z ii>SrSSKJr SSKJr SSKrSSKrSSKJ r J r SSK J r J r SSKJr SSKJr SS KJr SS KJrJr SS KJr SSS .SS jjjrSrSrSSSSS.SjjrSSjrSrSrSSjr g)zP Quantum Shannon Decomposition. Method is described in arXiv:quant-ph/0406176. ) annotations)CallableN)QuantumCircuitQuantumRegister)TwoQubitBasisDecomposertwo_qubit_decompose)one_qubit_decompose)is_hermitian_matrix)CXGate)UCPauliRotGate_EPS)"two_qubit_decompose_up_to_diagonal)_depthc ^!URSnUR5S- nUcSn[R"[R"U5U5(a [ U5$US:Xa"Uc[ R"5nU"U5nU$US:XaGUc/U(aUS:aSSKJ m! U!4Sjn U nO[[55n[U5nU"U5nU$Uc6Sn[U5H%n [X 5upp[X5(dM#SnM' USLaM[U5H>n [X 5upp[X5(dM#[!U U UUS UUS- U - S 9un nUs $ [#U5n[%[R&"U[(S 95unnnn[R*"SUS- -5n[!UUXS US 9unnn[!UUXSUS 9unnn[R,"S/US--S/US---5nUU-nU(aUU-U-U-U-nOUU-U-n[!UUXS US 9un n[ U5nUR/UR15U5 UR3US- 5 UR/U R15U5 UR3US- 5 UR/UR15U5 U(aUS:XaUS:a [5U5$U$)u Decomposes a unitary matrix into one and two qubit gates using Quantum Shannon Decomposition, based on the Block ZXZ-Decomposition. This decomposition is described in Krol and Al-Ars [2] and improves the method of Shende et al. [1]. .. code-block:: text ┌───┐ ┌───┐ ┌───┐ ─┤ ├─ ────□──┤ H ├──□──┤ H ├──□── │ │ ≃ ┌─┴─┐└───┘┌─┴─┐└───┘┌─┴─┐ /─┤ ├─ ──┤ C ├─────┤ B ├─────┤ A ├ └───┘ └───┘ └───┘ └───┘ The number of :class:`.CXGate`\ s generated with the decomposition without optimizations is the same as the unoptimized method in [1]: .. math:: \frac{9}{16} 4^n - \frac{3}{2} 2^n If ``opt_a1 = True``, the CX count is reduced, improving [1], by: .. math:: \frac{2}{3} (4^{n - 2} - 1). Saving two :class:`.CXGate`\ s instead of one in each step of the recursion. If ``opt_a2 = True``, the CX count is reduced, as in [1], by: .. math:: 4^{n-2} - 1. Hence, the number of :class:`.CXGate`\ s generated with the decomposition with optimizations is .. math:: \frac{22}{48} 4^n - \frac{3}{2} 2^n + \frac{5}{3}. Args: mat: unitary matrix to decompose opt_a1: whether to try optimization A.1 from [1, 2]. This should eliminate 2 ``cx`` per call. opt_a2: whether to try optimization A.2 from [1, 2]. This decomposes two qubit unitaries into a diagonal gate and a two ``cx`` unitary and reduces overall ``cx`` count by :math:`4^{n-2} - 1`. This optimization should not be done if the original unitary is controlled. decomposer_1q: optional 1Q decomposer. If None, uses :class:`~qiskit.synthesis.OneQubitEulerDecomposer`. decomposer_2q: optional 2Q decomposer. If None, uses :class:`~qiskit.synthesis.TwoQubitBasisDecomposer`. Returns: QuantumCircuit: Decomposed quantum circuit. References: 1. Shende, Bullock, Markov, *Synthesis of Quantum Logic Circuits*, `arXiv:0406176 [quant-ph] `_ 2. Krol, Al-Ars, *Beyond Quantum Shannon: Circuit Construction for General n-Qubit Gates Based on Block ZXZ-Decomposition*, `arXiv:2403.13692 `_ rT UnitaryGatecT>T"U5n[SSS9nURUSS/5 U$)Nrqsd2q)namerr)rappend)matugateqcrs V/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/unitary/qsd.py decomp_2q#qs_decomposition..decomp_2qs0',E'8BIIeaV,IFall)opt_a1opt_a2_vw_typer _ctrl_index)dtypeonly_w)r"r#r$ronly_v)shape bit_lengthnpallcloseidentityrr OneQubitEulerDecomposer0qiskit.circuit.library.generalized_gates.unitaryrrr _closest_unitaryrange_extract_multiplex_blocks_off_diagonals_are_zero _demultiplexr_block_zxz_decompasarraycomplexeyediagrto_instructionh _apply_a2)"rr"r# decomposer_1q decomposer_2qrdimnqubitscircr ctrl_indexum00um11um01um10decirc_qrA1A2BCiden left_circvmatC_wmatC right_circ_vmatAwmatAzmatB1B2 middle_circrs" @rqs_decompositionrZ#sV ))A,Cnn"G ~ {{2;;s#S))g&& ax  /GGIMS!  ax  &1* !* 7 A s#S!  ~.J%>s%O "D&t22).J%>s%O "D&t22+!!"! '! j 8  1 )  !B%RZZ7%CDLBAq 66!! $ %D+ a Iuf!- Bvx!J 77A3#(#rdcQh&77 8D B E\A  % , QY $ BvuVKA " DKK ((*B/FF7Q;KK **,b1FF7Q;KK ))+R0 &A+#' Kr cURSnUS-nUSU2SU24nUSU2US24nXS2SU24nXS2US24n[RRU5upxn [R "U5n UR 5Rn Xz-U -n Xy-n [RRU5upn[R "U5n UR 5RnX-U-nX-nUR 5RnSU-U -nUR 5RnU SU--U -nUR 5RnXVSUU ----nSUU--[R"U5- nUUUU4$)z7Block ZXZ decomposition method, by Krol and Al-Ars [2].rrNy?) r*scipylinalgsvdr,r:conjTr9)Umatr@nXYU21U22VXSWXdgSigmaVXdgSXUXVYWYdgVYdgSYUYUYdgCdgrNrKA1dgrLrMs rr6r6sx **Q-C qA RaR!V A RaRV A r2A2v,C r12v,C,,""1%KB4 GGAJE 779;;D d B B,,""1%KB4 GGAJE 779;;D d B B 779;;D t)b.C  A rBw," B 779;;D bD2I&' 'B TAX"A r1a<r cR[RRU5upnX-nU$)z0Find the closest unitary matrix to a matrix mat.)r\r]r^)rV_SWdgs rr1r1s(!!#&JA3 'C Jr r!)r$rr%cURSURS-nUR5S- nUcUS- n[[SU55[[US-U55-U/-n XRR 5-n [ U 5(a"[RRU 5upO0[RRU SS9upU R5n [RRU 5n[R"U5nXRR 5-U-n[!U5nUS;a4[#UX#US-S9R%5nUR'UU SUS- 5 S[R("[R*"U55-nUS :XaU(a [-UU5nO3US :Xa"U(a[-UU5R/5nO [-UUS S 9nUR'UU S /U SUS- -5 US;a3[#XX5S-S9R%5nUR'UU SUS- 5 UU U4$)uDecompose a generic multiplexer. ────□──── ┌──┴──┐ /─┤ ├─ └─────┘ represented by the block diagonal matrix ┏ ┓ ┃ um0 ┃ ┃ um1 ┃ ┗ ┛ to ┌───┐ ───────┤ Rz├────── ┌───┐└─┬─┘┌───┐ /─┤ w ├──□──┤ v ├─ └───┘ └───┘ where v and w are general unitaries determined from decomposition. Args: um0 (ndarray): applied if MSB is 0 um1 (ndarray): applied if MSB is 1 opt_a1 (bool): whether to try optimization A.1 from [1, 2]. This should eliminate two ``cx`` gates per call. opt_a2 (bool): whether to try optimization A.2 from [1, 2]. This decomposes two qubit unitaries into a diagonal gate and a two cx unitary and reduces overall ``cx`` count by 4^(n-2) - 1. This optimization should not be done if the original unitary is controlled. _vw_type (string): "only_v", "only_w" or "all" for reductions. This is needed in order to combine the vmat or wmat into the B matrix in [2], instead of decomposing them. _depth (int): This is an internal variable to track the recursion depth. _ctrl_index (int): The index wrt which um0 and um1 are controlled. Returns: QuantumCircuit: decomposed circuit rrNr8)output)r'r!)r"r#rrr'r(r!)r$r))r(r!)r*r+listr2r` conjugater r\r]eighschurdiagonalr,emathsqrtr:rrZr;rangler_ _get_ucrz reverse_ops)um0um1r"r#r$rr%r@rAlayoutum0um1eigvalsvmatevalsdvalsdmatwmatrB left_gateanglesucrz right_gates rr5r5s)V ))A,1 %Cnn"Gk %;' (4kAow0O+P PT_S` `F 55??$ $F6"" ))&1 ll(( (B .." HHMM' "E 775>D &&""$ $s *D ' "D$$$ vz .   Ivm! 45"''%.) )F8&) X &&)557&59KKvbzlVMgk%::;$$% z .   J}1 56 t r cD[U5nURSSnURSn[R"US[ U5S5 [ U5Hupg[ R"U5[:aURXu5 U[ U5S- :XdU[ R"US-5n[ U5[ URS55- n URXIU5 MUS:XdM[ U5S- n URXIU5 M U$)zTThis function synthesizes UCRZ without the final CX gate, unless _vw_type = ``all``.rNrF0r!) rqubitsr _dec_uc_rotationslen enumerater,absr rz binary_reprrstripcx) rArr$circuit q_controlsq_targetir binary_rep q_contr_indexs rrrOsW%G#J~~a H$$VQF UCf% 66%=4  JJu 'CK!O#A.J Oc*2C2CC2H.IIM JJz0( ;   Oa/M JJz0( ;& Nr cSSKJn SSKJn SSKJn [ nU"/SQSS9nU"U5n/n[UR5H2upU RRS:XdM!URU5 M4 [U5S:XaU$[U5S :Xa#S URUSRl U$S n [USS US S 5HupURU n U"U R5Rn URU nU"UR5RnU"U 5unn[R"U5nU R!UR#5S 9URU 'UU-nUR!U"U55URU 'M [$R&"W5nURU R!UR#5S 9URU 'U$)zThe optimization A.2 from [1, 2]. This decomposes two qubit unitaries into a diagonal gate and a two cx unitary and reduces overall ``cx`` count by 4^(n-2) - 1. This optimization should not be done if the original unitary is controlled. r)Operatorr)HighLevelSynthesis)urrF) basis_gatesqubits_initially_zerorrUnitaryNr)) operation)qiskit.quantum_inforr0r"qiskit.transpiler.passes.synthesisrrrdatarrrrzipr_from_circuit_datareplaceto_gatertwo_qubit_cnot_decompose)rBrrr decomposerhlsccircind2qr instructionind2ind1instr1mat1instr2mat2r qc2cx_dataqc2cxqc3s rr=r=es -LE3J )=UZ [C IE E#EJJ/  % % 0 LLO0 5zQ Uq.7 58&&+ D%",ac 3 D!(()..D!(()..%d+j11*=!>>EMMO>D 4d{!>>+d*;< 44  6 6t -Callable[[np.ndarray], QuantumCircuit] | Noner?r)FF)N)g-q=)!__doc__ __future__rtypingrr\numpyr,qiskit.circuit.quantumcircuitrrqiskit.synthesis.two_qubitrrqiskit.synthesis.one_qubitr (qiskit.quantum_info.operators.predicatesr %qiskit.circuit.library.standard_gatesr 5qiskit.circuit.library.generalized_gates.uc_pauli_rotr r &qiskit._accelerate.two_qubit_decomposerrZr6r1r5rr=r3r4r rrs # I;H8VUCGCG h h h h hA h A hV<$)X6;ASWXv,'T%"P Or