PauliTwoDesign
class PauliTwoDesign(num_qubits=None, reps=3, seed=None, insert_barriers=False, name='PauliTwoDesign')
Bases: qiskit.circuit.library.n_local.two_local.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 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.
Construct a new two-local circuit.
Parameters
- num_qubits (
Optional[int]) – The number of qubits of the two-local circuit. - rotation_blocks – The gates used in the rotation layer. Can be specified via the name of a gate (e.g. ‘ry’) or the gate type itself (e.g. RYGate). If only one gate is provided, the gate same gate is applied to each qubit. If a list of gates is provided, all gates are applied to each qubit in the provided order. See the Examples section for more detail.
- entanglement_blocks – The gates used in the entanglement layer. Can be specified in the same format as rotation_blocks.
- entanglement – Specifies the entanglement structure. Can be a string (‘full’, ‘linear’ , ‘circular’ or ‘sca’), a list of integer-pairs specifying the indices of qubits entangled with one another, or a callable returning such a list provided with the index of the entanglement layer. Default to ‘full’ entanglement. See the Examples section for more detail.
- reps (
int) – Specifies how often a block consisting of a rotation layer and entanglement layer is repeated. - skip_unentangled_qubits – If True, the single qubit gates are only applied to qubits that are entangled with another qubit. If False, the single qubit gates are applied to each qubit in the Ansatz. Defaults to False.
- skip_final_rotation_layer – If False, a rotation layer is added at the end of the ansatz. If True, no rotation layer is added.
- parameter_prefix – The parameterized gates require a parameter to be defined, for which we use instances of qiskit.circuit.Parameter. The name of each parameter will be this specified prefix plus its index.
- insert_barriers (
bool) – If True, barriers are inserted in between each layer. If False, no barriers are inserted. Defaults to False. - initial_state – A QuantumCircuit object to prepend to the circuit.
Attributes
ancillas
Returns a list of ancilla bits in the order that the registers were added.
Return type
List[AncillaQubit]
calibrations
Return calibration dictionary.
The custom pulse definition of a given gate is of the form
{‘gate_name’: {(qubits, params): schedule}}
Return type
dict
clbits
Returns a list of classical bits in the order that the registers were added.
Return type
List[Clbit]
data
entanglement
Get the entanglement strategy.
Return type
Union[str, List[str], List[List[str]], List[int], List[List[int]], List[List[List[int]]], List[List[List[List[int]]]], Callable[[int], str], Callable[[int], List[List[int]]]]
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.
Return type
List[Instruction]
Returns
The blocks in the entanglement layers.
extension_lib
Default value: 'include "qelib1.inc";'
global_phase
Return the global phase of the circuit in radians.
Return type
Union[ParameterExpression, float]
header
Default value: 'OPENQASM 2.0;'
initial_state
Return the initial state that is added in front of the n-local circuit.
Return type
Any
Returns
The initial state.
insert_barriers
If barriers are inserted in between the layers or not.
Return type
bool
Returns
True, if barriers are inserted in between the layers, False if not.
instances
Default value: 9
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.
Return type
dict
num_ancillas
Return the number of ancilla qubits.
Return type
int
num_clbits
Return number of classical bits.
Return type
int
num_layers
Return the number of layers in the n-local circuit.
Return type
int
Returns
The number of layers in the circuit.
num_parameters
Return type
int
num_parameters_settable
Return the number of settable parameters.
Return type
int
Returns
The number of possibly distinct parameters.
num_qubits
Returns the number of qubits in this circuit.
Return type
int
Returns
The number of qubits.
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])]Return type
List[Parameter]
Returns
The parameters objects used in the circuit.
parameter_bounds
The parameter bounds for the unbound parameters in the circuit.
Return type
Optional[List[Tuple[float, float]]]
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
Return type
ParameterView
preferred_init_points
The initial points for the parameters. Can be stored as initial guess in optimization.
Return type
Optional[List[float]]
Returns
The initial values for the parameters, or None, if none have been set.
prefix
Default value: 'circuit'
qregs
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.
Return type
List[Qubit]
reps
The number of times rotation and entanglement block are repeated.
Return type
int
Returns
The number of repetitions.
rotation_blocks
The blocks in the rotation layers.
Return type
List[Instruction]
Returns
The blocks in the rotation layers.