# PauliTwoDesign

class qiskit.circuit.library.PauliTwoDesign(num_qubits=None, reps=3, seed=None, insert_barriers=False, name='PauliTwoDesign')

GitHub(opens in a new tab)

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')

References

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

arXiv:1502.07514(opens in a new tab)

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

arXiv:1803.11173(opens in a new tab)

Parameters

• num_qubits (int(opens in a new tab) | None) – The number of qubits of the Pauli Two-Design circuit.
• reps (int(opens in a new tab)) – Specifies how often a block consisting of a rotation layer and entanglement layer is repeated.
• seed (int(opens in a new tab) | None) – The seed for randomly choosing the axes of the Pauli rotations.
• insert_barriers (bool(opens in a new tab)) – If True, barriers are inserted in between each layer. If False, no barriers are inserted. Defaults to False.

## 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.

### 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.

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_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(opens in a new tab) – 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.

### 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.