z iH4hSrSSKJr SSKJrJr SSKrSSKJrJ r J r SSK J r J r SSKJr \R "SS/SS //5r\R "SS/SS //5r\ "\5"S S \55r\ "\5"S S\55r\ "\SS9"SS\ 55r\ "\SS9"SS\ 55rg)zThe S, Sdg, CS and CSdg gates.) annotations)OptionalUnionN) SingletonGateSingletonControlledGatestdlib_singleton_key)with_gate_arraywith_controlled_gate_array) StandardGatey?yc^\rSrSrSr\R rS S U4Sjjjr\ "5r Sr S S U4Sjjjr SSSjjr SSSjjrSrS rU=r$)SGateuBSingle qubit S gate (Z**0.5). It induces a :math:`\pi/2` phase, and is sometimes called the P gate (phase). This is a Clifford gate and a square-root of Pauli-Z. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.s` method. Matrix representation: .. math:: S = \begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix} Circuit symbol: .. code-block:: text ┌───┐ q_0: ┤ S ├ └───┘ Equivalent to a :math:`\pi/2` radian rotation about the Z axis. c&>[TU]SS/US9 g)z2 Args: label: An optional label for the gate. sr labelNsuper__init__selfr __class__s a/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/s.pyrSGate.__init__?s a51cSSKJn UR[RR UR 5SURS9UlgzDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr_from_circuit_datar S_get_definitionparamsr! definitionrrs r_define SGate._defineHsA 2 );; NN * *4;; 7tRVR[R[< rcn>U(dUS:Xa[X#URS9nU$[TU] UUUUS9nU$)aReturn a (multi-)controlled-S gate. One control qubit returns a :class:`.CSGate`. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g.``'110'``), or ``None``. If ``None``, use all 1s. annotated: indicates whether the controlled gate should be implemented as an annotated gate. If ``None``, this is handled as ``False``. Returns: ControlledGate: controlled version of this gate. r r ctrl_state _base_labelnum_ctrl_qubitsrr- annotated)CSGaterrcontrolrr0rr-r1gaters rr3 SGate.controlUsN,_1$**UD 7? /%# #D  rc[5$)aReturn inverse of S (SdgGate). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.SdgGate`. Returns: SdgGate: inverse of :class:`.SGate` )SdgGaterr1s rinverse SGate.inversevs yrcFSSKJn U"S[R-U-5$)Nr  PhaseGate?pr>numpypirexponentr1r>s rpower SGate.powers uxx(233rc"[U[5$N) isinstancerrothers r__eq__ SGate.__eq__s%''rr'rIr Optional[str]r NNNr0intrz str | Noner-zint | str | Noner1z bool | NoneFr1boolrEfloatr1rW)__name__ __module__ __qualname____firstlineno____doc__r r$_standard_gaterr_singleton_lookup_keyr)r3r:rFrM__static_attributes__ __classcell__rs@rrrs:"^^N2212   ! '+!% %   B 4 ((rrc^\rSrSrSr\R rS S U4Sjjjr\ "5r Sr S S U4Sjjjr SSSjjr SSSjjrSrS rU=r$)r8u4Single qubit S-adjoint gate (~Z**0.5). It induces a :math:`-\pi/2` phase. This is a Clifford gate and a square-root of Pauli-Z. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.sdg` method. Matrix representation: .. math:: Sdg = \begin{pmatrix} 1 & 0 \\ 0 & -i \end{pmatrix} Circuit symbol: .. code-block:: text ┌─────┐ q_0: ┤ Sdg ├ └─────┘ Equivalent to a :math:`-\pi/2` radian rotation about the Z axis. c&>[TU]SS/US9 g)zCreate new Sdg gate.sdgr rNrrs rrSdgGate.__init__s 2U3rcSSKJn UR[RR UR 5SURS9Ulgr) r"rr#r Sdgr%r&r!r'r(s rr)SdgGate._definesC 2 );;    , ,T[[ 9TXT]T]< rcn>U(dUS:Xa[X#URS9nU$[TU] UUUUS9nU$)aReturn a (multi-)controlled-Sdg gate. One control qubit returns a :class:`.CSdgGate`. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g.``'110'``), or ``None``. If ``None``, use all 1s. annotated: indicates whether the controlled gate should be implemented as an annotated gate. If ``None``, this is handled as ``False``. Returns: ControlledGate: controlled version of this gate. r r,r/)CSdgGaterrr3r4s rr3SdgGate.controlsN,_1%DJJWD 7? /%# #D  rc[5$)aReturn inverse of Sdg (SGate). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.SGate`. Returns: SGate: inverse of :class:`.SdgGate` )rr9s rr:SdgGate.inverses wrcFSSKJn U"S[R-U-5$)Nr r=r@rDs rrF SdgGate.powers 8344rc"[U[5$rI)rJr8rKs rrMSdgGate.__eq__s%))rrOrIrPrRrSrUrVrX)rZr[r\r]r^r rjr_rrr`r)r3r:rFrMrarbrcs@rr8r8s:"%%N4412   ! '+!% %   B 5 **rr8r0c^\rSrSrSr\R rS SS.SU4Sjjjjr\ "SS9r Sr SSS jjr SSS jjr S rS rU=r$)r2u/Controlled-S gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.cs` method. Circuit symbol: .. code-block:: text q_0: ──■── ┌─┴─┐ q_1: ┤ S ├ └───┘ Matrix representation: .. math:: CS \ q_0, q_1 = I \otimes |0 \rangle\langle 0| + S \otimes |1 \rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & i \end{pmatrix} Nr.c <>[TU]SS/USU[US9US9 g)zCreate new CS gate.csr r)rr0r- base_gater.N)rrrrrr-r.rs rrCSGate.__init__s4   !+.#  rr rvcSSKJn UR[RR UR 5SURS9Ulgr) r"rr#r CSr%r&r!r'r(s rr)CSGate._define.sA 2);; OO + +DKK 8SWS\S\< rc([URS9$)aReturn inverse of CSGate (CSdgGate). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.CSdgGate`. Returns: CSdgGate: inverse of :class:`.CSGate` r-)rmr-r9s rr:CSGate.inverse=s4??33rcFSSKJn U"S[R-U-5$)Nr  CPhaseGater?rArrBrCrrEr1rs rrF CSGate.powerKs!#.8344rcb[U[5=(a URUR:H$rI)rJr2r-rKs rrM CSGate.__eq__Ps#%(PT__@P@P-PPrrONNrrQr-zOptional[Union[str, int]]rUrVrX)rZr[r\r]r^r rr_rrr`r)r:rFrMrarbrcs@rr2r2si8"__N $04    .  &1C   45 QQrr2c^\rSrSrSr\R rS SS.SU4Sjjjjr\ "SS9r Sr SSS jjr SSS jjr S rS rU=r$)rmiTu^Controlled-S^\dagger gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.csdg` method. Circuit symbol: .. code-block:: text q_0: ───■─── ┌──┴──┐ q_1: ┤ Sdg ├ └─────┘ Matrix representation: .. math:: CS^\dagger \ q_0, q_1 = I \otimes |0 \rangle\langle 0| + S^\dagger \otimes |1 \rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -i \end{pmatrix} Nryc :>[TU]SS/USU[US9S9 g)zCreate new CSdg gate.csdgr|r r)rr0r-r}N)rrr8r~s rrCSdgGate.__init__ts1   !K0  rr rvcSSKJn UR[RR UR 5SURS9Ulgr) r"rr#r CSdgr%r&r!r'r(s rr)CSdgGate._definesC 2);;    - -dkk :$UYU^U^< rc([URS9$)aReturn inverse of CSdgGate (CSGate). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.CSGate`. Returns: CSGate: inverse of :class:`.CSdgGate` r)r2r-r9s rr:CSdgGate.inverses11rcFSSKJn U"S[R-U-5$)Nr rrrrrs rrFCSdgGate.powers!$/H455rcb[U[5=(a URUR:H$rI)rJrmr-rKs rrMCSdgGate.__eq__s#%*Rt%BRBR/RRrrOrrrUrVrX)rZr[r\r]r^r rr_rrr`r)r:rFrMrarbrcs@rrmrmTsk8"&&N $04    .  $1C   26 SSrrm)r^ __future__rtypingrrrBqiskit.circuit.singletonrrrqiskit.circuit._utilsr r qiskit._accelerate.circuitr array_S_ARRAY _SDG_ARRAYrr8r2rmrrrs%"" aaM3 ;;AB( ) [[1a&1c(+ , k(Mk(k(\h*mh*h*VHa8WQ $WQ9WQtJ:VS&VS;VSr