z iSTSrSSKJr SSKJr SSKrSSKJr SSK J r J r J r SSK JrJr SSKJrJrJrJrJr SSS jjrSS jrSS jrSS jrSS jrSSjrSSSjjrSSjrSS Sjjr SSjr!SSjr"S!S"Sjjr#SS Sjjr$SSjr%SSjr&S#Sjr'S#Sjr(g)$zXModule containing multi-controlled circuits synthesis with and without ancillary qubits.) annotations)ceilN) QiskitError)QuantumCircuitQuantumRegisterAncillaRegister)HGateCU1Gate)c3xc4xsynth_mcx_n_dirty_i15synth_mcx_noaux_v24synth_mcx_noaux_hp24cB[R"[XU55$)a Synthesize a multi-controlled X gate with :math:`k` controls based on the paper by Iten et al. [1]. For :math:`k\ge 4` the method uses :math:`k - 2` dirty ancillary qubits, producing a circuit with :math:`2 * k - 1` qubits and at most :math:`8 * k - 6` CX gates. For :math:`k\le 3` explicit efficient circuits are used instead. Args: num_ctrl_qubits: The number of control qubits. relative_phase: when set to ``True``, the method applies the optimized multi-controlled X gate up to a relative phase, in a way that, by lemma 8 of [1], the relative phases of the ``action part`` cancel out with the phases of the ``reset part``. action_only: when set to ``True``, the method applies only the ``action part`` of lemma 8 of [1]. Returns: The synthesized quantum circuit. References: 1. Iten et. al., *Quantum Circuits for Isometries*, Phys. Rev. A 93, 032318 (2016), `arXiv:1501.06911 `_ )r_from_circuit_datasynth_mcx_n_dirty_i15_rs)num_ctrl_qubitsrelative_phase action_onlys i/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/multi_controlled/mcx_synthesis.pyr r #s!:  , , +N cSU-S- n[USS9n[USS9nUSUnX nX S-SnURUSUSUS5 Sn[SUS- 5H$nURXHXgXgS-5 US- nM& UR USXgU5 [ [SUS- 55H$nURXHXgS- Xg5 US-nM& URUSUSXg5 U$) a Synthesize a multi-controlled X gate with :math:`k` controls using :math:`k - 2` clean ancillary qubits with producing a circuit with :math:`2 * k - 1` qubits and at most :math:`6 * k - 6` CX gates, by Maslov [1]. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. References: 1. Maslov., Phys. Rev. A 93, 022311 (2016), `arXiv:1508.03273 `_ qname mcx_vchainNr)rrrccxrangeccxreversed) r num_qubitsrqc q_controlsq_target q_ancillasijs rsynth_mcx_n_clean_m15r+Es#"_$q(J -A  -B#O$J!HQ&()JGGJqM:a=*Q-8 A 1o) *  z}jQ.?@ Q+ FF:b>:=(3 eA23 4  za%0*-@ Q5 GGJqM:a=*-8 IrcbUS:Xa [5$US:Xa [5$US-n[USS9n[USS9n[ U5S- nUSnUS n[ US- 5n/US UQn[ [ U5S S 9n/UQUPX&XhR-[ U5- S- Qn /X&US- QUPn [ [ U 5S 9n /U QUPUSU R[ U 5- S- Qn URXS S9 URXS S9 URUR5U S S9 URXS S9 U$)a| Synthesize a multi-controlled X gate with :math:`k` controls using a single clean ancillary qubit producing a circuit with :math:`k + 2` qubits and at most :math:`16 * k - 24` CX gates, by [1], [2]. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. References: 1. Barenco et. al., *Elementary gates for quantum computation*, Phys.Rev. A52 3457 (1995), `arXiv:quant-ph/9503016 `_ 2. Iten et. al., *Quantum Circuits for Isometries*, Phys. Rev. A 93, 032318 (2016), `arXiv:1501.06911 `_ rrr mcx_recursiverrNT)rrrrinplace) synth_c3x synth_c4xrrlenrr r$composeinverse) rr$rr% q_ancillar'middle controls1mcx1qubits1 controls2mcx2 qc2_qubitss rsynth_mcx_1_clean_b95rApsh&!{ A { 1$J -A  0B!fqjO"IuH /A% &F!GV* I YPT UDa a9aq&??2JSQZ^2[^_2_'`aG=!_q01=9=I Y @DU9UhU1tY/ORS/S)TUJJJtdJ+JJtJ.JJt||~wJ5JJtJ. IrcVSSKJn US-n[USS9n[USS9nUR [ 5US//5 [ RSUS- -- n[U5nU"X0U5nUHupn UR XU 5 M UR [ 5US//5 U$) a[ Synthesize a multi-controlled X gate with :math:`k` controls using the Gray code. Produces a quantum circuit with :math:`k + 1` qubits. This method produces exponentially many CX gates and should be used only for small values of :math:`k`. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. r)_gray_code_chainrrrmcx_grayrr) (qiskit.circuit.library.standard_gates.u3rCrr_appendr nppir ) rrCr$rr% scaled_lam bottom_gate definitioninstrqargscargss rsynth_mcx_gray_coderOsJ 1$J -A  +BJJuw2$!! 345J*%K!!kBJ)e 5' *JJuw2$ IrcD[R"[U55nU$)av Synthesize a multi-controlled X gate with :math:`k` controls based on the implementation for MCPhaseGate. In turn, the MCPhase gate uses the decomposition for multi-controlled special unitaries described in [1]. Produces a quantum circuit with :math:`k + 1` qubits. The number of CX-gates is quadratic in :math:`k`. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. References: 1. Vale et. al., *Circuit Decomposition of Multicontrolled Special Unitary Single-Qubit Gates*, IEEE TCAD 43(3) (2024), `arXiv:2302.06377 `_ )rrsynth_mcx_noaux_v24_rsrcircs rrrs,  , ,-CO-T UD KrcD[R"[U55nU$)a Synthesize a multi-controlled X gate with :math:`k` controls based on the work by Huang and Palsberg. Produces a quantum circuit with :math:`k + 1` qubits. The number of CX-gates is linear in :math:`k`. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. References: 1. Huang and Palsberg, *Compiling Conditional Quantum Gates without Using Helper Qubits*, PLDI (2024), `_ )rrsynth_mcx_noaux_hp24_rsrRs rrrs&  , ,-D_-U VD KrcSU-n[USS9n[USU3S9nUSUX0SU-USU-SpvnU(aURU5 URXVU5 U$)a Construct a quantum circuit for creating n-condionally clean ancillae using 3n qubits. This implements Fig. 4a of [1]. The circuit applies n relative CCX (RCCX) gates . If apply_x is True, each RCCX gate is preceded by an X gate on the target qubit. The order of returned qubits is qr_a, qr_b, qr_target. Args: n: Number of conditionally clean ancillae to create. apply_x: If True, apply X gate to the target qubit. Returns: QuantumCircuit: The quantum circuit for creating n-conditionally clean ancillae. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ r-rrccxn_Nr)rrxr )napply_xn_qubitsrr%qr_aqr_b qr_targets r_n_parallel_ccx_xr_so&1uHs+A %s ,BbqE1Q<1q57 D YGGD " IrcxUS::a [S5eUS-n[U5n[[U55n[SUS- S5H5nUR X4S-X4S-X45 UR X45 M7 US-S:waUS- US- US- pvnOUS- US- US- pvnUS:a,UR X5X6X75 UR X75 [USS 5H8nUR X4X4S- X4S- 5 UR X4S- 5 M: S[ SSU- 5-nX8S- n X)4$) a Helper function to create linear-depth ladder operations used in Khattar and Gidney's MCX synthesis. In particular, this implements Step-1 and Step-2 on Fig. 3 of [1] except for the first and last CCX gates. Args: num_ladder_qubits: No. of qubits involved in the ladder operation. Returns: A tuple consisting of the linear-depth ladder circuit and the index of control qubit to apply the final CCX gate. Raises: QiskitError: If num_ladder_qubits <= 2. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ rz2n_ctrls >= 3 to use MCX ladder. Otherwise, use CCXrrr-r.r0)rrlistr!r rXmax) num_ladder_qubitsrYr%qregr)abtargetmid_second_ctrl final_ctrls r_linear_depth_ladder_opsrlsS*ANOOAA  B a>D1a!eQ  U Ta%[$'2 TW   1uz1ua!eQUff1ua!eQUf z $,/ T\ 61b ! !edq5k2 Ta%["#aQ-'O&*J >rcjUS::a [S5e[USS9n[SSS9n[SSS9n[X#USS9n[ U5upgUR US USUS 5 UR XdS S US S -S S 9 URXBUU5 UR UR5US S US S -S S 9 UR US USUS 5 U(dVUR XdS S US S -S S 9 URXBUU5 UR UR5US S US S -S S 9 U$) a Synthesize a multi-controlled X gate with :math:`k` controls using :math:`1` ancillary qubit as described in Sec. 5 of [1]. Args: num_ctrl_qubits: The number of control qubits. clean: If True, the ancilla is clean, otherwise it is dirty. Returns: The synthesized quantum circuit. Raises: QiskitError: If num_ctrl_qubits <= 2. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ rDkg24 synthesis requires at least 3 control qubits. Use CCX directly.ctrlrrtargancmcx_linear_depthrNTr2) rrrrrlr r7r"r8)rcleanr&r'r9r% ladder_opsrks rsynth_mcx_1_kg24ruLsR(!`aa v>Jqv.H.I  i>P QB5oFJGGJqM:a=)A,7JJzQ<*Q-7JFFF9,h7JJ! z!}$ GGJqM:a=)A,7  :|jm;T J yZ0(; :%%'1 1 )Et T Irc[USS9$)a. Synthesize a multi-controlled X gate with :math:`k` controls using :math:`1` clean ancillary qubit producing a circuit with :math:`2k-3` Toffoli gates or :math:`6k-6` CX gates and depth :math:`O(k)` as described in Sec. 5.1 of [1]. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. Raises: QiskitError: If num_ctrl_qubits <= 2. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ Trsrur1s rsynth_mcx_1_clean_kg24ry}( O4 88rc[USS9$)a0 Synthesize a multi-controlled X gate with :math:`k` controls using :math:`1` dirty ancillary qubit producing a circuit with :math:`4k-8` Toffoli gates or :math:`12k-18` CX gates and depth :math:`O(k)` as described in Sec. 5.3 of [1]. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. Raises: QiskitError: If num_ctrl_qubits <= 2. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ Frwrxr1s rsynth_mcx_1_dirty_kg24r|( O5 99rc :[[U5S-5nU/n/n[U5S:Ga[[[U5S-[U55nXSUSUpq/n[U5S:a[U5S-n [[U5S-5n XzX-XzU -SXI*Spn [U 5[U 5s=:Xa U s=:XaS:d4O [ S[U 5<S[U 5<S[U 5<35eX/:wa UR [ U 5X-U -SS9 O#U(dURU S U S U S 5 XU S- nXSU -nUSU *n[U5S:aM[XH-5nXW- n[U5S:aGM[XQ- n[U5nX5SS 4$) a Helper function to build a log-depth ladder compose of CCX and X gates as shown in Fig. 4b of [1]. Args: ancilla_idx: Index of the ancillary qubit. ctrls: List of control qubits. skip_cond_clean: If True, do not include the conditionally clean ancilla (step 1 and 5 in Fig. 4b of [1]). Returns: A tuple consisting of the log-depth ladder circuit of conditionally clean ancillae and the list of indices of control qubit to apply the linear-depth MCX gate. Raises: QiskitError: If no. of qubits in parallel CCX + X gates are not the same. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ rNrz(Invalid CCX gate parameters: len(ccx_x)=z != len(ccx_y)=z != len(ccx_n)=Tr2rr) rr6minintrr7r_r sorted) ancilla_idxctrlsskip_cond_cleanr%rq final_ctrlsnext_batch_len nxt_batchnew_ancccx_nstccx_xccx_yccx_ts r_build_logn_depth_ccx_ladderrs0 E Q 'B -CK e*q.SX\3u:6 15.3Iy)nq  Na'ES^a'(Brz*u*,'FG  E u:U9u99!?CJ=@PSZMQaVYZ_V`Ubc % ,U3U]U5JTX Y&GGE!HeAha9 ~ %G#2.Igv,C))nq ,S]# 7 e*q.:K%K 3B rcUS::a [S5e[USS9n[SSS9n[SSS9n[X#USS9n[ U[ [ U555upgURXbS S US /-S S 9 [U5S:XaURUS X'S U5 O>[[U5S-5nURUUS /X'-US S -US/-S S 9 URUR5US S US /-S S 9 U(d[ U[ [ U55S S 9upURXS S US /-S S 9 [U5S:XaURUS X'S U5 O'URWUS /X'-US S -US/-S S 9 URU R5US S US /-S S 9 U$)a Synthesize a multi-controlled X gate with :math:`k` controls using :math:`2` ancillary qubits. as described in Sec. 5 of [1]. Args: num_ctrl_qubits: The number of control qubits. clean: If True, the ancilla is clean, otherwise it is dirty. Returns: The synthesized quantum circuit. Raises: QiskitError: If num_ctrl_qubits <= 2. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ rrnrorrrprqmcx_logn_depthNrTr2)r) rrrrrrcr!r7r6r"ryr8) rrs q_controlr'r9r%rtrmid_mcxladder_ops_news rsynth_mcx_2_kg24rs(!`aaf=Iqv.H.I  Y=M NB:eO45JJJzQ<9Q<.8$JG ;1 y|Y1~6A([)9A)=>  q\N$ %qk |n   JJz!!#Yq\Yq\N%BDJQ &B T%"894' # >Q<9Q<.#@$ O { q FF9Q<q>!:H E JJ1!77(1+ESTV   >))+Yq\Yq\N-JTX Y Irc[USS9$)a5 Synthesize a multi-controlled X gate with :math:`k` controls using :math:`2` clean ancillary qubits producing a circuit with :math:`2k-3` Toffoli gates or :math:`6k-6` CX gates and depth :math:`O(\log(k))` as described in Sec. 5.2 of [1]. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. Raises: QiskitError: If num_ctrl_qubits <= 2. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ Trwrr1s rsynth_mcx_2_clean_kg24r*rzrc[USS9$)a7 Synthesize a multi-controlled X gate with :math:`k` controls using :math:`2` dirty ancillary qubits producing a circuit with :math:`4k-8` Toffoli gates or :math:`12k-18` CX gates and depth :math:`O(\log(k))` as described in Sec. 5.4 of [1]. Args: num_ctrl_qubits: The number of control qubits. Returns: The synthesized quantum circuit. Raises: QiskitError: If num_ctrl_qubits <= 2. References: 1. Khattar and Gidney, Rise of conditionally clean ancillae for optimizing quantum circuits `arXiv:2407.17966 `__ Frwrr1s rsynth_mcx_2_dirty_kg24rAr}rc>[R"[55$)z+Efficient synthesis of 3-controlled X-gate.)rrc3x_rsrrr4r4X  , ,VX 66rc>[R"[55$)z+Efficient synthesis of 4-controlled X-gate.)rrc4x_rsrrrr5r5]rr)FF)rrrboolrrreturnr)rrrr)T)rYrrZrrr)rerr tuple[QuantumCircuit, list[int]])rrrsrrr)F)rrrz list[int]rrrr)rr))__doc__ __future__rmathrnumpyrGqiskit.exceptionsrqiskit.circuit.quantumcircuitrrr%qiskit.circuit.library.standard_gatesr r -qiskit._accelerate.synthesis.multi_controlledr rr rr rrrQrrUr+rArOr_rlruryr|rrrrr4r5rrrrs_")ZZ ! D(V7t:4.@1h.b9.:0AF; ; &; 9=; %; |>B9.:.7 7r