z iGSrSSKJr SSKrSSKJr SSKJr SSKrSSK J r J r SSK r SSKJr SS KJrJr "S S 5rS rS rSSjrg)zZ2Symmetries for SparsePauliOp.) annotationsN)Iterable)deepcopy)Unioncast) QiskitError)Pauli SparsePauliOpc\rSrSrSrSSS.SSjjjr\SSj5r\SSj5r\SS j5r \SS j5r \SS j5r S r SS jr \SSj5rSSjrSSjrSSjrSSjrS SjrSrg)! Z2Symmetriesa The $Z_2$ symmetry converter identifies symmetries from the problem hamiltonian and uses them to provide a tapered - more efficient - representation of operators as Paulis for this problem. For each identified symmetry, one qubit can be eliminated in the Pauli representation at the cost of having to test two symmetry sectors (for the two possible eigenvalues - tapering values - of the symmetry). In certain problems such as the finding of the main operator's ground state, one can a priori identify the symmetry sector of the solution and thus effectively reduce the computational overhead. The following attributes can be read and updated once the ``Z2Symmetries`` object has been constructed. Attributes: tapering_values (list[int] or None): Values determining the sector. tol (float): The tolerance threshold for ignoring real and complex parts of a coefficient. References: [1]: Bravyi, S., et al, "Tapering off qubits to simulate fermionic Hamiltonians" `arXiv:1701.08213 `__ Ng+=)tolc[U5n[U5n[U5nUcSO [U5n[U5[U5:wa$[S[U5S[U5S35e[U5[U5:wa$[S[U5S[U5S35eUb<[U5[U5:wa$[S[U5S[U5S 35eXlX lX0lX@lXPlg) a Args: symmetries: Object representing the list of $Z_2$ symmetries. These correspond to the generators of the symmetry group $\langle \tau_1, \tau_2\dots \rangle>$. sq_paulis: Object representing the list of single-qubit Pauli $\sigma^x_{q(i)}$ anti-commuting with the symmetry $\tau_i$ and commuting with all the other symmetries $\tau_{j\neq i}$. These operators are used to construct the unitary Clifford operators. sq_list: The list of indices $q(i)$ of the single-qubit Pauli operators used to build the Clifford operators. tapering_values: List of eigenvalues determining the symmetry sector for each symmetry. tol: Tolerance threshold for ignoring real and complex parts of a coefficient. Raises: QiskitError: Invalid paulis. The lists of symmetries, single-qubit paulis support paulis and tapering values must be of equal length. This length is the number of applied symmetries and translates directly to the number of eliminated qubits. NzThe number of Z2 symmetries, zK, has to match the number of single-qubit pauli operators, .z,The number of single-qubit pauli operators, zG, has to match the length of the of single-qubit list, z%The length of the single-qubit list, zD, must match the length of the tapering values, z .)listlenr _symmetries _sq_paulis_sq_listtapering_valuesr)self symmetries sq_paulissq_listrrs d/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/analysis/z2_symmetries.py__init__Z2Symmetries.__init__2s4*% O w-"1"9$tO?T z?c)n ,/J/@A225i.1AD  y>S\ )>s9~>NO..1'l^1>   &7|s?33!;CL>J&&)/&:%;2? &# .cUR$)zReturn symmetries.)rrs rrZ2Symmetries.symmetriesjsrcUR$)zReturn sq paulis.)rr!s rrZ2Symmetries.sq_paulisosrc[URUR5VVs/sH3up[U5[U5-[R "S5- PM5 nnnU$s snnf)z Get clifford operators, built based on symmetries and single-qubit X. Returns: A list of unitaries used to diagonalize the Hamiltonian. r )ziprrr mathsqrt)r pauli_symmsq_pauli cliffordss rr+Z2Symmetries.cliffordstsa),D,<,'Z2Symmetries.__str__..s'C?a?sz - Possible values:  ) appendrto_labelrr+strrr itertoolsproductrrjoin)rretsymmetryr;ccoeffpossible_valuess r__str__Z2Symmetries.__str__sf  =!((H JJx((* +) *+A JJqzz| $! < A JJs1v   >" 3t}}%& %&    '.7.?.?BPSTXTaTaPb.c.cUDK .c #ii'C?'CCO JJ.@ A JJs4//0 1iin sG c[UR5S:H=(d7 [UR5S:H=(d [UR5S:H$)zF Check the z2_symmetries is empty or not. Returns: Empty or not. r)rrrrr!s ris_emptyZ2Symmetries.is_emptysA4##$)aS-AQ-Fa#dmmJ\`aJaarc ^^^^/n/n/n/nSS/SS/SS/S.nSS/SS/SS/S.nSS/SS/SS/S.n[U5(a U"///S 5$[U5Hjn UR[R"U R R S U R RS 4S S 9R[55 Ml [R"U5n [U 5n U (d U"///S 5$[R"U 5mTRmTS S -m[TS 5V s/sHn [R"TU S S 9PM sn mSUUUU4Sjjn [TS 5Hn UR[TU S T24TU TS 24455 [T5HnSHnU "XXoX5nU(dMUR[[R "T5[R "T5455 XS X<RU'XS X<R U'URU5 O W(dM M M U"X#US 5$s sn f)zi Finds Z2 Pauli-type symmetries of a :class:`.SparsePauliOp`. Returns: A ``Z2Symmetries`` instance. )rr)r3r)r3r3)rr3)X_or_IY_or_IZ_or_I)rRrPrQFTNraxisr3r c >[R"[T SS- 5Vs/sHnTUXA4TUXAT-44U;PM sn5nT X4T XT-44U;n[[R"U55=(a U$s snf)a~ Utility method that determines how to build the list of single-qubit Pauli X operators and the list of corresponding qubit indices from the stacked symmetries. This method is successively applied to Z type, X type and Y type symmetries (in this order) to build the letter at position (col) of the Pauli word corresponding to the symmetry at position (row). Args: row (int): Index of the symmetry for which the single-qubit Pauli X operator is being built. col (int): Index of the letter in the Pauli word corresponding to the single-qubit Pauli X operator. idx_test (list): List of possibilities for the stacked symmetries at all other rows than row. row_test (list): List of possibilities for the stacked symmetries at row. Returns: Whether or not this symmetry type should be used to build this letter of this single-qubit Pauli X operator. rr3)nparrayrangeboolall) rowcolidx_testrow_testsymm_idxstacked_symm_idx_testsstacked_symm_row_testhalf_symm_shapestacked_symm_delstacked_symmetries symm_shapes r_test_symmetry_row_col?Z2Symmetries.find_z2_symmetries.._test_symmetry_row_cols*&(XX%**Q-!*;$<  %= )-hm<(-ho8M.MN  %=  & "#38,"3o(=#=>%% ! 567Q>!3DEANUUVYZ $ .1/ r2r4( (XXj1'-- $Q-1,BG ST BV BV3BII(#A 6BV % R% RNA'C  # #*30@0@+@A*30@+@A _-9C*@(-+'+*!((!288O#W"XY1;0B ((-0:0B ((-s+:'&.(<#>>S s2 I&cUR5(dG[U5(d7URH'n[[X!-U-5nUR SS9nM) U$)aThis method operates the first part of the tapering. It converts the operator by composing it with the clifford unitaries defined in the current symmetry. Args: operator: The to-be-tapered operator. Returns: ``SparsePauliOp`` corresponding to the converted operator. atol)rMrjr+rr simplify)rrvcliffords rconvert_cliffordZ2Symmetries.convert_clifford/sV}}'?'I'I NN x/BX/MN#,,#,6+rc <UR5(aUnU$URcU[R"SS/[ UR 5S9Vs/sHnUR U[U55PM nnU$UR XR5nU$s snf)aOperate the second part of the tapering. This function assumes that the input operators have already been transformed using :meth:`convert_clifford`. The redundant qubits due to the symmetries are dropped and replaced by their two possible eigenvalues. Args: operator: Partially tapered operator resulting from a call to :meth:`convert_clifford`. Returns: If tapering_values is None: [:class:`SparsePauliOp`]; otherwise, :class:`SparsePauliOp`. r3r4r5)rMrrBrCrr_taperr)rrv tapered_opsrHs rtaper_cliffordZ2Symmetries.taper_cliffordDs ==??"K##+"+!2!2Ar73t}}CU!V!VKK$u+6!V#kk(4H4HI s%BcJURU5nURU5nU$)ar Taper an operator based on the z2_symmetries info and sector defined by `tapering_values`. Returns operator if the symmetry object is empty. The tapering is a two-step algorithm which first converts the operator into a :class:`SparsePauliOp` with same eigenvalues but where some qubits are only acted upon with the Pauli operators I or X. The number M of these redundant qubits is equal to the number M of identified symmetries. The second step of the reduction consists in replacing these qubits with the possible eigenvalues of the corresponding Pauli X, giving 2^M new operators with M less qubits. If an eigenvalue sector was previously identified for the solution, then this reduces to 1 new operator with M less qubits. Args: operator: The to-be-tapered operator. Returns: If tapering_values is None: [:class:`SparsePauliOp`]; otherwise, :class:`SparsePauliOp`. )rr)rrv converted_opsrs rtaperZ2Symmetries.tapercs*.--h7 ))-8 rcX/n[U5GHYnURSn[UR5HNupgURR SU4(d"URR SU4(dMGX&U-nMP [R"URR SR5[R"UR55n[R"URR SR5[R"UR55n UR[X45R5U45 GM\ [R"U5R!SS9n U R#UR$5n U $)Nrrr)rkcoeffs enumeraterrmrnr;rVrscopyasarrayr?r r@r from_listrchopr) ropcurr_tapering_values pauli_list pauli_term coeff_outidx qubit_idxz_tempx_tempspos rrZ2Symmetries._tapersD r(J"))!,I"+DMM":$$&&q)|4 8I8I8K8KAyL8Y8Y 4 9I EI#;YYz002215::WXFYYz002215::WXF   uf%56??A9M N#%%j1:::Dhhtxx  rc [U[5(dgURUR:H=(aY URUR:H=(a9 URUR:H=(a UR UR :H$)z Overload `==` operation to evaluate equality between Z2Symmetries. Args: other: The `Z2Symmetries` to compare to self. Returns: A bool equal to the equality of self and other. F) isinstancer rrrr)rothers r__eq__Z2Symmetries.__eq__sr%.. OOu// / >%//1 >  - >$$(=(==  r)rrrrrr8) rIterable[Pauli]rrrz Iterable[int]rzIterable[int] | Nonerfloat)riz list[Pauli])rizlist[SparsePauliOp])ri list[int])ridict)rirY)rvr rir )rvr rir )rvr riz)Union[SparsePauliOp, list[SparsePauliOp]])rr rrrir )rr rirY)__name__ __module__ __qualname____firstlineno____doc__rpropertyrrr+rr0rJrM classmethodrrrrrr__static_attributes__r9rrr r s215 66#6#6 6 . 66p      4bx?x?t*>8  rr c&URn/n[R"U[R"US545n[ UR 55R 5n[ US5Hn[R"USUS2U4[R"US55(dMB[R"XASS2U4[R"US55(aMURXASS2U45 M U$)z Compute the kernel of a binary matrix on the binary finite field. Args: matrix_in (numpy.ndarray): Binary matrix. Returns: The list of kernel vectors. r3rN) rrrVvstackidentity_row_echelon_f2 transposerX array_equalrtr?) matrix_insizekernel matrix_in_idmatrix_in_id_echr\s rrqrqs ??D F99iT!W)=>?L' (>(>(@ALLNT!W~ >> Qa[#- .a0A  ..!1q')S.!A288DQRGCTUU MM*79c>: ;  Mrc URn[US5H|nSn[US5HnXU4S:XdMUn O [US5HBnXR:wdM XU4S:XdM[R"XSS24XSS24-S5XSS24'MD M~ [ U5n/n[R "U5n[USS- 5HOn[R "XbSS24[R "US55(dM>URU5 MQ [R"U5SSS2Hn [R"XiSS9nM XhSUS[U5- 2SS24'UR[5nU$)z Compute the row Echelon form of a binary matrix on the binary finite field. Args: matrix_in (numpy.ndarray): Binary matrix. Returns: Matrix_in in Echelon row form. rr3Nr r4rS) rrrXrVmodrrtrr?sortrsrrorh) rri pivot_indexjkmatrix_out_tempindices matrix_outr[s rrrsf ??D 47^ tAwAA!#  tAwAv){N3q8"$&&a49T?)JA"N Q$ y)OG$J 47Q;  >>/Q$/$q'1B C C NN1  www"%))OC&1@q47S\))1,-""3'J rcUR5n[UR5S:H=(a URSS:H$)zAReturns whether or not this operator represents a zero operation.r3r)rrr)rs rrjrjs2 B ryy>Q  4299Q<1#44r)rr rirY)r __future__rrBcollections.abcrrrr'typingrrnumpyrVqiskit.exceptionsr operatorsr r r rqrrjr9rrrsB&"$ ),C C L 0#L5r