σ Σz i‘<γσ•SrSSKJr SSKrSSKJrJr SSKJr SSK J r J r SSK J r JrJr SSKJr S S KJrJr S S KJr \R,(aSSKrSSS jjr"SS \5rg)z!The EfficientSU2 2-local circuit.ι)Ϊ annotationsN)ΪCallableΪIterable)Ϊpi)ΪQuantumCircuitΪGate)ΪRYGateΪRZGateΪCXGate)Ϊdeprecate_funcι)Ϊn_localΪBlockEntanglement)ΪTwoLocalΪ EfficientSU2c σP•UcSS/nUS:”aS/O/n [UUU UUUUSUUU5 $)uSThe hardware-efficient :math:`SU(2)` 2-local circuit. The ``efficient_su2`` circuit consists of layers of single qubit operations spanned by :math:`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. :math:`SU(2)` is the special unitary group of degree 2, its elements are :math:`2 \times 2` unitary matrices with determinant 1, such as the Pauli rotation gates. On 3 qubits and using the Pauli :math:`Y` and :math:`Z` rotations as single qubit gates, the this circuit is represented by: .. parsed-literal:: β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” β–‘ β–‘ β–‘ β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” ─ RY(ΞΈ[0]) β”œβ”€ RZ(ΞΈ[3]) β”œβ”€β–‘β”€β”€β”€β”€β”€β”€β”€β”€β– β”€β”€β”€β–‘β”€ ... ─░── RY(ΞΈ[12]) β”œβ”€ RZ(ΞΈ[15]) β”œ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ β–‘ β”Œβ”€β”΄β”€β” β–‘ β–‘ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ ─ RY(ΞΈ[1]) β”œβ”€ RZ(ΞΈ[4]) β”œβ”€β–‘β”€β”€β”€β– β”€β”€β”€ X β”œβ”€β–‘β”€ ... ─░── RY(ΞΈ[13]) β”œβ”€ RZ(ΞΈ[16]) β”œ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ β–‘ β”Œβ”€β”΄β”€β”β””β”€β”€β”€β”˜ β–‘ β–‘ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ ─ RY(ΞΈ[2]) β”œβ”€ RZ(ΞΈ[5]) β”œβ”€β–‘β”€β”€ X β”œβ”€β”€β”€β”€β”€β”€β–‘β”€ ... ─░── RY(ΞΈ[14]) β”œβ”€ RZ(ΞΈ[17]) β”œ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ β–‘ β””β”€β”€β”€β”˜ β–‘ β–‘ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ Examples: Per default, the ``"reverse_linear"`` entanglement is used, which, in the case of CX gates, is equivalent to an all-to-all entanglement: .. plot:: :alt: Circuit diagram output by the previous code. :include-source: :context: 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: .. plot:: :alt: Circuit diagram output by the previous code. :include-source: :context: close-figs circuit = efficient_su2(4, su2_gates=["rx", "y"], entanglement="circular", reps=1) circuit.draw("mpl") Args: num_qubits: The number of qubits. su2_gates: The :math:`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: Specifies how often the structure of a rotation layer followed by an entanglement layer is repeated. entanglement: The indices specifying on which qubits the input blocks act. See :func:`.n_local` for detailed information. skip_final_rotation_layer: Whether a final rotation layer is added to the circuit. skip_unentangled_qubits: If ``True``, the rotation gates act only on qubits that are entangled. If ``False``, the rotation gates act on all qubits. parameter_prefix: The name of the free parameters. insert_barriers: If True, barriers are inserted in between each layer. If False, no barriers are inserted. name: The name of the circuit. Returns: An efficient-SU(2) circuit. ΪryΪrzr ΪcxT)r) Ϊ num_qubitsΪ su2_gatesΪ entanglementΪrepsΪskip_unentangled_qubitsΪskip_final_rotation_layerΪparameter_prefixΪinsert_barriersΪnameΪentanglement_blockss Ϊf/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/n_local/efficient_su2.pyΪ efficient_su2r!sT€πjΡΨ˜4Lˆ π%/°£N˜4™&ΈΠδ ΨΨΨΨΨ ΨΨΨ Ψ!ΨΨ σ π σcσ’^•\rSrSrSr\"SSSS9S S U4Sjjj5r\S Sj5rS r U=r $) rι‰uThe hardware efficient SU(2) 2-local circuit. The ``EfficientSU2`` circuit consists of layers of single qubit operations spanned by SU(2) and :math:`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 :math:`2 \times 2` unitary matrices with determinant 1, such as the Pauli rotation gates. On 3 qubits and using the Pauli :math:`Y` and :math:`Z` su2_gates as single qubit gates, the hardware efficient SU(2) circuit is represented by: .. code-block:: text β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” β–‘ β–‘ β–‘ β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” ─ RY(ΞΈ[0]) β”œβ”€ RZ(ΞΈ[3]) β”œβ”€β–‘β”€β”€β”€β”€β”€β”€β”€β”€β– β”€β”€β”€β–‘β”€ ... ─░── RY(ΞΈ[12]) β”œβ”€ RZ(ΞΈ[15]) β”œ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ β–‘ β”Œβ”€β”΄β”€β” β–‘ β–‘ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ ─ RY(ΞΈ[1]) β”œβ”€ RZ(ΞΈ[4]) β”œβ”€β–‘β”€β”€β”€β– β”€β”€β”€ X β”œβ”€β–‘β”€ ... ─░── RY(ΞΈ[13]) β”œβ”€ RZ(ΞΈ[16]) β”œ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ β–‘ β”Œβ”€β”΄β”€β”β””β”€β”€β”€β”˜ β–‘ β–‘ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ ─ RY(ΞΈ[2]) β”œβ”€ RZ(ΞΈ[5]) β”œβ”€β–‘β”€β”€ X β”œβ”€β”€β”€β”€β”€β”€β–‘β”€ ... ─░── RY(ΞΈ[14]) β”œβ”€ RZ(ΞΈ[17]) β”œ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ β–‘ β””β”€β”€β”€β”˜ β–‘ β–‘ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ See :class:`~qiskit.circuit.library.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.decompose()) β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” q_0: ─ RY(ΞΈ[0]) β”œβ”€ RZ(ΞΈ[3]) β”œβ”€β”€β– β”€β”€β”€β”€β– β”€β”€β”€ RY(ΞΈ[6]) β”œβ”€ RZ(ΞΈ[9]) β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”Œβ”€β”΄β”€β” β”‚ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” q_1: ─ RY(ΞΈ[1]) β”œβ”€ RZ(ΞΈ[4]) β”œβ”€ X β”œβ”€β”€β”Όβ”€β”€β”€β”€β”€β”€β”€β– β”€β”€β”€β”€β”€β”€β”€ RY(ΞΈ[7]) β”œβ”€ RZ(ΞΈ[10]) β”œ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β””β”€β”€β”€β”˜β”Œβ”€β”΄β”€β” β”Œβ”€β”΄β”€β” β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ q_2: ─ RY(ΞΈ[2]) β”œβ”€ RZ(ΞΈ[5]) β”œβ”€β”€β”€β”€β”€β”€ X β”œβ”€β”€β”€β”€ X β”œβ”€β”€β”€β”€β”€ RY(ΞΈ[8]) β”œβ”€ RZ(ΞΈ[11]) β”œ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ β””β”€β”€β”€β”˜ β””β”€β”€β”€β”˜ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ >>> ansatz = EfficientSU2(4, su2_gates=['rx', 'y'], entanglement='circular', reps=1, ... flatten=True) >>> qc = QuantumCircuit(4) # create a circuit and append the RY variational form >>> qc.compose(ansatz, inplace=True) >>> qc.draw() β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”β”Œβ”€β”€β”€β” β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” β”Œβ”€β”€β”€β” q_0: ─ RX(ΞΈ[0]) β”œβ”€ Y β”œβ”€ X β”œβ”€β”€β– β”€β”€β”€ RX(ΞΈ[4]) β”œβ”€β”€β”€β”€ Y β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€β””β”€β”¬β”€β”˜β”Œβ”€β”΄β”€β”β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β”Œβ”€β”€β”΄β”€β”€β”€β”΄β”€β”€β”€β” β”Œβ”€β”€β”€β” q_1: ─ RX(ΞΈ[1]) β”œβ”€ Y β”œβ”€β”€β”Όβ”€β”€β”€ X β”œβ”€β”€β”€β”€β”€β– β”€β”€β”€β”€β”€β”€β”€ RX(ΞΈ[5]) β”œβ”€β”€β”€β”€ Y β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€ β”‚ β””β”€β”€β”€β”˜ β”Œβ”€β”΄β”€β” β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β”Œβ”€β”€β”΄β”€β”€β”€β”΄β”€β”€β”€β”β”Œβ”€β”€β”€β” q_2: ─ RX(ΞΈ[2]) β”œβ”€ Y β”œβ”€β”€β”Όβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ X β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β– β”€β”€β”€β”€β”€β”€β”€ RX(ΞΈ[6]) β”œβ”€ Y β”œ β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€ β”‚ β””β”€β”€β”€β”˜ β”Œβ”€β”΄β”€β” β”œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”œβ”€β”€β”€β”€ q_3: ─ RX(ΞΈ[3]) β”œβ”€ Y β”œβ”€β”€β– β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€ X β”œβ”€β”€β”€β”€β”€ RX(ΞΈ[7]) β”œβ”€ Y β”œ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”˜ β””β”€β”€β”€β”˜ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”˜ .. seealso:: The :func:`.efficient_su2` function constructs a functionally equivalent circuit, but faster. z2.1z>Use the function qiskit.circuit.library.efficient_su2 instead.z in Qiskit 3.0)ΪsinceΪadditional_msgΪremoval_timelinec σ\>•Uc [[/n[T U] UU[UUUUUUU U U S9 g)aΩ Args: num_qubits: The number of qubits of the EfficientSU2 circuit. reps: Specifies how often the structure of a rotation layer followed by an entanglement layer is repeated. su2_gates: 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: Specifies the entanglement structure. Can be a string ('full', 'linear', 'reverse_linear', 'pairwise', '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. Defaults to 'reverse_linear' entanglement. Note that 'reverse_linear' entanglement provides the same unitary as 'full' with fewer entangling gates. See the Examples section of :class:`~qiskit.circuit.library.TwoLocal` for more detail. initial_state: A `QuantumCircuit` object to prepend to the circuit. 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 :class:`~qiskit.circuit.ParameterVector`. insert_barriers: If True, barriers are inserted in between each layer. If False, no barriers are inserted. flatten: 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. N) rΪrotation_blocksrrrrrrrΪ initial_staterΪflatten)r r ΪsuperΪ__init__r ) Ϊselfrrrrrrrrr*rr+Ϊ __class__s €r r-ΪEfficientSU2.__init__ΔsLψ€π| Ρ ά€Π(ˆIά ‰ΡΨ!Ψ%ά &Ψ%ΨΨ$;Ψ&?Ψ-Ψ+Ψ'ΨΨπ ς r"cσ8•UR[*[4/-$)zAReturn the parameter bounds. Returns: The parameter bounds. )Ϊnum_parametersr)r.s r Ϊparameter_boundsΪEfficientSU2.parameter_boundss€πΧ"Ρ"¬ s¬B i [Ρ0Π0r"©) NNΪreverse_linearιFFυΞΈFNrN)rz int | Nonerz€str | type | qiskit.circuit.Instruction | QuantumCircuit | list[str | type | qiskit.circuit.Instruction | QuantumCircuit] | Nonerz2str | list[list[int]] | Callable[[int], list[int]]rΪintrΪboolrr:rΪstrrr:r*zQuantumCircuit | Nonerr;r+z bool | NoneΪreturnΪNone)r<zlist[tuple[float, float]]) Ϊ__name__Ϊ __module__Ϊ __qualname__Ϊ__firstlineno__Ϊ__doc__r r-Ϊpropertyr3Ϊ__static_attributes__Ϊ __classcell__)r/s@r rr‰sκψ†ρ8ρtΨΨWΨ(ρπ"&π ΨK[ΨΨ(-Ψ*/Ψ $Ψ %Ψ/3Ψ"Ψ#π'H ΰπH π π H πIπH ππH π"&πH π$(πH ππH π π!H π"-π#H π$π%H π&π'H π( χ)H σ π H πTσ1σφ1r")Nr6r7FFr8Fr)rr9rz(str | Gate | Iterable[str | Gate] | NonerzrBlockEntanglement | Iterable[BlockEntanglement] | Callable[[int], BlockEntanglement | Iterable[BlockEntanglement]]rr9rr:rr:rr;rr:rr;r<r)rBΪ __future__rΪtypingΪcollections.abcrrΪnumpyrΪqiskit.circuitrrΪ%qiskit.circuit.library.standard_gatesr r r Ϊqiskit.utils.deprecationr rrΪ two_localrΪ TYPE_CHECKINGΪqiskitr!rr5r"r ΪrPsΠπρ(ε"Ϋ ί.εη/ίHΡHέ3ί/έΰ ΧΧΫπ ;?π ΨΨ$)Ψ&+Ψ Ψ!ΨπgΨπgΰ7πgπ Kπ gπ πgπ"πgπ $πgππgππgπ πgπυgτTQ18υQ1r"