z iaSrSSKJr SSKrSSKJrJrJr SSKrSSK J r SSK J r J r Jr SSKJrJrJr SSKJr SS KJr SS /S S//rS S /S S //r\"\5"S S\ 55r\"\S S9"SS\ 55r\"\SSS9"SS\ 55r\"/SQ/SQ/SQ/SQ/SQ/SQ/SQ/SQ/5"SS \ 55r\"\S!S"S9"S#S$\ 55r\"\S!S"S9"S%S&\ 55r\"/S'Q/S(Q/S)Q/S*Q/S+Q/S,Q/S-Q/S.Q/S/Q/S0Q/S1Q/S2Q/S3Q/S4Q/S5Q/S6Q/5"S7S8\ 55r\"\S9S:S9"S;S<\ 55r "S=S>\ 5r!"S?S@\!5r""SASB\!5r#"SCSD\!5r$g)Ez(X, CX, CCX and multi-controlled X gates.) annotationsN)OptionalUnionType)ControlledGate) SingletonGateSingletonControlledGatestdlib_singleton_key)_ctrl_state_to_intwith_gate_arraywith_controlled_gate_array) StandardGate)deprecate_funcy??y?c^\rSrSrSr\R rS S U4Sjjjr\ "5r Sr S S Sjjr S SSjjr SrSrU=r$)XGateugThe single-qubit Pauli-X gate (:math:`\sigma_x`). Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.x` method. Matrix representation: .. math:: X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} Circuit symbol: .. code-block:: text ┌───┐ q_0: ┤ X ├ └───┘ Equivalent to a :math:`\pi` radian rotation about the X axis. .. note:: A global phase difference exists between the definitions of :math:`RX(\pi)` and :math:`X`. .. math:: RX(\pi) = \begin{pmatrix} 0 & -i \\ -i & 0 \end{pmatrix} = -i X The gate is equivalent to a classical bit flip. .. math:: |0\rangle \rightarrow |1\rangle \\ |1\rangle \rightarrow |0\rangle c&>[TU]SS/US9 g)z2 Args: label: An optional label for the gate. xrlabelNsuper__init__selfr __class__s a/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/x.pyrXGate.__init__Ms a51cSSKJn UR[RR UR 5SURS9UlgDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr$_from_circuit_datarX_get_definitionparamsr& definitionrr$s r_define XGate._defineVsA 2 );; NN * *4;; 7tRVR[R[< r c2[UUUURS9nU$)aReturn a (multi-)controlled-X gate. One control returns a CX gate. Two controls returns a CCX 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: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with a control modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as a controlled X gate is a multi-controlled X-gate. Returns: ControlledGate: controlled version of this gate. num_ctrl_qubitsr ctrl_state _base_label)MCXGater)rr2rr3 annotatedgates rcontrol XGate.controlcs%0+!    r c[5$)ajReturn inverted X gate (itself). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as this gate is self-inverse. Returns: XGate: inverse gate (self-inverse). )rrr6s rinverse XGate.inverses wr c"[U[5$N) isinstancerrothers r__eq__ XGate.__eq__s%''r r,r?r Optional[str]rNNFr2intrrGr3Optional[Union[str, int]]r6boolFr6rL)__name__ __module__ __qualname____firstlineno____doc__rr)_standard_gaterr _singleton_lookup_keyr.r8r<rC__static_attributes__ __classcell__rs@rrrsw+Z"^^N2212   !#04 .   @ ((r rr2c^\rSrSrSr\R rS SS.S U4Sjjjjr\ "SS9r SSSjjr SSS jjr S r S rU=r$)CXGateu8Controlled-X gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.cx` and :meth:`~qiskit.circuit.QuantumCircuit.cnot` methods. Circuit symbol: .. code-block:: text q_0: ──■── ┌─┴─┐ q_1: ┤ X ├ └───┘ Matrix representation: .. math:: CX\ q_0, q_1 = I \otimes |0\rangle\langle0| + X \otimes |1\rangle\langle1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{pmatrix} .. note:: In Qiskit's convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be q_1. Thus a textbook matrix for this gate will be: .. code-block:: text ┌───┐ q_0: ┤ X ├ └─┬─┘ q_1: ──■── .. math:: CX\ q_1, q_0 = |0 \rangle\langle 0| \otimes I + |1 \rangle\langle 1| \otimes X = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix} In the computational basis, this gate flips the target qubit if the control qubit is in the :math:`|1\rangle` state. In this sense it is similar to a classical XOR gate. .. math:: `|a, b\rangle \rightarrow |a, a \oplus b\rangle` Nr4c <>[TU]SS/SUU[US9US9 g)zCreate new CX gate.cxrr)r2rr3 base_gater4Nrrrrrr3r4rs rrCXGate.__init__s4   !+.#  r rrYcr[X15nURU-U-n[US-UUURS9nU$)aReturn a controlled-X gate with more control lines. 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: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with a control modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as a controlled CX gate is a multi-controlled X-gate. Returns: ControlledGate: controlled version of this gate. rr1r r3r5rrr2rr3r6new_ctrl_stater7s rr8CXGate.controlG,( D //_< J+a/%    r c([URS9$)alReturn inverted CX gate (itself). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as this gate is self-inverse. Returns: CXGate: inverse gate (self-inverse). r3)r[r3r;s rr<CXGate.inverse s11r cb[U[5=(a URUR:H$r?)r@r[r3rAs rrC CXGate.__eq__s#%(PT__@P@P-PPr NNrrGr3rKrHrIrMrN)rOrPrQrRrSrCXrTrr rUr8r<rCrVrWrXs@rr[r[s=~"__N $04    .  &1C !#04 .   @ 2QQr r[r`))r2 cached_statesc^\rSrSrSr\R rS SS.SU4Sjjjjr\ "SS9r Sr SSS jjr SSS jjr S rS rU=r$)CCXGateiuCCX gate, also known as Toffoli gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.ccx` method. Circuit symbol: .. code-block:: text q_0: ──■── │ q_1: ──■── ┌─┴─┐ q_2: ┤ X ├ └───┘ Matrix representation: .. math:: CCX q_0, q_1, q_2 = I \otimes I \otimes |0 \rangle \langle 0| + CX \otimes |1 \rangle \langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \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_2 and q_1. Thus a textbook matrix for this gate will be: .. code-block:: text ┌───┐ q_0: ┤ X ├ └─┬─┘ q_1: ──■── │ q_2: ──■── .. math:: CCX\ q_2, q_1, q_0 = |0 \rangle \langle 0| \otimes I \otimes I + |1 \rangle \langle 1| \otimes CX = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \end{pmatrix} Nr]c :>[TU]SS/SUU[US9S9 g)zCreate new CCX gate.ccxrtr`rr2rr3raNrbrcs rrCCXGate.__init__f1   !+.  r r`rYcSSKJn UR[RR UR 5SURS9Ulgr") r'r$r(rCCXr*r+r&r,r-s rr.CCXGate._definezsC 2);;    , ,T[[ 9TXT]T]< r cr[X15nURU-U-n[US-UUURS9nU$)awControlled version of this 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: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with a control modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as a controlled CCX gate is a multi-controlled X-gate. Returns: ControlledGate: controlled version of this gate. r`r1rfrgs rr8CCXGate.controlrjr c([URS9$)auReturn an inverted CCX gate (also a CCX). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as this gate is self-inverse. Returns: CCXGate: inverse gate (self-inverse). rl)rwr3r;s rr<CCXGate.inverse$//22r cb[U[5=(a URUR:H$r?)r@rwr3rAs rrCCCXGate.__eq__#%)QdooAQAQ.QQr rErqrrrHrIrMrN)rOrPrQrRrSrr~rTrr rUr.r8r<rCrVrWrXs@rrwrwsAF"%%N $04    .  $1C & !#04 .   @ 3RRr rw)rrrrrrrr)rrrrrrrr)rrrrrrrr)rrrrrrr)rrrrrrrr)rrrrrrr)rrrrrrrr)rrr?rrrrcf^\rSrSrSr\R rSSU4Sjjjr\ "5r Sr Sr Sr U=r$) RCCXGateia|The simplified Toffoli gate, also referred to as Margolus gate. The simplified Toffoli gate implements the Toffoli gate up to relative phases. This implementation requires three CX gates which is the minimal amount possible, as shown in https://arxiv.org/abs/quant-ph/0312225. Note, that the simplified Toffoli is not equivalent to the Toffoli. But can be used in places where the Toffoli gate is uncomputed again. This concrete implementation is from https://arxiv.org/abs/1508.03273, the dashed box of Fig. 3. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.rccx` method. c&>[TU]SS/US9 g)z!Create a new simplified CCX gate.rccxrtrNrrs rrRCCXGate.__init__s Be4r cSSKJn UR[RR UR 5SURS9Ulgr") r'r$r(rRCCXr*r+r&r,r-s rr.RCCXGate._definesC 2);;    - -dkk :$UYU^U^< r c"[U[5$r?)r@rrAs rrCRCCXGate.__eq__%**r rEr?rF)rOrPrQrRrSrrrTrr rUr.rCrVrWrXs@rrrs9 "&&N5512 "++r rrt)cv^\rSrSrSr\R rS SS.S U4Sjjjjr\ "SS9r Sr S r S r U=r$) C3SXGateizThe 3-qubit controlled sqrt-X gate. This implementation is based on Page 17 of [1]. References: [1] Barenco et al., 1995. https://arxiv.org/pdf/quant-ph/9503016.pdf Nr]c @>SSKJn [TU] SS/SUUU"US9S9 g) zCreate a new 3-qubit controlled sqrt-X gate. Args: 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. r)SXGatec3sxrtrrzN)sxrrr)rrr3r4rrs rrC3SXGate.__init__s4    !;/  r rtrYcSSKJn UR[RR UR 5SURS9Ulgr") r'r$r(rC3SXr*r+r&r,r-s rr.C3SXGate._defineA 2(;;    - -dkk :$UYU^U^< r cb[U[5=(a URUR:H$r?)r@rr3rAs rrCC3SXGate.__eq__'s#%*Rt%BRBR/RRr rErqrr)rOrPrQrRrSrrrTrr rUr.rCrVrWrXs@rrrsa"&&N $04    .  41C SSr rc^\rSrSrSr\R rS SS.SU4Sjjjjr\ "SS9r Sr SSS jjr SSS jjr S rS rU=r$)C3XGatei+zaThe X gate controlled on 3 qubits. This implementation uses :math:`\sqrt{T}` and 14 CNOT gates. Nr]c :>[TU]SS/SUU[US9S9 g)z'Create a new 3-qubit controlled X gate.mcxrrtrrzNrbrcs rrC3XGate.__init__4r|r rtrYcSSKJn UR[RR UR 5SURS9Ulgr") r'r$r(rC3Xr*r+r&r,r-s rr.C3XGate._defineIsA 2(;;    , ,T[[ 9TXT]T]< r cr[X15nURU-U-n[US-UUURS9nU$)awControlled version of this 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: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with a control modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as a controlled C3X gate is a multi-controlled X-gate. Returns: ControlledGate: controlled version of this gate. rtr1rfrgs rr8C3XGate.controlRrjr c([URS9$)ayInvert this gate. The C3X is its own inverse. Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as this gate is self-inverse. Returns: C3XGate: inverse gate (self-inverse). rl)rr3r;s rr<C3XGate.inverserrr cb[U[5=(a URUR:H$r?)r@rr3rAs rrCC3XGate.__eq__rr rErqrrrHrIrMrN)rOrPrQrRrSrrrTrr rUr.r8r<rCrVrWrXs@rrr+s "%%N $04    .  $1C  !#04 .   @ 3RRr r)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrcf^\rSrSrSr\R rSSU4Sjjjr\ "5r Sr Sr Sr U=r$) RC3XGateiaThe simplified 3-controlled Toffoli gate. The simplified Toffoli gate implements the Toffoli gate up to relative phases. Note, that the simplified Toffoli is not equivalent to the Toffoli. But can be used in places where the Toffoli gate is uncomputed again. This concrete implementation is from https://arxiv.org/abs/1508.03273, the complete circuit of Fig. 4. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.rcccx` method. c&>[TU]SS/US9 g)zCreate a new RC3X gate.rcccxrrNrrs rrRC3XGate.__init__s !Ru5r cSSKJn UR[RR UR 5SURS9Ulgr") r'r$r(rRC3Xr*r+r&r,r-s rr.RC3XGate._definerr c"[U[5$r?)r@rrAs rrCRC3XGate.__eq__rr rEr?rF)rOrPrQrRrSrrrTrr rUr.rCrVrWrXs@rrrs9* "&&N6612 ++r rr)c^\rSrSrSrS SS.SU4Sjjjjr\"SS9rSrSSS jjr SSS jjr S r S r U=r $)C4XGateia(The 4-qubit controlled X gate. This implementation is based on Page 21, Lemma 7.5, of [1], with the use of the relative phase version of c3x, the rc3x [2]. References: 1. Barenco et al., 1995. https://arxiv.org/pdf/quant-ph/9503016.pdf 2. Maslov, 2015. https://arxiv.org/abs/1508.03273 Nr]c :>[TU]SS/SUU[US9S9 g)z'Create a new 4-qubit controlled X gate.rrrrzNrbrcs rrC4XGate.__init__r|r rrYc`SSKJnJn SSKJn SSKJn U"SSS9nU"XPRS9nU"5US //4U"[RS - 5US US //4U"5US //4[5USUSUS US //4U"5US //4U"[R*S - 5US US //4U"5US //4[5R5USUSUS US //4[5USUSUS US //4/ nUHupn URXU 5 M X`lg ) r#r)r$QuantumRegisterr)HGate) CPhaseGaterqr&rr`rtN)r'r$rhrprr&numpypirr<r_appendr,) rr$rrrrqcrulesinstrqargscargss rr.C4XGate._defines_ C! AC ( AII . Wqtfb ! 1 %!ad|R 8 Wqtfb ! Z!A$!adAaD12 6 Wqtfb !  A &1qt b 9 Wqtfb ! Z   !AaD!A$!ad#;R @ Z!A$!adAaD12 6  $) E% JJuU +$)r cr[X15nURU-U-n[US-UUURS9nU$)awControlled version of this gate. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g. ``'110'``), or ``None``. If ``None``, use all 1s. annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with a control modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as a controlled C4X gate is a multi-controlled X-gate. Returns: ControlledGate: controlled version of this gate. rr1rfrgs rr8C4XGate.controlrjr c([URS9$)ayInvert this gate. The C4X is its own inverse. 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: C4XGate: inverse gate (self-inverse). rl)rr3r;s rr<C4XGate.inverserr cb[U[5=(a URUR:H$r?)r@rr3rAs rrCC4XGate.__eq__$rr rErqrrrHrIrMrN)rOrPrQrRrSrr rUr.r8r<rCrVrWrXs@rrrs $04    .  $1C8 !#04 .   @ 3RRr rc^\rSrSrSrSSS.SU4SjjjjrSSSS.SU4SjjjjrSSS jjr\\ "S S S S 9SSSjj55r Sr \ S5r SSSjjrSU4SjjrSU4SjjrSrU=r$) r5i(zThe general, multi-controlled X gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.mcx` method. Nr]c>[[S.nURUS5nUb#URXbX4S9nUR UUUS9 U$[ TU] U5$)zCreate a new MCX instance. Depending on the number of controls and which mode of the MCX, this creates an explicit CX, CCX, C3X or C4X instance or a generic MCX gate. )rr`Nrr3r4)r[rwget__new__rr clsr2rr3r4explicit gate_classr7rs rrMCXGate.__new__/sq9?74K\\/48  !%%J&D MM%'   Kws##r r)_namer4c >UR[[[[4;aU[ R "5 [ R"S[SSS9 URRU5nSSS5 OURRU5n[TU]-UUS-W-/UUU[US9S9 g!,(df  N/=f) zCreate new MCX gate.ignorezP.+qiskit\.circuit\.library\.standard_gates\.x\.MCXGate\.get_num_ancilla_qubits.+qiskit)categorymessagemoduleNrrrz) rr5 MCXGrayCode MCXRecursive MCXVChainwarningscatch_warningsfilterwarningsDeprecationWarningget_num_ancilla_qubitsrrr)rr2rr3rr4num_ancilla_qubitsrs rrMCXGate.__init__Ms >>g{L)L L ((*''/0# &*^^%J%J?%["+*"&!F!F!W    a "4 4 +!+.  +*s 7B77 Cc>[URURS9$)ayInvert this gate. The MCX is its own inverse. Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as this gate is self-inverse. Returns: MCXGate: inverse gate (self-inverse). r2r3)r5r2r3r;s rr<MCXGate.inversetst';';XXr aFor an MCXGate it is no longer possible to know the number of ancilla qubits that would be eventually used by the transpiler when the gate is created. Instead, it is recommended to use MCXGate and let HighLevelSynthesis choose the best synthesis method depending on the number of ancilla qubits available. However, if a specific synthesis method using a specific number of ancilla qubits is require, one can create a custom gate by calling the corresponding synthesis function directly.2.1 in Qiskit 3.0)additional_msgsinceremoval_timelinecUS:XagUS;a[US:5$USSS:Xd USSS :Xa[SUS - 5$[S US 35e) zGet the number of required ancilla qubits without instantiating the class. This staticmethod might be necessary to check the number of ancillas before creating the gate, or to use the number of ancillas in the initialization. noancillar) recursionadvancedrNrv-chainrbasicr`zUnsupported mode (z ) specified!)rJmaxAttributeErrorr2modes rrMCXGate.get_num_ancilla_qubitssj( ;  , ,*+ + 8y D!H$7q/A-. .1$|DEEr c@SSKJn U"UR5nX lg)z7This definition is based on MCPhaseGate implementation.r)synth_mcx_noaux_v24N)!qiskit.synthesis.multi_controlledr r2r,)rr rs rr.MCXGate._define J !5!5 6r c8URUR5$)zThe number of ancilla qubits.)rr2)rs rrMCXGate.num_ancilla_qubitss**4+?+?@@r c[X15nURU-U-nUR[[[ 4;aX[ R"5 [ R"S[SS9 URURU-UUS9nSSS5 U$[URU-UUURS9nU$!,(df  W$=f)aReturn a multi-controlled-X gate with more control lines. 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: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with a control modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as a controlled multi-controlled X gate is another multi-controlled X-gate. Returns: ControlledGate: controlled version of this gate. rrrrrr3Nr) r r3rrrrrrrrr2r5rrgs rr8MCXGate.controls,( D //_< J >>k<C C ((*''/# ~~((?:-& +$ $$6) JJ D  %+*$ s 9B:: C c >UR[[[4;aF[R "5 [R "S[SS9 [TU]%US9sSSS5 $[TU]%US9$!,(df  N=f)z Copy of the instruction. Args: name (str): name to be given to the copied circuit, if ``None`` then the name stays the same. Returns: qiskit.circuit.Instruction: a copy of the current instruction, with the name updated if it was provided rz/.*qiskit\.circuit\.library\.standard_gates\.x.*rrrN) rrrrrrrrrcopy)rr&rs rr MCXGate.copyso >>k<C C((*''/N w||. +*w||&&+* 'A44 Bc >UR[[[4;aF[R "5 [R "S[SS9 [TU]%US9sSSS5 $[TU]%US9$!,(df  N=f)Nrz .+MCXVChain.+r)memo) rrrrrrrrr __deepcopy__)rrrs rrMCXGate.__deepcopy__sp >>k<C C((*'''9?w++6 +* w##.. +*rrENNNr2 Optional[int]rrGr3rKrqr2rJrrGr3rKrMrN)r)r2rJrstrreturnrJrHrIr?)rOrPrQrRrSrrr< staticmethodrrr.propertyrr8rrrVrWrXs@rr5r5(s*.#04 $  $&$$. $$B $04 % % % % . % % N Y +(  F  FAA !#04 222. 2  2h'*//r r5c^\rSrSrSr\"SSSS9SSS.SU4S jjjj5rSSU4S jjjrSSS jjrS r S r U=r $)rizImplement the multi-controlled X gate using the Gray code. This delegates the implementation to the MCU1 gate, since :math:`X = H \cdot U1(\pi) \cdot H`. rahIt is recommended to use MCXGate and let HighLevelSynthesis choose the best synthesis method depending on the number of ancilla qubits available. If this specific synthesis method is required, one can specify it using the high-level-synthesis plugin 'gray_code' for MCX gates, or, alternatively, one can use synth_mcx_gray_code' to construct the gate directly.rrrrNr]c>[[[[S.nUR US5nUb$UR UUUUS9nUR UUS9 U$[TU]U5$)z!Create a new MCXGrayCode instance)rr`rtrNrr)r[rwrrrrrrrs rrMCXGrayCode.__new__sy*'g'B\\/48  !%%%' &D MM%  Kws##r c$>[TU]XUSS9 g)Nmcx_grayrr3rr)rr2rr3rs rrMCXGrayCode.__init__*s *T^_r c[R"5 [R"S[SS9 [ UR UR S9nSSS5 U$!,(df  W$=f)a}Invert this gate. The MCX is its own inverse. Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as this gate is self-inverse. Returns: MCXGrayCode: inverse gate (self-inverse). rrrrN)rrrrrr2r3rr6r<s rr<MCXGrayCode.inverse2sY $ $ &  # #H7IRZ [!$2F2FSWSbSbcG'' & 9A A(c@SSKJn U"UR5nX lg)z(Define the MCX gate using the Gray code.r)synth_mcx_gray_codeN)r r1r2r,)rr1rs rr.MCXGrayCode._defineCr r rErrrqrrMrN) rOrPrQrRrSrrrr<r.rVrWrXs@rrrs  O ) *.#04 $  $&$$. $$ $< $04 ```. ``"r rc^\rSrSrSr\"SSSS9SSS.SU4S jjjj5rSSS.SU4S jjjjr\SSS jj5r SSS jjr S r Sr U=r $)riLaImplement the multi-controlled X gate using recursion. Using a single clean ancilla qubit, the multi-controlled X gate is split into four sub-registers, each one of them uses the V-chain method. The method is based on Lemma 9 of [2], first shown in Lemma 7.3 of [1]. References: 1. Barenco et al., 1995. https://arxiv.org/pdf/quant-ph/9503016.pdf 2. Iten et al., 2015. https://arxiv.org/abs/1501.06911 raoIt is recommended to use MCXGate and let HighLevelSynthesis choose the best synthesis method depending on the number of ancilla qubits available. If this specific synthesis method is required, one can specify it using the high-level-synthesis plugin ``'gray_code'`` for MCX gates, or, alternatively, one can use ``'synth_mcx_1_clean'`` to construct the gate directly.rr%Nr]c">[TU]XX#US9$)Nr]rr)rr2rr3r4rs rrMCXRecursive.__new__Ys&wsUT_``r c(>[TU]UUUSSS9 g)N mcx_recursiverr3rr4r)rr2rr3r4rs rrMCXRecursive.__init__ns&  !!  r c,[RX5$z*Get the number of required ancilla qubits.r5rrs rr#MCXRecursive.get_num_ancilla_qubits~--oDDr c[R"5 [R"S[SS9 [ UR UR S9nSSS5 U$!,(df  W$=f)a~Invert this gate. The MCX is its own inverse. 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: MCXRecursive: inverse gate (self-inverse). rrrrN)rrrrrr2r3r-s rr<MCXRecursive.inversesY $ $ &  # #H7IRZ ["43G3GTXTcTcdG'' &r/c@SSKJn U"UR5nX lg)z$Define the MCX gate using recursion.r)synth_mcx_1_clean_b95N)r rCr2r,)rrCrs rr.MCXRecursive._defines L "4#7#7 8r rErrrqr)rr2rJrr rMrN)rOrPrQrRrSrrrr"rr<r.rVrWrXs@rrrLs  R ) *.#04 a  a&aa. aa a $04      .   EE"r rc^\rSrSrSr\"SSSS9SSSSS .SU4S jjjj5rSSSSS .SU4S jjjjrSSS jjr\ SSS jj5r Sr Sr U=r $)rizBImplement the multi-controlled X gate using a V-chain of CX gates.raIt is recommended to use MCXGate and let HighLevelSynthesis choose the best synthesis method depending on the number of ancilla qubits available. If this specific synthesis method is required, one can specify it using the high-level-synthesis plugins `n_clean_m15` (using clean ancillas) or `n_dirty_i15` (using dirty ancillas) for MCX gates. Alternatively, one can use synth_mcx_n_dirty_i15 and synth_mcx_n_clean_m15 to construct the gate directly.rr%NF)r4relative_phase action_onlyc&>[TU]UUUUUS9$)zmCreate a new MCX instance. This must be defined anew to include the additional argument ``dirty_ancillas``. rr5) rr2dirty_ancillasrr3r4rGrHrs rrMCXVChain.__new__s*6w  !#   r cj>[TU]UUUSUS9 X lX`lXpl[TU]XUSS9 g)a  Args: dirty_ancillas: when set to ``True``, the method applies an optimized multicontrolled-X gate up to a relative phase using dirty ancillary qubits with the properties of lemmas 7 and 8 from arXiv:1501.06911, with at most 8*k - 6 CNOT gates. For k within the range {1, ..., ceil(n/2)}. And for n representing the total number of qubits. relative_phase: when set to ``True``, the method applies the optimized multicontrolled-X gate up to a relative phase, in a way that, by lemma 7 of arXiv:1501.06911, the relative phases of the ``action part`` cancel out with the phases of the ``reset part``. action_only: when set to ``True``, the method applies only the action part of lemma 8 from arXiv:1501.06911. mcx_vchainr9r*N)rr_dirty_ancillas_relative_phase _action_only) rr2rJrr3r4rGrHrs rrMCXVChain.__init__sO4  !#   .-' *T`ar c [R"5 [R"S[SS9 [ UR UR URURURS9nSSS5 U$!,(df  W$=f)a{Invert this gate. The MCX is its own inverse. 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: MCXVChain: inverse gate (self-inverse). rz<.+qiskit\.circuit\.library\.standard_gates\.x\.MCXVChain\..+r)r2rJr3rGrHN) rrrrrr2rNr3rOrPr-s rr<MCXVChain.inversesz $ $ &  # #+W   $ 4 4#33??#33 -- G '' &s AA:: B c,[RX5$r<r=rs rr MCXVChain.get_num_ancilla_qubitsr?r cUR(a/SSKJn U"URURUR 5nOSSKJn U"UR5nX lg)z0Define the MCX gate using a V-chain of CX gates.r)synth_mcx_n_dirty_i15)synth_mcx_n_clean_m15N)rNr rWr2rOrPrXr,)rrWrrXs rr.MCXVChain._define sP    O&$$$$!!B P&t';';rcs"/"(( 8aaaa33 FQF * % J'? @ u(Mu(u(pHa8FQ $FQ9FQRHatLZR%ZRMZRz   " ! !  *+}*+ *+ZIqM1S&1SN1ShHatLUR%URMURp88898888888:8889!( +} +)( +FHauMiR%iRNiRXS/nS/lK'K\O7Odr