z iSrSSKJr SSKJr SSKJrJr SSKrSSK J r J r J r SSK JrJr SSKJr S \"S 5- \R$"S S /S S //\R&S 9-r\"\5"S S\ 55r\"\S S9"SS\ 55rg)zHadamard gate.) annotations)sqrt)OptionalUnionN) SingletonGateSingletonControlledGatestdlib_singleton_key)with_gate_arraywith_controlled_gate_array) StandardGate)dtypec^\rSrSrSr\R rS S U4Sjjjr\ "5r Sr S S U4Sjjjr S SSjjr SrSrU=r$)HGateuGSingle-qubit Hadamard gate. This gate is a \pi rotation about the X+Z axis, and has the effect of changing computation basis from :math:`|0\rangle,|1\rangle` to :math:`|+\rangle,|-\rangle` and vice-versa. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.h` method. Circuit symbol: .. code-block:: text ┌───┐ q_0: ┤ H ├ └───┘ Matrix representation: .. math:: H = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix} c&>[TU]SS/US9 g)z2 Args: label: An optional label for the gate. hr labelN)super__init__)selfr __class__s a/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/h.pyrHGate.__init__;s a51cSSKJn UR[RR UR 5SURS9UlgzDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr!_from_circuit_datar H_get_definitionparamsr# definitionrr!s r_define HGate._defineDsA 2 );; NN * *4;; 7tRVR[R[< rcn>U(dUS:Xa[X#URS9nU$[TU] UUUUS9nU$)a Return a (multi-)controlled-H gate. One control qubit returns a CH 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: ControlledGate: controlled version of this gate. r )r ctrl_state _base_label)num_ctrl_qubitsrr. annotated)CHGaterrcontrol)rr0rr.r1gaters rr3 HGate.controlQsN,_1$**UD 7? /%# #D  rc[5$)ajReturn inverted H gate (itself). 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 this gate is self-inverse. Returns: HGate: inverse gate (self-inverse). )rrr1s rinverse HGate.inversers wrc"[U[5$N) isinstancerrothers r__eq__ HGate.__eq__s%''rr)r;)r Optional[str])r NNN)r0intrz str | Noner.zint | str | Noner1z bool | NoneFr1bool)__name__ __module__ __qualname____firstlineno____doc__r r&_standard_gaterr _singleton_lookup_keyr+r3r8r?__static_attributes__ __classcell__rs@rrrs{8"^^N2212   ! '+!% %   B ((rrr0c^\rSrSrSr\R rS SS.S U4Sjjjjr\ "SS9r Sr SSS jjr S r S rU=r$)r2uControlled-Hadamard gate. Applies a Hadamard on the target qubit if the control is in the :math:`|1\rangle` state. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.ch` method. Circuit symbol: .. code-block:: text q_0: ──■── ┌─┴─┐ q_1: ┤ H ├ └───┘ Matrix representation: .. math:: CH\ q_0, q_1 = I \otimes |0\rangle\langle 0| + H \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ 0 & 0 & 1 & 0 \\ 0 & \frac{1}{\sqrt{2}} & 0 & -\frac{1}{\sqrt{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: ┤ H ├ └─┬─┘ q_1: ──■── .. math:: CH\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes H = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ 0 & 0 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{pmatrix} N)r/c <>[TU]SS/SUU[US9US9 g)zCreate new CH gate.chrr r)r0rr. base_gater/N)rrr)rrr.r/rs rrCHGate.__init__s4   !+.#  rr rQcSSKJn UR[RR UR 5SURS9Ulgr ) r$r!r%r CHr'r(r#r)r*s rr+CHGate._definesA 2);; OO + +DKK 8SWS\S\< rc([URS9$)z!Return inverted CH gate (itself).)r.)r2r.r7s rr8CHGate.inverses11rcb[U[5=(a URUR:H$r;)r<r2r.r=s rr? CHGate.__eq__s#%(PT__@P@P-PPrrA)NN)rrBr.zOptional[Union[int, str]]rDrE)rGrHrIrJrKr rYrLrr rMr+r8r?rNrOrPs@rr2r2se7r"__N $04    .  &1C  2QQrr2)rK __future__rmathrtypingrrnumpyqiskit.circuit.singletonrrr qiskit.circuit._utilsr r qiskit._accelerate.circuitr array complex128_H_ARRAYrr2rrrjs"" aaM3 tAw;q!fq"g%6e>N>NO Oe(Me(e(PHa8dQ $dQ9dQr