z i):SrSSKJr SSKrSSKJr SSKJrJr SSK r SSK J r SSK J r SSKJrJr SS KJr "S S \ 5r"S S \ 5rSrSrg)zTwo-pulse single-qubit gate.) annotationsN)exp)OptionalUnion)ControlledGate)Gate)ParameterValueTypeParameterExpression) StandardGatec^\rSrSrSr\R rS S U4SjjjrS S Sjjr SSU4Sjjjr Sr SSjr Sr S rU=r$)U3GateuMGeneric single-qubit rotation gate with 3 Euler angles. .. warning:: This gate is deprecated. Instead, the following replacements should be used .. math:: U3(\theta, \phi, \lambda) = U(\theta, \phi, \lambda) .. code-block:: python circuit = QuantumCircuit(1) circuit.u(theta, phi, lambda) Circuit symbol: .. code-block:: text ┌───────────┐ q_0: ┤ U3(ϴ,φ,λ) ├ └───────────┘ Matrix representation: .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} U3(\theta, \phi, \lambda) = \begin{pmatrix} \cos\left(\rotationangle\right) & -e^{i\lambda}\sin\left(\rotationangle\right) \\ e^{i\phi}\sin\left(\rotationangle\right) & e^{i(\phi+\lambda)}\cos\left(\rotationangle\right) \end{pmatrix} .. note:: The matrix representation shown here differs from the `OpenQASM 2.0 specification `_ by a global phase of :math:`e^{i(\phi+\lambda)/2}`. Examples: .. math:: U3(\theta, \phi, \lambda) = P(\phi) R_Y(\theta) P(\lambda) = e^{i\frac{\phi + \lambda}{2}} R_Z(\phi) R_Y(\theta) R_Z(\lambda) .. math:: U3\left(\theta, -\frac{\pi}{2}, \frac{\pi}{2}\right) = RX(\theta) .. math:: U3(\theta, 0, 0) = RY(\theta) c*>[TU]SSXU/US9 g)a0 Args: theta: The angle :math:`\theta corresponding to the :math:`R_Y(\theta)` rotation. phi: The angle :math:`\phi` corresponding to the :math:`R_Z(\phi)` rotation. lam: The angle :math:`\lambda` corresponding to the :math:`R_Z(\lambda)` rotation. label: An optional label for the gate. u3labelN)super__init__)selfthetaphilamr __class__s b/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/u3.pyrU3Gate.__init__Xs  q5s"35Acp[URS*URS*URS*5$)aReturn inverted U3 gate. :math:`U3(\theta,\phi,\lambda)^{\dagger} =U3(-\theta,-\lambda,-\phi))` 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:`.U3Gate` with inverse parameter values. Returns: U3Gate: inverse gate. rr)r paramsr annotateds rinverseU3Gate.inversehs1t{{1~o AQHHrc>U(d8US:Xa2[URX#S.6nURURlU$Uc[ SUR55n[ TU]UUUUS9nU$)aReturn a (multi-)controlled-U3 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 set to ``True`` if the gate contains free parameters and more than one control qubit, in which case it cannot yet be synthesized. Otherwise it is set to ``False``. Returns: ControlledGate: controlled version of this gate. r)r ctrl_statec3B# UHn[U[5v M g7fN) isinstancer ).0ps r !U3Gate.control..sXKq 1.A B BKs)num_ctrl_qubitsrr&r")CU3Gater r base_gateanyrcontrol)rr.rr&r"gaters rr2U3Gate.controlxsx,_1DKKuLD#'::DNN   XDKKXX 7? /%# #D  rcSSKJn UR[RR UR 5SURS9UlgzDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr7_from_circuit_datar U3_get_definitionr r9 definitionrr7s r_defineU3Gate._definesA 2 );; OO + +DKK 8SWS\S\< rc USLa [S5eURup4n[U5[U5[U5pTn[R"US- 5n[R "US- 5n[ R"U[SU-5*U-/[SU-5U-[SXE--5U-//U=(d [S9$)z%Return a Numpy.array for the U3 gate.F9unable to avoid copy while creating an array as requestedr?dtype) ValueErrorr floatmathcossinnumpyarrayrcomplexrrFcopyrrrrJrKs r __array__U3Gate.__array__s 5=XY Y++C,c E#JChhuqy!hhuqy!{{s28}ns*+R#X$c" *:&;c&AB "7   rcR[U[5=(a URU5$r()r)r _compare_parametersrothers r__eq__ U3Gate.__eq__s%(LT-E-Ee-LLrr>r()rr rr rr r Optional[str]Fr"bool)rNNN)r.intrz str | Noner&zstr | int | Noner"z bool | NoneNN)__name__ __module__ __qualname____firstlineno____doc__r r<_standard_gaterr#r2r@rQrW__static_attributes__ __classcell__rs@rr r s8t"__N $ B!B B B  BB I$ ! '+!% %%%% %  %%N   MMrr c^\rSrSrSr\R rS SS.S U4SjjjjrSr S SSjjr S Sjr S r S r U=r$)r/ua Controlled-U3 gate (3-parameter two-qubit gate). This is a controlled version of the U3 gate (generic single qubit rotation). It is restricted to 3 parameters, and so cannot cover generic two-qubit controlled gates). .. warning:: This gate is deprecated. Instead, the :class:`.CUGate` should be used .. math:: CU3(\theta, \phi, \lambda) = CU(\theta, \phi, \lambda, 0) .. code-block:: python circuit = QuantumCircuit(2) gamma = 0 circuit.cu(theta, phi, lambda, gamma, 0, 1) Circuit symbol: .. code-block:: text q_0: ──────■────── ┌─────┴─────┐ q_1: ┤ U3(ϴ,φ,λ) ├ └───────────┘ Matrix representation: .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} CU3(\theta, \phi, \lambda)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + U3(\theta,\phi,\lambda) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\rotationangle) & 0 & -e^{i\lambda}\sin(\rotationangle) \\ 0 & 0 & 1 & 0 \\ 0 & e^{i\phi}\sin(\rotationangle) & 0 & e^{i(\phi+\lambda)}\cos(\rotationangle) \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: ┤ U3(ϴ,φ,λ) ├ └─────┬─────┘ q_1: ──────■────── .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} CU3(\theta, \phi, \lambda)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes U3(\theta,\phi,\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos(\rotationangle) & -e^{i\lambda}\sin(\rotationangle) \\ 0 & 0 & e^{i\phi}\sin(\rotationangle) & e^{i(\phi+\lambda)}\cos(\rotationangle) \end{pmatrix} N) _base_labelc@>[TU]SSXU/SUU[XX6S9S9 g)zCreate new CU3 gate.cu3rrr)r.rr&r0N)rrr )rrrrrr&rkrs rrCU3Gate.__init__s8    !U@  rcSSKJn UR[RR UR 5SURS9Ulgr6) r:r7r;r CU3r=r r9r>r?s rr@CU3Gate._define&sC 2);;    , ,T[[ 9TXT]T]< rc[URS*URS*URS*URS9$)aReturn inverted CU3 gate. :math:`CU3(\theta,\phi,\lambda)^{\dagger} =CU3(-\theta,-\phi,-\lambda))` 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:`.CU3Gate` with inverse parameter values. Returns: CU3Gate: inverse gate. rrr)r&)r/r r&r!s rr#CU3Gate.inverse5s< [[^Odkk!n_t{{1~o$//  rc USLa [S5eURup4n[U5[U5[U5pTn[R"US- 5n[R "US- 5nUR (ab[R"/SQSUS[SU-5*U-//SQS[SU-5U-S[SXE--5U-//U=(d [S9$[R"US[SU-5*U-S//S Q[SU-5U-S[SXE--5U-S//S Q/U=(d [S9$) z&Return a numpy.array for the CU3 gate.FrCr)rrrrrrD)rrrrrE)rrrr)rrrr) rGr rHrIrJrKr&rLrMrrNrOs rrQCU3Gate.__array__Hs< 5=XY Y++C,c E#JChhuqy!hhuqy! ??;; QR#X 45 BH +QB#)4D0E0KL  &w ;;!c"s(m^c115 c]S(!Ssy1A-BS-H!L  &w rc[U[5=(a1 URUR:H=(a URU5$r()r)r/r&rTrUs rrWCU3Gate.__eq__es; ug & 05#3#33 0((/ rrYr_) rr rr rr rrZr&zOptional[Union[str, int]]r[r\)r`rarbrcrdr rprerr@r#rQrWrfrgrhs@rr/r/s|L\"%%N $04   !       .   *   &:  rr/c US::a [S5eS/n[U5H'nU[U5Vs/sH o3SU--PM sn- nM) UVs/sHn[USUS35PM sn$s snfs snf)z-Generate the gray code for ``num_bits`` bits.rz2Cannot generate the gray code for less than 1 bit.r0b)rGrangereversedformat)num_bitsresultixs r_generate_gray_coderms|1}MNNSF 8_Xf%56%5q!t8%56606 71F1(1o & 777 7s A,A1cSSKJn /nUSUXpe[U5nSnUGH:n SU ;aM UcU n[U 5R S5n [ X5V V s/sH upX:gPM n n n SU ;aU R S5nOSnUbxX:wa UR U"5X^XZ//45 OS[U 5V Vs/sHupUS:XdM U PM nn nUSSH#nUR U"5UUXZ//45 M% U RS5S-S:Xa'UR UR5XZU//45 OUR X%U U//45 U nGM= U$s sn n fs snn f)a+Apply the gate to the last qubit in the register ``q``, controlled on all preceding qubits. This function uses the gray code to propagate down to the last qubit. Ported and adapted from Aqua (github.com/Qiskit/qiskit-aqua), commit 769ca8d, file qiskit/aqua/circuits/gates/multi_control_u1_gate.py. r)CXGateN1Trr) rrrlistindexzipappend enumeratecountr#)qr.r3rrule q_controlsq_target gray_code last_patternpatternlm_posrjcompposrindicesidxs r_gray_code_chainrws D-o.0B#O4IL g    "Lg$$S)$'w#=>#=41#=> 4<**T"CC ?} VX 9K'LbQR)27);H);qCx1);H"12;CKKJsOZ=O+PRT UV' ==  !Q & KK**rsO#" " 8$V3bMTbMJj nj Z8+r