EfficientSU2

class qiskit.circuit.library.EfficientSU2(num_qubits=None, su2_gates=None, entanglement='reverse_linear', reps=3, skip_unentangled_qubits=False, skip_final_rotation_layer=False, parameter_prefix='θ', insert_barriers=False, initial_state=None, name='EfficientSU2', flatten=None)

Bases: TwoLocal

The hardware efficient SU(2) 2-local circuit.

The EfficientSU2 circuit consists of layers of single qubit operations spanned by SU(2) and $CX$ entanglements. This is a heuristic pattern that can be used to prepare trial wave functions for variational quantum algorithms or classification circuit for machine learning.

SU(2) stands for special unitary group of degree 2, its elements are $2 \times 2$ unitary matrices with determinant 1, such as the Pauli rotation gates.

On 3 qubits and using the Pauli $Y$ and $Z$ su2_gates as single qubit gates, the hardware efficient SU(2) circuit is represented by:

┌──────────┐┌──────────┐ ░            ░       ░ ┌───────────┐┌───────────┐
┤ RY(θ[0]) ├┤ RZ(θ[3]) ├─░────────■───░─ ... ─░─┤ RY(θ[12]) ├┤ RZ(θ[15]) ├
├──────────┤├──────────┤ ░      ┌─┴─┐ ░       ░ ├───────────┤├───────────┤
┤ RY(θ[1]) ├┤ RZ(θ[4]) ├─░───■──┤ X ├─░─ ... ─░─┤ RY(θ[13]) ├┤ RZ(θ[16]) ├
├──────────┤├──────────┤ ░ ┌─┴─┐└───┘ ░       ░ ├───────────┤├───────────┤
┤ RY(θ[2]) ├┤ RZ(θ[5]) ├─░─┤ X ├──────░─ ... ─░─┤ RY(θ[14]) ├┤ RZ(θ[17]) ├
└──────────┘└──────────┘ ░ └───┘      ░       ░ └───────────┘└───────────┘

See RealAmplitudes for more detail on the possible arguments and options such as skipping unentanglement qubits, which apply here too.

Examples

>>> circuit = EfficientSU2(3, reps=1)
>>> print(circuit)
     ┌──────────┐┌──────────┐          ┌──────────┐┌──────────┐
q_0: ┤ RY(θ[0]) ├┤ RZ(θ[3]) ├──■────■──┤ RY(θ[6]) ├┤ RZ(θ[9]) ├─────────────
     ├──────────┤├──────────┤┌─┴─┐  │  └──────────┘├──────────┤┌───────────┐
q_1: ┤ RY(θ[1]) ├┤ RZ(θ[4]) ├┤ X ├──┼───────■──────┤ RY(θ[7]) ├┤ RZ(θ[10]) ├
     ├──────────┤├──────────┤└───┘┌─┴─┐   ┌─┴─┐    ├──────────┤├───────────┤
q_2: ┤ RY(θ[2]) ├┤ RZ(θ[5]) ├─────┤ X ├───┤ X ├────┤ RY(θ[8]) ├┤ RZ(θ[11]) ├
     └──────────┘└──────────┘     └───┘   └───┘    └──────────┘└───────────┘

>>> ansatz = EfficientSU2(4, su2_gates=['rx', 'y'], entanglement='circular', reps=1)
>>> qc = QuantumCircuit(4)  # create a circuit and append the RY variational form
>>> qc.compose(ansatz, inplace=True)
>>> qc.draw()
     ┌──────────┐┌───┐┌───┐     ┌──────────┐   ┌───┐
q_0: ┤ RX(θ[0]) ├┤ Y ├┤ X ├──■──┤ RX(θ[4]) ├───┤ Y ├─────────────────────
     ├──────────┤├───┤└─┬─┘┌─┴─┐└──────────┘┌──┴───┴───┐   ┌───┐
q_1: ┤ RX(θ[1]) ├┤ Y ├──┼──┤ X ├─────■──────┤ RX(θ[5]) ├───┤ Y ├─────────
     ├──────────┤├───┤  │  └───┘   ┌─┴─┐    └──────────┘┌──┴───┴───┐┌───┐
q_2: ┤ RX(θ[2]) ├┤ Y ├──┼──────────┤ X ├─────────■──────┤ RX(θ[6]) ├┤ Y ├
     ├──────────┤├───┤  │          └───┘       ┌─┴─┐    ├──────────┤├───┤
q_3: ┤ RX(θ[3]) ├┤ Y ├──■──────────────────────┤ X ├────┤ RX(θ[7]) ├┤ Y ├
     └──────────┘└───┘                         └───┘    └──────────┘└───┘

Parameters

• num_qubits (int | None) – The number of qubits of the EfficientSU2 circuit.
• reps (int) – Specifies how often the structure of a rotation layer followed by an entanglement layer is repeated.
• su2_gates (str |type |qiskit.circuit.Instruction |QuantumCircuit |list[str |type |qiskit.circuit.Instruction |QuantumCircuit] | None) – The SU(2) single qubit gates to apply in single qubit gate layers. If only one gate is provided, the 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.
• entanglement (str |list[list[int]] | Callable[[int], list[int]]) – Specifies the entanglement structure. Can be a string (‘full’, ‘linear’ , ‘reverse_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 ‘reverse_linear’ entanglement. Note that ‘reverse_linear’ entanglement provides the same unitary as ‘full’ with fewer entangling gates. See the Examples section of TwoLocal for more detail.
• initial_state (QuantumCircuit | None) – A QuantumCircuit object to prepend to the circuit.
• skip_unentangled_qubits (bool) – 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 (bool) – If False, a rotation layer is added at the end of the ansatz. If True, no rotation layer is added.
• parameter_prefix (str) – The parameterized gates require a parameter to be defined, for which we use ParameterVector.
• insert_barriers (bool) – If True, barriers are inserted in between each layer. If False, no barriers are inserted.
• flatten (bool | None) – Set this to True to output a flat circuit instead of nesting it inside multiple layers of gate objects. By default currently the contents of the output circuit will be wrapped in nested objects for cleaner visualization. However, if you’re using this circuit for anything besides visualization its strongly recommended to set this flag to True to avoid a large performance overhead for parameter binding.

Attributes

ancillas

calibrations

clbits

data

entanglement

entanglement_blocks

flatten

global_phase

initial_state

insert_barriers

instances

layout

metadata

num_ancillas

num_clbits

num_layers

num_parameters

num_parameters_settable

num_qubits

op_start_times

ordered_parameters

>>> # 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])]

parameter_bounds

parameters

preferred_init_points

prefix

qregs

qubits

reps

rotation_blocks