gdZddlmZddlmZmZmZddlmZddl Z ddl m Z ddl m Z mZmZddlmZdd lmZmZmZdd lmZdd lmZdd gd dggZd dgdd ggZeeGdde Zeed GddeZeeddGddeZegdgdgdgdgdgdgdgd gGd!d"e Zeed#d$Gd%d&eZ eed#d$Gd'd(eZ!egd)gd*gd+gd,gd-gd.gd/gd0gd1gd2gd3gd4gd5gd6gd7gd8gGd9d:e Z"eed;d<Gd=d>eZ#Gd?d@e Z$GdAdBe$Z%GdCdDe$Z&GdEdFe$Z'dS)Gz(X, CX, CCX and multi-controlled X gates.) annotations)OptionalUnionType)piN)ControlledGate) SingletonGateSingletonControlledGatestdlib_singleton_key)QuantumRegister)_ctrl_state_to_intwith_gate_arraywith_controlled_gate_array) StandardGate)deprecate_funcy??y?c|eZdZdZejZdddddfdZeZ dZ ddfd Z dddZ dZ xZS)XGateuThe 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 Ndtdurationunitlabel Optional[str]cVtddg|||dS)zCreate new X gate.xrrrrNsuper__init__selfrrr __class__s ]/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/standard_gates/x.pyr zXGate.__init__Ns. a58$OOOOOcddlm}ddlm}t dd}|||j}|t dt |dggfg}|D]\}}}||||||_dS)z- gate x a { u3(pi,0,pi) a; } rQuantumCircuitr)U3GateqnameN) qiskit.circuit.quantumcircuitr(u3r)r r,r_append definition) r"r(r)r*qcrulesinstrqargscargss r$_definez XGate._defineTs A@@@@@ As # # ^ADI . . .&Q##adVR01#( , , E5% JJueU + + + +r%rFnum_ctrl_qubitsint ctrl_stateOptional[Union[str, int]] annotatedboolc|st||||j}n%t||||}|S)aTReturn 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: indicates whether the controlled gate should be implemented as an annotated gate. Returns: ControlledGate: controlled version of this gate. r7rr9 _base_labelr7rr9r;)MCXGaterrcontrolr"r7rr9r;gater#s r$rBz XGate.controldsb,  /% J DD77?? /%# #D  r%ctS)aReturn inverted X gate (itself). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as this gate is self-inverse. Returns: XGate: inverse gate (self-inverse). )rr"r;s r$inversez XGate.inverses wwr%c,t|tSN) isinstancerr"others r$__eq__z XGate.__eq__s%'''r%rIrrrNNFr7r8rrr9r:r;r<Fr;r<)__name__ __module__ __qualname____doc__rr_standard_gater r _singleton_lookup_keyr6rBrGrM __classcell__r#s@r$rrs++Z"'NP4PPPPPPPP1022$ !#04 $$$$$$$L     (((((((r%rr7ceZdZdZejZ ddddddfd Zed Z ddfd Z dddZ dZ xZ S)CXGateuControlled-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` Nrrrr?rrr9r:c ztddgd||t|||| dS)zCreate new CX gate.cxrr)r7rr9 base_gater?rrNrr rr"rr9rrr?r#s r$r zCXGate.__init__sY   !+...#  r%rr[Fr7r8r;r<c|s9t||}|j|z|z}t|dz|||j}n%t ||||}|S)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: indicates whether the controlled gate should be implemented as an annotated gate. Returns: ControlledGate: controlled version of this gate. rr>r@r r9rArrrBr"r7rr9r;new_ctrl_staterDr#s r$rBzCXGate.control( +JHHJ"o@JNN /! 3) J DD77?? /%# #D  r%c,t|jS)aReturn 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). r9)r]r9rFs r$rGzCXGate.inverses1111r%cLt|to|j|jkSrI)rJr]r9rKs r$rMz CXGate.__eq__,s!%((PT_@P-PPr%NNrrr9r:rOrPrQrR)rSrTrUrVrr]rWr r rXrBrGrMrYrZs@r$r]r]s==~"(N $04          .10CCC !#04 $$$$$$$L 2 2 2 2 2QQQQQQQr%r]ra))r7 cached_statesceZdZdZejZ ddddddfd Zed Z d Z ddfd Z dddZ dZ xZS)CCXGateuCCX gate, also known as Toffoli gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.ccx` and :meth:`~qiskit.circuit.QuantumCircuit.toffoli` methods. **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} Nrr^rrr9r:c xtddgd||t||| dS)zCreate new CCX gate.ccxrprarbr7rr9rcrrNrdres r$r zCCXGate.__init__xV   !+...  r%rar[cddlm}ddlm}ddlm}m}tdd}|||j}||d ggft|d|d ggf||d ggft|d|d ggf||d ggft|d|d ggf||d ggft|d|d ggf||dggf||d ggf||d ggft|d|dggf||dggf||dggft|d|dggfg}|D]\}} } | || | ||_ d S) z gate ccx a,b,c { h c; cx b,c; tdg c; cx a,c; t c; cx b,c; tdg c; cx a,c; t b; t c; h c; cx a,b; t a; tdg b; cx a,b;} rr'rHGate)TGateTdgGaterpr*r+raN) r-r(hrztr{r|r r,r]r/r0) r"r(rzr{r|r*r1r2r3r4r5s r$r6zCCXGate._defines  A@@@@@%%%%%%%% As # # ^ADI . . . UWWqtfb ! XX!ad|R ( WYY1 # XX!ad|R ( UWWqtfb ! XX!ad|R ( WYY1 # XX!ad|R ( UWWqtfb ! UWWqtfb ! UWWqtfb ! XX!ad|R ( UWWqtfb ! WYY1 # XX!ad|R ( "$) , , E5% JJueU + + + +r%rFr7r8r;r<c|s9t||}|j|z|z}t|dz|||j}n%t ||||}|S)Controlled 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: indicates whether the controlled gate should be implemented as an annotated gate. Returns: ControlledGate: controlled version of this gate. rar>r@rgrhs r$rBzCCXGate.controlrjr%c,t|jS)aReturn 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)rsr9rFs r$rGzCCXGate.inverse$/2222r%cLt|to|j|jkSrI)rJrsr9rKs r$rMzCCXGate.__eq__!%))QdoAQ.QQr%rnrorOrPrQrR)rSrTrUrVrrsrWr r rXr6rBrGrMrYrZs@r$rsrs0sBBH")N $04          ,10CCC+++^ !#04 $$$$$$$L 3 3 3 3 3RRRRRRRr%rs)rrrrrrrr)rrrrrrrr)rrrrrrrr)rrrrrrr)rrrrrrrr)rrrrrrr)rrrrrrrr)rrr?rrrrc\eZdZdZejZd dddd fdZeZ dZ d Z xZ S) RCCXGateaThe 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. NrrrrcVtddg|||dS)z!Create a new simplified CCX gate.rccxrprNrr!s r$r zRCCXGate.__init__s. BehTRRRRRr%c ddlm}ddlm}ddlm}t dd}|||j}|dt|d ggf|td z |d ggft|d|d ggf|t d z |d ggft|d|d ggf|td z |d ggft|d|d ggf|t d z |d ggf|dt|d ggfg }|D]\}}} | ||| ||_ d S) z gate rccx a,b,c { u2(0,pi) c; u1(pi/4) c; cx b, c; u1(-pi/4) c; cx a, c; u1(pi/4) c; cx b, c; u1(-pi/4) c; u2(0,pi) c; } rr'rU1GateU2Gaterpr*r+raN r-r(u1ru2rr r,rr]r/r0 r"r(rrr*r1r2r3r4r5s r$r6zRCCXGate._defines A@@@@@ As # # ^ADI . . . VAr]]QqTFB ' VBF^^adVR ( XX!ad|R ( VRC!G__qtfb ) XX!ad|R ( VBF^^adVR ( XX!ad|R ( VRC!G__qtfb ) VAr]]QqTFB '  $) , , E5% JJueU + + + +r%c,t|tSrI)rJrrKs r$rMzRCCXGate.__eq__>%***r%rIrN) rSrTrUrVrrrWr r rXr6rMrYrZs@r$rrs  "*NS4SSSSSSSS1022###J+++++++r%rrp)cfeZdZdZejZ ddddddfd Zed Z d Z d Z xZ S)C3SXGatezThe 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 Nrr^rrr9r:c |ddlm}tddgd|||||| dS) aCreate 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)SXGatec3sxrrprbrvN)sxrrr )r"rr9rrr?rr#s r$r zC3SXGate.__init__Nsj    !f;///  r%rpr[cddlm}ddlm}ddlm}t jdz }tdd }||d ggf|||d|d ggf||d ggft|d|dggf||d ggf|| |d|d ggf||d ggft|d|dggf||d ggf|||d|d ggf||d ggft|d|d ggf||d ggf|| |d |d ggf||d ggft|d|d ggf||d ggf|||d |d ggf||d ggft|d|d ggf||d ggf|| |d |d ggf||d ggft|d|d ggf||d ggf|||d |d ggf||d ggfg}||}|D]\}} } | || | ||_ d S) a gate c3sqrtx a,b,c,d { h d; cu1(pi/8) a,d; h d; cx a,b; h d; cu1(-pi/8) b,d; h d; cx a,b; h d; cu1(pi/8) b,d; h d; cx b,c; h d; cu1(-pi/8) c,d; h d; cx a,c; h d; cu1(pi/8) c,d; h d; cx b,c; h d; cu1(-pi/8) c,d; h d; cx a,c; h d; cu1(pi/8) c,d; h d; } rr'rCU1Gateryrr*r+rpraN) r-r(rrr}rznumpyrr r]r/r0) r"r(rrzangler*r2r1r3r4r5s r$r6zC3SXGate._definensR( A@@@@@1  AC ( ( ( UWWqtfb ! WU^^adAaD\2 . UWWqtfb ! XX!ad|R ( UWWqtfb ! WeV__qtQqTlB / UWWqtfb ! XX!ad|R ( UWWqtfb ! WU^^adAaD\2 . UWWqtfb ! XX!ad|R ( UWWqtfb ! WeV__qtQqTlB / UWWqtfb ! XX!ad|R ( UWWqtfb ! WU^^adAaD\2 . UWWqtfb ! XX!ad|R ( UWWqtfb ! WeV__qtQqTlB / UWWqtfb ! XX!ad|R ( UWWqtfb ! WU^^adAaD\2 . UWWqtfb !7 :^A  #( , , E5% JJueU + + + +r%cLt|to|j|jkSrI)rJrr9rKs r$rMzC3SXGate.__eq__s!%**Rt%BR/RRr%rnro) rSrTrUrVrrrWr r rXr6rMrYrZs@r$rrBs"*N $04          <10CCC;;;zSSSSSSSr%rceZdZdZejZ ddddddfd Zed Z d Z ddfd Z dddZ dZ xZS)C3XGateziThe X gate controlled on 3 qubits. This implementation uses :math:`\sqrt{T}` and 14 CNOT gates. Nr)r?rrrrr9r:c xtddgd||t||| dS)z'Create a new 3-qubit controlled X gate.mcxrrprbrvNrd)r"rr9r?rrr#s r$r zC3XGate.__init__rwr%rpr[cddlm}tdd}|||j}|d|t dz gd|dd |t dz d |dd |d d |t dz d |dd |t dz d |d d |t dz d |dd |d d|t dz d|d d|t dz d|d d|t dz d|dd|t dz d|d d|t dz d|d d|t dz d|d d|t dz d|dd|d||_d S) a gate c3x a,b,c,d { h d; p(pi/8) a; p(pi/8) b; p(pi/8) c; p(pi/8) d; cx a, b; p(-pi/8) b; cx a, b; cx b, c; p(-pi/8) c; cx a, c; p(pi/8) c; cx b, c; p(-pi/8) c; cx a, c; cx c, d; p(-pi/8) d; cx b, d; p(pi/8) d; cx c, d; p(-pi/8) d; cx a, d; p(pi/8) d; cx c, d; p(-pi/8) d; cx b, d; p(pi/8) d; cx c, d; p(-pi/8) d; cx a, d; h d; } rr'rr*r+rpr)rrrarprraN) r-r(r r,r}prr`r0)r"r(r*r1s r$r6zC3XGate._defines}J A@@@@@ AC ( ( ( ^ADI . . . Q R!V\\\""" a  bS1Wa a  a  bS1Wa a  R!VQ a  bS1Wa a  a  bS1Wa a  R!VQ a  bS1Wa a  R!VQ a  bS1Wa a  R!VQ a  bS1Wa a  Qr%rFr7r8r;r<c|s9t||}|j|z|z}t|dz|||j}n%t ||||}|S)rrpr>r@rgrhs r$rBzC3XGate.controlrjr%c,t|jS)aInvert 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)rr9rFs r$rGzC3XGate.inverse?rr%cLt|to|j|jkSrI)rJrr9rKs r$rMzC3XGate.__eq__Mrr%rnrorOrPrQrR)rSrTrUrVrrrWr r rXr6rBrGrMrYrZs@r$rrs ")N $04          ,10CCCFFFT !#04 $$$$$$$L 3 3 3 3 3RRRRRRRr%r)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrc\eZdZdZejZd dddd fdZeZ dZ d Z xZ S) RC3XGateaThe 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. NrrrrcVtddg|||dS)zCreate a new RC3X gate.rcccxrrNrr!s r$r zRC3XGate.__init__us. !RuxdSSSSSr%cddlm}ddlm}ddlm}t dd}|||j}|dt|d ggf|tdz |d ggft|d |d ggf|t dz |d ggf|dt|d ggft|d|d ggf|tdz |d ggft|d|d ggf|t dz |d ggft|d|d ggf|tdz |d ggft|d|d ggf|t dz |d ggf|dt|d ggf|tdz |d ggft|d |d ggf|t dz |d ggf|dt|d ggfg}|D]\}}} | ||| ||_ d S) a gate rc3x a,b,c,d { u2(0,pi) d; u1(pi/4) d; cx c,d; u1(-pi/4) d; u2(0,pi) d; cx a,d; u1(pi/4) d; cx b,d; u1(-pi/4) d; cx a,d; u1(pi/4) d; cx b,d; u1(-pi/4) d; u2(0,pi) d; u1(pi/4) d; cx c,d; u1(-pi/4) d; u2(0,pi) d; } rr'rrrrr*r+rpraNrrs r$r6zRC3XGate._define{s0 A@@@@@ As # # ^ADI . . . VAr]]QqTFB ' VBF^^adVR ( XX!ad|R ( VRC!G__qtfb ) VAr]]QqTFB ' XX!ad|R ( VBF^^adVR ( XX!ad|R ( VRC!G__qtfb ) XX!ad|R ( VBF^^adVR ( XX!ad|R ( VRC!G__qtfb ) VAr]]QqTFB ' VBF^^adVR ( XX!ad|R ( VRC!G__qtfb ) VAr]]QqTFB '% ($) , , E5% JJueU + + + +r%c,t|tSrI)rJrrKs r$rMzRC3XGate.__eq__rr%rIrN) rSrTrUrVrrrWr r rXr6rMrYrZs@r$rrQs*  "*NT4TTTTTTTT1022555n+++++++r%rr)cxeZdZdZ ddddddfd Zed Zd Z ddfd ZdddZ dZ xZ S)C4XGatea@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 Nrr^rrr9r:c |d}tddgd||t||| dS)z'Create a new 4-qubit controlled X gate.Nrrrrbrvrdres r$r zC4XGate.__init__s` <D   !+...  r%rr[c(ddlm}ddlm}ddlm}t dd}|||j}||d ggf|tj d z |d |d ggf||d ggft|d|d|d |d ggf||d ggf|tj d z |d |d ggf||d ggft |d|d|d |d ggft|d|d|d |d ggfg }|D]\}}} | ||| ||_d S) a gate c3sqrtx a,b,c,d { h d; cu1(pi/8) a,d; h d; cx a,b; h d; cu1(-pi/8) b,d; h d; cx a,b; h d; cu1(pi/8) b,d; h d; cx b,c; h d; cu1(-pi/8) c,d; h d; cx a,c; h d; cu1(pi/8) c,d; h d; cx b,c; h d; cu1(-pi/8) c,d; h d; cx a,c; h d; cu1(pi/8) c,d; h d; } gate c4x a,b,c,d,e { h e; cu1(pi/2) d,e; h e; rc3x a,b,c,d; h e; cu1(-pi/2) d,e; h e; rc3x a,b,c,d; c3sqrtx a,b,c,e; } rr'rrryrr*r+rrarpN)r-r(rrr}rzr r,rrrrGrr/r0) r"r(rrzr*r1r2r3r4r5s r$r6zC4XGate._defines8 A@@@@@ AC ( ( ( ^ADI . . . UWWqtfb ! WUX\ " "QqT1Q4L" 5 UWWqtfb ! ZZ!A$!adAaD12 6 UWWqtfb ! WehY] # #adAaD\2 6 UWWqtfb ! ZZ   ! !AaD!A$!ad#;R @ ZZ!A$!adAaD12 6  $) , , E5% JJueU + + + +r%rFr7r8r;r<c|s9t||}|j|z|z}t|dz|||j}n%t ||||}|S)rrr>r@rgrhs r$rBzC4XGate.controlrjr%c,t|jS)aInvert 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)rr9rFs r$rGzC4XGate.inverse5rr%cLt|to|j|jkSrI)rJrr9rKs r$rMzC4XGate.__eq__Crr%rnrorOrPrQrR) rSrTrUrVr r rXr6rBrGrMrYrZs@r$rrs $04          010CCC000h !#04 $$$$$$$L 3 3 3 3 3RRRRRRRr%rceZdZdZ d!ddddd"fd Z d#ddd dd d$fdZd%d&dZeedddd'd(dZ dZ e dZ d)d*fd Z xZS)+rAzThe general, multi-controlled X gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.mcx` method. Nrr^r7 Optional[int]rrr9r:cttd}||d}|5|||||} | |||||| St |S)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. )rraNrr9r?rr9r?rr)r]rsget__new__r r clsr7rr9rrr?explicit gate_classrDr#s r$rzMCXGate.__new__Ns"9?74K4K\\/488  !%%%JK&D MM%'!    Kwws###r%r)rr_namer?r8c |j|}t||dz|zg|||t |dS)zCreate new MCX gate.rrb)r7rr9rcN)r#get_num_ancilla_qubitsrr r) r"r7rr9rrrr?num_ancilla_qubitsr#s r$r zMCXGate.__init__psq"^BB?SS   a "4 4 +!+...      r%Fr;r<c8t|j|jS)aInvert 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). r7r9)rAr7r9rFs r$rGzMCXGate.inversest';XXXXr%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.1.3Tadditional_msgsincepending noancillamodestrreturnc|dkrdS|dvrt|dkS|dddks|ddd krtd|d z Std |d ) 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. rr) recursionadvancedrNrv-chainrbasicrazUnsupported mode (z ) specified!)r8maxAttributeErrorr7rs r$rzMCXGate.get_num_ancilla_qubitss( ;  1 , , ,*++ + 8y D!H$7$7q/A-.. .D$DDDEEEr%c@ddlm}||j}||_dS)z7This definition is based on MCPhaseGate implementation.r)synth_mcx_noaux_v24N)!qiskit.synthesis.multi_controlledrr7r0)r"rr1s r$r6zMCXGate._define5 JIIIII !5 6 6r%c@|j|jS)zThe number of ancilla qubits.)r#rr7)r"s r$rzMCXGate.num_ancilla_qubitss~44T5IJJJr%rc|s)|'||j|z|||j}n$t|||}|S)a!Return 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: indicates whether the controlled gate should be implemented as an annotated gate. Returns: ControlledGate: controlled version of this gate. Nr)rr9)r#r7rrrBrCs r$rBzMCXGate.controlse( XZ/>>$6% J "DD77???%J?WWD r%NNNr7rrrr9r:rnr7r8rrr9r:rQrR)r)r7r8rrrr8rOrP)rSrTrUrVrr rG staticmethodrrr6propertyrrBrYrZs@r$rArAGs*.#04 $   $ $ $ $ $ $ $ $J $04           . Y Y Y Y Y^ +    F F F F  \ FKKXK !#04 r%rAceZdZdZ ddddddfd Zed d d ddfd ZdddZdZxZ S) MCXGrayCodezImplement 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`. Nrr^r7rrrr9r:cttttd}||d}|6|||||||} | ||||| St|S)z!Create a new MCXGrayCode instance)rrarprNr)rr9rr)r]rsrrrrr rrs r$rzMCXGrayCode.__new__s'g'BB\\/488  !%%%'! &D MM%!     Kwws###r%agIt 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.rTrr8cRt|||ddS)Nmcx_grayrr9rr)r"r7rr9r#s r$r zMCXGrayCode.__init__s-" *T^_____r%Fr;r<c8t|j|jS)aInvert 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). r)rr7r9rFs r$rGzMCXGrayCode.inverses4+?DO\\\\r%c@ddlm}||j}||_dS)z(Define the MCX gate using the Gray code.r)synth_mcx_gray_codeN)rrr7r0)r"rr1s r$r6zMCXGrayCode._define'rr%rrrnrrQrR) rSrTrUrVrrr rGr6rYrZs@r$rrs*.#04 $  $$$$$$$$B^ N     $04 ``````  ` ] ] ] ] ]r%rceZdZdZeddd ddddddfdZedddZdddZdZ xZ S) MCXRecursiveaImplement 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 agIt 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 '1_clean_b95' for MCX gates, or, alternatively, one can use synth_mcx_1_clean to construct the gate directly.rTrNrr^r7r8rrr9r:c Xt|||d||ddS)N mcx_recursive)rr9rrrr?r)r"r7rr9rrr?r#s r$r zMCXRecursive.__init__=sE*  !!      r%rrrc8t||Sz*Get the number of required ancilla qubits.rArrs r$rz#MCXRecursive.get_num_ancilla_qubits\--otDDDr%Fr;r<c8t|j|jS)aInvert 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). r)rr7r9rFs r$rGzMCXRecursive.inverseasD,@T_]]]]r%c@ddlm}||j}||_dS)z$Define the MCX gate using recursion.r)synth_mcx_1_clean_b95N)rrr7r0)r"rr1s r$r6zMCXRecursive._defineos5 LKKKKK " "4#7 8 8r%rnr)rr7r8rrrQrR) rSrTrUrVrr rrrGr6rYrZs@r$rr0s  ^ L     $04             (EEEE\E ^ ^ ^ ^ ^r%rceZdZdZ ddddddddfdZeddd d ddddddd!fdZd"d#dZed$d%dZ dZ xZ S)& MCXVChainzBImplement the multi-controlled X gate using a V-chain of CX gates.NFr)rrr?relative_phase action_onlyr7rdirty_ancillasr<rrr9r:rrc Tt|||||||S)z}Create a new MCX instance. This must be defined anew to include the additional argument ``dirty_ancillas``. r)rr) rr7rrr9rrr?rrr#s r$rzMCXVChain.__new__|s9"ww  !#   r%aIt 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.rTrr8c t|||d|||||_||_| |_t|||ddS)aj 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_vchain)rr9rr?rrrN)rr _dirty_ancillas_relative_phase _action_only) r"r7rrr9rrr?rrr#s r$r zMCXVChain.__init__s~P  !#     .-' *T`aaaaar%r;c\t|j|j|j|j|jS)aInvert 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). )r7rr9rr)rr7rr9r r rFs r$rGzMCXVChain.inverses8 0//)     r%rrrc8t||Srrrs r$rz MCXVChain.get_num_ancilla_qubitsrr%c|jr#ddlm}||j|j|j}nddlm}||j}||_dS)z0Define the MCX gate using a V-chain of CX gates.r)synth_mcx_n_dirty_i15)synth_mcx_n_clean_m15N)rrrr7r r rr0)r"rr1rs r$r6zMCXVChain._definesz   = O O O O O O&&$$!BB P O O O O O&&t';<rsb/.""""""(((((((((( 888888aaaaaaaaaa::::::aaaaaaaaaa333333333333 FQF * % J'? @ {({({({({(M{({({(|Ha888PQPQPQPQPQ $PQPQ98PQfHatLLLARARARARAR%ARARMLARH         """   !!!   !!!   >+>+>+>+>+}>+>+  >+BIqMMMiSiSiSiSiS&iSiSNMiSXHatLLL^R^R^R^R^R%^R^RML^RB888888888999888888888888888888888:::888888888999!(N+N+N+N+N+}N+N+)(N+bHauMMMMRMRMRMRMR%MRMRNMMR`UUUUUnUUUpNNNNN'NNNbFFFFF7FFFR@@@@@@@@@@r%