efficient_su2

class qiskit.circuit.library.efficient_su2(num_qubits, su2_gates=None, entanglement='reverse_linear', reps=3, skip_unentangled_qubits=False, skip_final_rotation_layer=False, parameter_prefix='θ', insert_barriers=False, name='EfficientSU2')

Bases:

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

The efficient_su2 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.

$SU(2)$ is the 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 $Z$ rotations as single qubit gates, the this 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]) ├
└──────────┘└──────────┘ ░ └───┘      ░       ░ └───────────┘└───────────┘

Examples

Per default, the "reverse_linear" entanglement is used, which, in the case of CX gates, is equivalent to an all-to-all entanglement:

from qiskit.circuit.library import efficient_su2
 
circuit = efficient_su2(3, reps=1)
circuit.draw("mpl")

To specify which SU(2) gates should be used in the rotation layer, we can set the su2_gates argument. In addition, we can change the entanglement structure. For example:

circuit = efficient_su2(4, su2_gates=["rx", "y"], entanglement="circular", reps=1)
circuit.draw("mpl")

Parameters

• num_qubits (int) – The number of qubits.
• su2_gates (str |Gate | Iterable[str |Gate] | 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.
• reps (int) – Specifies how often the structure of a rotation layer followed by an entanglement layer is repeated.
• entanglement (BlockEntanglement | Iterable[BlockEntanglement] | Callable[[int], BlockEntanglement | Iterable[BlockEntanglement]]) – The indices specifying on which qubits the input blocks act. See n_local() for detailed information.
• skip_final_rotation_layer (bool) – Whether a final rotation layer is added to the circuit.
• skip_unentangled_qubits (bool) – If True, the rotation gates act only on qubits that are entangled. If False, the rotation gates act on all qubits.
• parameter_prefix (str) – The name of the free parameters.
• insert_barriers (bool) – If True, barriers are inserted in between each layer. If False, no barriers are inserted.
• name (str) – The name of the circuit.

Returns

An efficient-SU(2) circuit.