z iP SrSSKJr SSKrSSKrSSKrSSKJrJrJ r SSK r SSK r SSK JrJr SSKJrJrJrJrJrJrJrJrJrJrJrJr SSKJr SSKJ r SS K!J"r" SS K#J$r$ SS K%J&r& \ (aSS K'J(r(J)r) \ RT"\+5r,\\\\\\\\\\\\S . r-SSjr."SS5r/"SS5r0"SS5r1"SS\15r2\2"5r3g)a Expand 2-qubit Unitary operators into an equivalent decomposition over SU(2)+fixed 2q basis gate, using the KAK method. May be exact or approximate expansion. In either case uses the minimal number of basis applications. Method is described in Appendix B of Cross, A. W., Bishop, L. S., Sheldon, S., Nation, P. D. & Gambetta, J. M. Validating quantum computers using randomized model circuits. arXiv:1811.12926 [quant-ph] (2018). ) annotationsN)OptionalType TYPE_CHECKING)QuantumCircuitGate) CXGateU3GateU2GateU1GateUGate PhaseGateRXGateRYGateRZGateSXGateXGateRGate) QiskitError)Operator) DEFAULT_ATOL)deprecate_func)two_qubit_decompose) DAGCircuit DAGOpNode) cxrxsxxrzupu1u2u3ryrcZ[R"U[S9n[R"U5upn[R "X5n[ [ UR5RRU5R55S- 5nUS:a[SU35eXU4$)zDecompose :math:`U = U_l \otimes U_r` where :math:`U \in SU(4)`, and :math:`U_l,~U_r \in SU(2)`. Args: special_unitary_matrix: special unitary matrix to decompose Raises: QiskitError: if decomposition isn't possible. dtypegvIh%<=zMdecompose_two_qubit_product_gate: decomposition failed: deviation too large: ) npasarraycomplexr decompose_two_qubit_product_gatekronabsconjTdottracer)special_unitary_matrixLRphasetemp deviations h/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/two_qubit/two_qubit_decompose.pyr/r/Qs ZZ(>gN'HHI_`MQ5 771=DC ))*@AGGIJQNOI7 $$-; 0  %=c@\rSrSr%SrS\S'S\S'S\S'S\S'S\S 'S\S 'S\S 'S\S 'S\S 'S\S'S\S'\RrS SS.S!Sjjjr \ "SSS9S5r SS\ S.S"Sjjr S#SjrSr\SS.S$Sjj5rSrSrg)%TwoQubitWeylDecompositioniaTwo-qubit Weyl decomposition. Decompose two-qubit unitary .. math:: U = ({K_1}^l \otimes {K_1}^r) e^{(i a XX + i b YY + i c ZZ)} ({K_2}^l \otimes {K_2}^r) where .. math:: U \in U(4),~ {K_1}^l, {K_1}^r, {K_2}^l, {K_2}^r \in SU(2) and we stay in the "Weyl Chamber" .. math:: \pi /4 \geq a \geq b \geq |c| This class avoids some problems of numerical instability near high-symmetry loci within the Weyl chamber. If there is a high-symmetry gate "nearby" (in terms of the requested average gate fidelity), then it return a canonicalized decomposition of that high-symmetry gate. References: 1. Cross, A. W., Bishop, L. S., Sheldon, S., Nation, P. D. & Gambetta, J. M., *Validating quantum computers using randomized model circuits*, `arXiv:1811.12926 [quant-ph] `_ 2. B. Kraus, J. I. Cirac, *Optimal Creation of Entanglement Using a Two-Qubit Gate*, `arXiv:0011050 [quant-ph] `_ 3. B. Drury, P. J. Love, *Constructive Quantum Shannon Decomposition from Cartan Involutions*, `arXiv:0806.4015 [quant-ph] `_ floatabc global_phase np.ndarrayK1lK2lK1rK2runitary_matrixzOptional[float]requested_fidelitycalculated_fidelityN)_specializationc[R"U[S9n[R"XUS9UlUR R UlUR RUlUR RUlUR RUl UR RUl UR RUl UR RUl UR RUl XlX lUR R Ul["R%[&R(5(a}UR+5n["R-SURUR U5 [/UR U- 5S:a$["R1SUR U- 5 ggg)Nr)fidelityrNzARequested fidelity: %s calculated fidelity: %s actual fidelity %sg-q=z.Requested fidelity different from actual by %s)r,r-r.rr?_inner_decompositionrBrCrDrErGrIrHrJrKrLrMlogger isEnabledForloggingDEBUGactual_fidelitydebugr1warning)selfrKrQrNrWs r<__init__"TwoQubitWeylDecomposition.__init__spN'B$7$Q$Q % !**,,**,,**,, 55BB,,00,,00,,00,,00,"*#'#<#<#P#P   w}} - -"224O LLS''((   4++o=>HD,,>I .r=z1.1.0zin the 2.0.0 release)sinceremoval_timelinec[e)zMake changes to the decomposition to comply with any specializations. This method will always raise a ``NotImplementedError`` because there are no specializations to comply with in the current implementation. )NotImplementedErrorrZs r< specialize$TwoQubitWeylDecomposition.specializes "!r=F euler_basissimplifyatolc`URRXUS9n[R"USS9$)z+Returns Weyl decomposition in circuit form.rdT legacy_qubits)rRcircuitr_from_circuit_data)rZrerfrg circuit_datas r<rk!TwoQubitWeylDecomposition.circuits90088#T9 00TRRr=c UR"S0UD6n[R"[U5RR R 5UR-5n[R"U5$)zNCalculates the actual fidelity of the decomposed circuit to the input unitary.) rkr,r5rdatar3r2rKr trace_to_fid)rZkwargscircr5s r<rW)TwoQubitWeylDecomposition.actual_fidelitysV||%f%$,,..3358K8KKL"//66r=c [U5RS3n[R"5n[R "X R SS9 [R"UR55R5nSSS5 WVs/sHn[U5PM nnUS==S- ss'[U5R5Vs/sHnSUR53PM nnSn[URR5R!S 5S n[U5RS U3n U/U-U-S UR"S3S U S3SUR$S3SUR'5S3SUR(UR*UR,4S3/-n UR/U 5$!,(df  GN7=fs snfs snf)zQRepresent with enough precision to allow copy-paste debugging of all corner casesz .from_bytes(F allow_pickleN,z# z .z._specializations.zrequested_fidelity=z_specialization=zcalculated_fidelity=zactual_fidelity=zabc=))type __qualname__ioBytesIOr,saverKbase64 encodebytesgetvalue splitlinesreprstrrstriprRspecializationsplitrLrMrWrBrCrDjoin) rZprefixfb64rb64asciiprettyindentspecialization_variantspecialization_reprliness r<__repr__"TwoQubitWeylDecomposition.__repr__sJ++,L9 ZZ\Q GGA** ?$$QZZ\2==?C&))SDGS)  -0Y-A-A-CD-CBqxxzl#-CD!$T%>%>%M%M!N!T!TUX!YZ[!\!%d!8!8 99KLbKcd H  &d&=&=%>a@"#6"7q9&t'?'?&@B"4#7#7#9":!</02   {{5!!+\*DsAF0 G G0 F?c A[R"U5n[R"U5n[R "USS9nSSS5 U"WX#S9$!,(df  N=f)z6Decode bytes into :class:`.TwoQubitWeylDecomposition`.FrwNrP)r decodebytesrrr,load)clsbytes_inrLrNrsrrarrs r< from_bytes$TwoQubitWeylDecomposition.from_bytessO   * ZZ_''!%0C3!3UU_s A A!c"[URR5RS5SnURR SUS3nSR URSS9RS5RS 55nUUS 3$) Nr{r|z [specialization=z] ( z T)rftextryz )) rrRrr __class____name__rrkdrawr)rZrpre circ_indents r<__str__!TwoQubitWeylDecomposition.__str__sT66EEFLLSQRST(()):>:J'Rkk$,,,"="B"B6"J"P"PQS"TU {m3''r=) rGrIrHrJrRrBrCrDrMrErLrK)gv?)rKrFrQ float | NonerN)two_qubit_decompose.Specialization | None)rez str | NonerfboolrgrAreturnr)rrA)rbytesrLrArNrrz'TwoQubitWeylDecomposition')r __module__r__firstlineno____doc____annotations__rSpecialization_specializationsr[rrbrrkrWr classmethodrr__static_attributes__rpr=r<r?r?is-"J H H H O O O O''*99 "." FJ """" C "H'4JK"L",0%WcS(S;?SOTS S7 "4 FJ VV" V C V %VV (r=r?cD\rSrSrSrSS SjjrS \S.S SjjjrSrg) TwoQubitControlledUDecomposeri zDecompose two-qubit unitary in terms of a desired :math:`U \sim U_d(\alpha, 0, 0) \sim \text{Ctrl-U}` gate that is locally equivalent to an :class:`.RXXGate`.c&URbB[R"URU5UlURRUlO[R"X5UlXlURRUlX lg)aInitialize the KAK decomposition. Args: rxx_equivalent_gate: Gate that is locally equivalent to an :class:`.RXXGate`: :math:`U \sim U_d(\alpha, 0, 0) \sim \text{Ctrl-U}` gate. Valid options are [:class:`.RZZGate`, :class:`.RXXGate`, :class:`.RYYGate`, :class:`.RZXGate`, :class:`.CPhaseGate`, :class:`.CRXGate`, :class:`.CRYGate`, :class:`.CRZGate`]. euler_basis: Basis string to be provided to :class:`.OneQubitEulerDecomposer` for 1Q synthesis. Valid options are [``'ZXZ'``, ``'ZYZ'``, ``'XYX'``, ``'XZX'``, ``'U'``, ``'U3'``, ``'U321'``, ``'U1X'``, ``'PSX'``, ``'ZSX'``, ``'ZSXX'``, ``'RR'``]. Raises: QiskitError: If the gate is not locally equivalent to an :class:`.RXXGate`. N) _standard_gaterr_inner_decomposername gate_namerxx_equivalent_gatescalere)rZrres r<r[&TwoQubitControlledUDecomposer.__init__sz"  - - 9%8%V%V#22K&D "1??DDDN%8%V%V#&D "$7 ++11 &r=)rgc~UR[R"U[S9U5n[R "USS9$)zReturns the Weyl decomposition in circuit form. Args: unitary (Operator or ndarray): :math:`4 imes 4` unitary to synthesize. Returns: QuantumCircuit: Synthesized quantum circuit. Note: atol is passed to OneQubitEulerDecomposer. r)Tri)rr,r-r.rrl)rZunitary approximateuse_dagrg circ_datas r<__call__&TwoQubitControlledUDecomposer.__call__/s4**2::gW+MtT 00$OOr=)rrerrrN)ZXZ)rz Type[Gate]rer)FF)rOperator | np.ndarrayrr) rrrrrr[rrrrpr=r<rr s;@'>JOPXdP,P PPr=rc\rSrSrSrSSSjjrSr\S5rSr Sr S r SSS .SS jjjr S r S rg)TwoQubitBasisDecomposeri@axA class for decomposing 2-qubit unitaries into minimal number of uses of a 2-qubit basis gate. Args: gate: Two-qubit gate to be used in the KAK decomposition. basis_fidelity: Fidelity to be assumed for applications of KAK Gate. Defaults to ``1.0``. euler_basis: Basis string to be provided to :class:`.OneQubitEulerDecomposer` for 1Q synthesis. Valid options are [``'ZYZ'``, ``'ZXZ'``, ``'XYX'``, ``'U'``, ``'U3'``, ``'U1X'``, ``'PSX'``, ``'ZSX'``, ``'RR'``]. pulse_optimize: If ``True``, try to do decomposition which minimizes local unitaries in between entangling gates. This will raise an exception if an optimal decomposition is not implemented. Currently, only [{CX, SX, RZ}] is known. If ``False``, don't attempt optimization. If ``None``, attempt optimization but don't raise if unknown. .. automethod:: __call__ Nc.XlX lX@lURUl[ R "U[U5RUUUS9Ul URRUl UR(d[R"SSS9 gg)N)basis_fidelityrepulse_optimizezEOnly know how to decompose properly for a supercontrolled basis gate.) stacklevel)gaterrrrrrrrqrsuper_controlledis_supercontrolledwarningswarn)rZrrrers r<r[ TwoQubitBasisDecomposer.__init__Ts ,,!4!L!L  TN  )#) " #'"8"8"I"I&& MMW 'r=cj[R"U[S9nURR U5$)zNComputes the number of basis gates needed in a decomposition of input unitary r))r,r-r.rnum_basis_gatesrZrs r<r'TwoQubitBasisDecomposer.num_basis_gatesns+**WG4%%55g>>r=c@[RRU5$)a4 Decompose target :math:`\sim U_d(x, y, z)` with :math:`0` uses of the basis gate. Result :math:`U_r` has trace: .. math:: \Big\vert\text{Tr}(U_r\cdot U_\text{target}^{\dag})\Big\vert = 4\Big\vert (\cos(x)\cos(y)\cos(z)+ j \sin(x)\sin(y)\sin(z)\Big\vert which is optimal for all targets and bases )rrdecomp0)targets r<rTwoQubitBasisDecomposer.decomp0us#::BB6JJr=c8URRU5$)atDecompose target :math:`\sim U_d(x, y, z)` with :math:`1` use of the basis gate :math:`\sim U_d(a, b, c)`. Result :math:`U_r` has trace: .. math:: \Big\vert\text{Tr}(U_r \cdot U_\text{target}^{\dag})\Big\vert = 4\Big\vert \cos(x-a)\cos(y-b)\cos(z-c) + j \sin(x-a)\sin(y-b)\sin(z-c)\Big\vert which is optimal for all targets and bases with ``z==0`` or ``c==0``. )rdecomp1rZrs r<rTwoQubitBasisDecomposer.decomp1s%%--f55r=c8URRU5$)a Decompose target :math:`\sim U_d(x, y, z)` with :math:`2` uses of the basis gate. For supercontrolled basis :math:`\sim U_d(\pi/4, b, 0)`, all b, result :math:`U_r` has trace .. math:: \Big\vert\text{Tr}(U_r \cdot U_\text{target}^\dag) \Big\vert = 4\cos(z) which is the optimal approximation for basis of CNOT-class :math:`\sim U_d(\pi/4, 0, 0)` or DCNOT-class :math:`\sim U_d(\pi/4, \pi/4, 0)` and any target. It may be sub-optimal for :math:`b \neq 0` (i.e. there exists an exact decomposition for any target using :math:`B \sim U_d(\pi/4, \pi/8, 0)`, but it may not be this decomposition). This is an exact decomposition for supercontrolled basis and target :math:`\sim U_d(x, y, 0)`. No guarantees for non-supercontrolled basis. )rdecomp2_supercontrolledrs r<r/TwoQubitBasisDecomposer.decomp2_supercontrolleds"%%==fEEr=c8URRU5$)z Decompose target with :math:`3` uses of the basis. This is an exact decomposition for supercontrolled basis :math:`\sim U_d(\pi/4, b, 0)`, all b, and any target. No guarantees for non-supercontrolled basis. )rdecomp3_supercontrolledrs r<r/TwoQubitBasisDecomposer.decomp3_supercontrolleds %%==fEEr=_num_basis_usesc[R"U[S9nU(aURR XX55$URR UUUUS9n[ R"USS9$)aQDecompose a two-qubit ``unitary`` over fixed basis and :math:`SU(2)` using the best approximation given that each basis application has a finite ``basis_fidelity``. Args: unitary (Operator or ndarray): :math:`4 \times 4` unitary to synthesize. basis_fidelity (float or None): Fidelity to be assumed for applications of KAK Gate. If given, overrides ``basis_fidelity`` given at init. approximate (bool): Approximates if basis fidelities are less than 1.0. use_dag (bool): If true a :class:`.DAGCircuit` is returned instead of a :class:`QuantumCircuit` when this class is called. _num_basis_uses (int): force a particular approximation by passing a number in [0, 3]. Returns: QuantumCircuit: Synthesized quantum circuit. Raises: QiskitError: if ``pulse_optimize`` is True but we don't know how to do it. r)rTri)r,r-r.rto_dag to_circuitrrl)rZrrrrrrs r<r TwoQubitBasisDecomposer.__call__ss8**WG4 ))00 ..99 / :I "44YdS Sr=cLURRUR5$)z Give the expected traces :math:`\Big\vert\text{Tr}(U \cdot U_\text{target}^{\dag})\Big\vert` for a different number of basis gates. )rtracesrRrs r<rTwoQubitBasisDecomposer.tracess! %%,,V-H-HIIr=)rrrrrr)g?UN)rrrrArerrz bool | None)NTF) rrrrrrrrrz int | NonerzQuantumCircuit | DAGCircuit)rrrrrr[r staticmethodrrrrrrrrpr=r<rr@s,!$&*   $ 4? K K 6F&F(,  (T'+(T&(T%(T (T  (T$(T %(TTJr=rcL\rSrSrSrSrSrS SjrSrSr Sr S r S r Sr g ) _LazyTwoQubitCXDecomposeri_innercSUlgNrras r<r["_LazyTwoQubitCXDecomposer.__init__s  r=cPURc[[55Ulggr)rrr ras r<_load_LazyTwoQubitCXDecomposer._loads ;; 1&(;DK r=cFUR5 UR"U0UD6$r)rr)rZargsrss r<r"_LazyTwoQubitCXDecomposer.__call__s {{D+F++r=cXUR5 URRU5$r)rrrrs r<r _LazyTwoQubitCXDecomposer.tracess  {{!!&))r=cXUR5 URRU5$r)rrrrs r<r!_LazyTwoQubitCXDecomposer.decomp1s  {{""6**r=cXUR5 URRU5$r)rrrrs r<r1_LazyTwoQubitCXDecomposer.decomp2_supercontrolled  {{226::r=cXUR5 URRU5$r)rrrrs r<r1_LazyTwoQubitCXDecomposer.decomp3_supercontrolledrr=cXUR5 URRU5$r)rrrrs r<r)_LazyTwoQubitCXDecomposer.num_basis_gatess  {{**733r=N)rr)rrrr __slots__r[rrrrrrrrrpr=r<rrs/I<,*+;;4r=r)r6rF)4r __future__rrrrtypingrrrrUnumpyr,qiskit.circuitrr%qiskit.circuit.library.standard_gatesr r r r r rrrrrrrqiskit.exceptionsrqiskit.quantum_info.operatorsr.qiskit.synthesis.one_qubit.one_qubit_decomposerqiskit.utils.deprecationrqiskit._acceleraterqiskit.dagcircuit.dagcircuitrr getLoggerrrS GATE_NAME_MAPr/r?rrrtwo_qubit_cnot_decomposerpr=r<rs # 00/    *242B   8 $              0`(`(F1P1Ph]J]JP 4 7 4F56 r=