z i!lSrSSKJr SSKrSSKrSSKJr SSKJ r SSK J r S S Sjjr Sr g) z Implementation of the GraySynth algorithm for synthesizing CNOT-Phase circuits with efficient CNOT cost, and the Patel-Hayes-Markov algorithm for optimal synthesis of linear (CNOT-only) reversible circuits. ) annotationsN)QuantumCircuit) QiskitError)synth_cnot_count_full_pmhc [U5n[U5n[US5[U5:wa [S5e[[ U55nUn/n[ R "[ R"[R"U555n[ R"U5RS5n [ U5GHn Sn UHn [ R"XU 5(aXS:XaURU 5 OXS:XaURU 5 OsXS:XaURU 5 OYXS:XaUR!U 5 O?XS:XaUR#U 5 O%UR%X[ R&-U 5 X [ R("XSS 9nU [U5:Xa MU S -n U S - n M GM UR+XU/5 U(GaUR-5up n U/:XaM#SU s=::aU:GaO GOS nU(GaS n[ U5GHnX:wdM [/X5[X5:XdM)S nUR1X5 X==X-ss'Sn UHn [ R"XU 5(aXS:XaURU 5 OXS:XaURU 5 OsXS:XaURU 5 OYXS:XaUR!U 5 O?XS:XaUR#U 5 O%UR%X[ R&-U 5 X [ R("XSS 9nU [U5:Xa OU S -n U S - n M [3XpX//-5HEnUun nU/:XaM[ [UU55HnUUU==UU U-ss'M MG GM U(aGMU /:XaGM U [ R4"U VVs/sHAnUVs/sH-n[7UR9S5UR9S 55PM/ snUPMC snn5n/n/n[[;[[=U655H;nUUS:XaUR+U5 MUUS :XdM*UR+U5 M= [[;[[=U655n[[;[[=U655nX:Xa7UR+U[[?U 5RAU/55U/5 O6UR+U[[?U 5RAU/55U /5 UR+U[[?U 5RAU/55U /5 U(aGMU[CX5RE5-nU$s snfs snnf) u This function is an implementation of the `GraySynth` algorithm of Amy, Azimadeh and Mosca. GraySynth is a heuristic algorithm from [1] for synthesizing small parity networks. It is inspired by Gray codes. Given a set of binary strings :math:`S` (called ``cnots`` bellow), the algorithm synthesizes a parity network for :math:`S` by repeatedly choosing an index :math:`i` to expand and then effectively recursing on the co-factors :math:`S_0` and :math:`S_1`, consisting of the strings :math:`y \in S`, with :math:`y_i = 0` or :math:`1` respectively. As a subset :math:`S` is recursively expanded, ``cx`` gates are applied so that a designated target bit contains the (partial) parity :math:`\chi_y(x)` where :math:`y_i = 1` if and only if :math:`y'_i = 1` for all :math:`y' \in S`. If :math:`S` contains a single element :math:`\{y'\}`, then :math:`y = y'`, and the target bit contains the value :math:`\chi_{y'}(x)` as desired. Notably, rather than uncomputing this sequence of ``cx`` (CNOT) gates when a subset :math:`S` is finished being synthesized, the algorithm maintains the invariant that the remaining parities to be computed are expressed over the current state of bits. This allows the algorithm to avoid the 'backtracking' inherent in uncomputing-based methods. The algorithm is described in detail in section 4 of [1]. Args: cnots: A matrix whose columns are the parities to be synthesized e.g.:: [[0, 1, 1, 1, 1, 1], [1, 0, 0, 1, 1, 1], [1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0]] corresponds to:: x1^x2 + x0 + x0^x3 + x0^x1^x2 + x0^x1^x3 + x0^x1 angles: A list containing all the phase-shift gates which are to be applied, in the same order as in ``cnots``. A number is interpreted as the angle of :math:`p(angle)`, otherwise the elements have to be ``'t'``, ``'tdg'``, ``'s'``, ``'sdg'`` or ``'z'``. section_size: The size of every section in the Patel–Markov–Hayes algorithm. ``section_size`` must be a factor of the number of qubits. Returns: The decomposed quantum circuit. Raises: QiskitError: when dimensions of ``cnots`` and ``angles`` don't align. References: 1. Matthew Amy, Parsiad Azimzadeh, and Michele Mosca. *On the controlled-NOT complexity of controlled-NOT–phase circuits.*, Quantum Science and Technology 4.1 (2018): 015002. `arXiv:1712.01859 `_ rz*Size of "cnots" and "angles" do not match.intttdgssdgz)axisTF)#lenrrlistrangenp transposearraycopydeepcopyeyeastype array_equalr r r r r ppideleteappendpopsumcx_remove_duplicatesargmaxmaxcountmapzipset differencerinverse)cnotsangles section_size num_qubitsqcir range_listepsilonsta cnots_copystatequbitindexicnotsilist conditionjxcnotsp_tttkrowcnots0cnots1ys h/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/linear_phase/cnot_phase_synth.pysynth_cnot_phase_aamrEstUJ * %D 58}F #FGGeJ'(JG Cbhht}}U';<=J FF:  % %e ,Ez" F~~fEl33=C'FF5M]e+HHUO]c)FF5M]e+HHUO]c)FF5MFF6=2550%8MYYzqA C O+  QJE'!#0JJ7+, # u B;   " " "I! z*A UX#eh-)G$( ) 0 !&0F!~~fElCC#)=C#7$(FF5M%+]e%;$(HHUO%+]c%9$(FF5M%+]e%;$(HHUO%+]c%9$(FF5M$(FF6=255+@%$H$*M-/YYzq-Q #(C O#;$) % !QJE''1("4C5;P:Q4Q!RA-.NVQ%| (',S^'< &q #&-2D D(= "S5+)D B;  "))\ab\aWXO#c#))A, ! =OPQR\abc dc$U ,-Atqy a 1 a . c$V -.c$V -.   JJSZ%:%:A3%? @!D E JJSZ%:%:A3%? @%H I FDU!6!6s!;rTsU # ))=DEa a$-a=@aaHrJ