers.