z iS%SrSSKJr SSKJrJr SSKJrJrJ r SSK J r J r SSK Jr SS/SS//rSS/SS//r\ "\5"S S \55r\ "\5"S S \55r\ "\S S9"SS\55rg)zSqrt(X) and C-Sqrt(X) gates.) annotations)OptionalUnion) SingletonGateSingletonControlledGatestdlib_singleton_key)with_gate_arraywith_controlled_gate_array) StandardGatey??y?c^\rSrSrSr\R rS S U4Sjjjr\ "5r Sr S S Sjjr S SU4Sjjjr SrSrU=r$)SXGateuThe single-qubit Sqrt(X) gate (:math:`\sqrt{X}`). Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.sx` method. Matrix representation: .. math:: \sqrt{X} = \frac{1}{2} \begin{pmatrix} 1 + i & 1 - i \\ 1 - i & 1 + i \end{pmatrix} Circuit symbol: .. code-block:: text ┌────┐ q_0: ┤ √X ├ └────┘ .. note:: A global phase difference exists between the definitions of :math:`RX(\pi/2)` and :math:`\sqrt{X}`. .. math:: RX(\pi/2) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & -i \\ -i & 1 \end{pmatrix} = e^{-i \pi/4} \sqrt{X} c&>[TU]SS/US9 g)z2 Args: label: An optional label for the gate. sxlabelNsuper__init__selfr __class__s b/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/sx.pyrSXGate.__init__Ds q"E2cSSKJn UR[RR UR 5SURS9UlgzDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr_from_circuit_datar SX_get_definitionparamsr! definitionrrs r_defineSXGate._defineMsA 2);; OO + +DKK 8SWS\S\< rc[5$)aReturn inverse SX gate (i.e. SXdg). 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:`.SXdgGate`. Returns: SXdgGate: inverse of :class:`.SXGate`. )SXdgGater annotateds rinverseSXGate.inverse[s zrcn>U(dUS:Xa[X#URS9nU$[TU] UUUUS9nU$)aReturn a (multi-)controlled-SX gate. One control returns a CSX gate. 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: SingletonControlledGate: controlled version of this gate. r)r ctrl_state _base_label)num_ctrl_qubitsrr2r.)CSXGaterrcontrol)rr4rr2r.gaters rr6SXGate.controlisN,_14::VD 7? /%# #D  rc"[U[5$N) isinstancer rothers r__eq__ SXGate.__eq__s%((rr'r:r Optional[str]Fr.bool)rNNN)r4intrz str | Noner2zstr | int | Noner.z bool | None)__name__ __module__ __qualname____firstlineno____doc__r r$_standard_gaterr_singleton_lookup_keyr)r/r6r>__static_attributes__ __classcell__rs@rr r s|#J"__N3312    ! '+!% %   B))rr ct^\rSrSrSr\R rSS U4Sjjjr\ "5r Sr S S Sjjr Sr SrU=r$) r,aThe inverse single-qubit Sqrt(X) gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.sxdg` method. .. math:: \sqrt{X}^{\dagger} = \frac{1}{2} \begin{pmatrix} 1 - i & 1 + i \\ 1 + i & 1 - i \end{pmatrix} .. note:: A global phase difference exists between the definitions of :math:`RX(-\pi/2)` and :math:`\sqrt{X}^{\dagger}`. .. math:: RX(-\pi/2) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & i \\ i & 1 \end{pmatrix} = e^{-i \pi/4} \sqrt{X}^{\dagger} c&>[TU]SS/US9 g)zCreate new SXdg gate.sxdgrrNrrs rrSXdgGate.__init__s Be4rcSSKJn UR[RR UR 5SURS9Ulgr) r"rr#r SXdgr%r&r!r'r(s rr)SXdgGate._definesC 2);;    - -dkk :$UYU^U^< rc[5$)aReturn inverse SXdg gate (i.e. SX). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.SXGate`. Returns: SXGate: inverse of :class:`.SXdgGate` )r r-s rr/SXdgGate.inverses xrc"[U[5$r:)r;r,r<s rr>SXdgGate.__eq__s%**rr@r:rArCrD)rGrHrIrJrKr rWrLrrrMr)r/r>rNrOrPs@rr,r,s>6"&&N5512   ++rr,rr4cv^\rSrSrSr\R rS SS.S U4Sjjjjr\ "SS9r Sr S r S r U=r$) r5uControlled-√X gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.csx` method. Circuit symbol: .. code-block:: text q_0: ──■── ┌─┴──┐ q_1: ┤ √X ├ └────┘ Matrix representation: .. math:: C\sqrt{X} \ q_0, q_1 = I \otimes |0 \rangle\langle 0| + \sqrt{X} \otimes |1 \rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & (1 + i) / 2 & 0 & (1 - i) / 2 \\ 0 & 0 & 1 & 0 \\ 0 & (1 - i) / 2 & 0 & (1 + i) / 2 \end{pmatrix} .. note:: In Qiskit's convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be `q_1`. Thus a textbook matrix for this gate will be: .. code-block:: text ┌────┐ q_0: ┤ √X ├ └─┬──┘ q_1: ──■── .. math:: C\sqrt{X}\ q_1, q_0 = |0 \rangle\langle 0| \otimes I + |1 \rangle\langle 1| \otimes \sqrt{X} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & (1 + i) / 2 & (1 - i) / 2 \\ 0 & 0 & (1 - i) / 2 & (1 + i) / 2 \end{pmatrix} N)r3c :>[TU]SS/SUU[US9S9 g)zCreate new CSX gate.csxrr)r4rr2 base_gateN)rrr )rrr2r3rs rrCSXGate.__init__s1   !;/  rrr]cSSKJn UR[RR UR 5SURS9Ulgr) r"rr#r CSXr%r&r!r'r(s rr)CSXGate._define#sC 2);;    , ,T[[ 9TXT]T]< rcb[U[5=(a URUR:H$r:)r;r5r2r<s rr>CSXGate.__eq__1s#%)QdooAQAQ.QQrr@)NN)rrBr2zOptional[Union[str, int]])rGrHrIrJrKr rfrLrrrMr)r>rNrOrPs@rr5r5sb6p"%%N $04    .  $1C  RRrr5N)rK __future__rtypingrrqiskit.circuit.singletonrrrqiskit.circuit._utilsr r qiskit._accelerate.circuitr _SX_ARRAY _SXDG_ARRAYr r,r5rrrrs#""aaM3* % J'? @ J'*j)AB o)]o)o)dA+}A+A+HIq9^R%^R:^Rr