g'LdZddlmZddlmZddlmZmZddlm Z m Z m Z ddl m Z ddlmZmZddlmZd d gd d ggZd d gd d ggZeeGd d e ZeeGd de ZeedGdde ZdS)zSqrt(X) and C-Sqrt(X) gates.) annotations)pi)OptionalUnion) SingletonGateSingletonControlledGatestdlib_singleton_key)QuantumRegister)with_gate_arraywith_controlled_gate_array) StandardGatey??y?c|eZdZdZejZdddddfdZeZ dZ ddd Z ddfd Z dZ xZS)SXGateuaThe 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} Ndtdurationunitlabel Optional[str]cVtddg|||dS)zCreate new SX gate.sxrrrNsuper__init__selfrrr __class__s ^/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/standard_gates/sx.pyrzSXGate.__init__Fs. q"EH4PPPPPcDddlm}ddlm}ddlm}t dd}|||jtdz }||dggf||dggf||dggfg}|D]\}}} | ||| ||_ d S) z< gate sx a { rz(-pi/2) a; h a; rz(-pi/2); } rQuantumCircuitr)SdgGateHGateqname global_phaseN) qiskit.circuit.quantumcircuitr$sr%hr'r r+r_append definition) rr$r%r'r(qcrules operationqubitsclbitss r _definezSXGate._defineLs A@@@@@ As # # ^ADIBF C C C'))adVR(5577QqTFB*?''))aPQdVUWAXY). 2 2 %Ivv JJy&& 1 1 1 1r!F annotatedboolctS)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`. )SXdgGaterr8s r inversezSXGate.inverse\szzr!rnum_ctrl_qubitsint str | None ctrl_statestr | int | None bool | Nonec|s|dkrt|||j}n%t||||}|S)ahReturn 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)rrA _base_label)r>rrAr8)CSXGaterrcontrol)rr>rrAr8gaters r rGzSXGate.controljs^, _11:4:VVVDD77?? /%# #D  r!c,t|tSN) isinstancerrothers r __eq__z SXGate.__eq__s%(((r!rJrrFr8r9)rNNN)r>r?rr@rArBr8rC)__name__ __module__ __qualname____doc__r r_standard_gaterr _singleton_lookup_keyr7r=rGrN __classcell__rs@r rrs##J"(NQ4QQQQQQQQ1022      ! '+!% B)))))))r!rcfeZdZdZejZdddddfdZeZ dZ ddd Z d Z xZ S)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} NrrrrcVtddg|||dS)zCreate new SXdg gate.sxdgrrNrrs r rzSXdgGate.__init__s. BehTRRRRRr!cFddlm}ddlm}ddlm}t dd}|||jt dz }||dggf||dggf||dggfg}|D]\}}} | ||| ||_ d S) z< gate sxdg a { rz(pi/2) a; h a; rz(pi/2); } rr#r)SGater&r(r)r*N) r-r$r.r^r/r'r r+rr0r1) rr$r^r'r(r2r3r4r5r6s r r7zSXdgGate._defines A@@@@@ As # # ^ADIRC!G D D D%''AaD62&1Q4&"(=!A$QS?TU). 2 2 %Ivv JJy&& 1 1 1 1r!Fr8r9ctS)aReturn inverse SXdg gate (i.e. SX). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.SXGate`. Returns: SXGate: inverse of :class:`.SXdgGate` )rr<s r r=zSXdgGate.inverses xxr!c,t|tSrJ)rKr;rLs r rNzSXdgGate.__eq__s%***r!rJrOrPrQ)rRrSrTrUr r;rVrr rWr7r=rNrXrYs@r r;r;s6"*NS4SSSSSSSS1022     +++++++r!r;rr>cfeZdZdZejZ ddddddfd Zed Z d Z d Z xZ S)rFuGControlled-√X gate. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.csx` method. **Circuit symbol:** .. code-block:: text q_0: ──■── ┌─┴──┐ q_1: ┤ √X ├ └────┘ **Matrix representation:** .. math:: C\sqrt{X} \ q_0, q_1 = I \otimes |0 \rangle\langle 0| + \sqrt{X} \otimes |1 \rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & (1 + i) / 2 & 0 & (1 - i) / 2 \\ 0 & 0 & 1 & 0 \\ 0 & (1 - i) / 2 & 0 & (1 + i) / 2 \end{pmatrix} .. note:: In Qiskit's convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be `q_1`. Thus a textbook matrix for this gate will be: .. code-block:: text ┌────┐ q_0: ┤ √X ├ └─┬──┘ q_1: ──■── .. math:: C\sqrt{X}\ q_1, q_0 = |0 \rangle\langle 0| \otimes I + |1 \rangle\langle 1| \otimes \sqrt{X} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & (1 + i) / 2 & (1 - i) / 2 \\ 0 & 0 & (1 - i) / 2 & (1 + i) / 2 \end{pmatrix} Nr)rrrErrrAOptional[Union[str, int]]c xtddgd||t||| dS)zCreate new CSX gate.csxr)r)r>rrA base_gaterrN)rrr)rrrArrrErs r rzCSXGate.__init__sV   !;///  r!rracRddlm}ddlm}ddlm}t dd}|||j}||dggf|tdz |d|dggf||dggfg}|D]\}}} | ||| ||_ d S) z; gate csx a,b { h b; cu1(pi/2) a,b; h b; } rr#rr&)CU1Gaterfr()r+N) r-r$r/r'u1rir r+rr0r1) rr$r'rir(r2r3r4r5r6s r r7zCSXGate._define*s A@@@@@ As # # ^ADI . . .%''AaD62&a1Q41,(KeeggXYZ[X\W]_aMbc). 2 2 %Ivv JJy&& 1 1 1 1r!cLt|to|j|jkSrJ)rKrFrArLs r rNzCSXGate.__eq__:s!%))QdoAQ.QQr!)NN)rrrArc) rRrSrTrUr rFrVrr rWr7rNrXrYs@r rFrFs66p")N $04          ,10CCC RRRRRRRr!rFN)rU __future__rmathrtypingrrqiskit.circuit.singletonrrr qiskit.circuit.quantumregisterr qiskit.circuit._utilsr r qiskit._accelerate.circuitr _SX_ARRAY _SXDG_ARRAYrr;rFr!r rvs#"""""""""""""""aaaaaaaaaa::::::MMMMMMMM333333* % J'? @ J'*j)AB n)n)n)n)n)]n)n)n)bC+C+C+C+C+}C+C+C+LIq999dRdRdRdRdR%dRdR:9dRdRdRr!