z i-04SrSSKrSSKJrJr "SS5rg)zQ Matrix designed for fast multiplication by permutation and block-diagonal ones. N)Layer1QLayer2Qc\rSrSrSrS\4SjrS\R4Sjr \ S\S\R4S j5r S \ S \RS \ 4S jrSS \S \RS \ 4SjjrS \ S \R4SjrS \S \R4SjrS \ S\RS\RS\R&4SjrS \S\RS\RS\R&4SjrS \RS\R4SjrSrg)PMatrixzk Wrapper around a matrix that enables fast multiplication by permutation matrices and block-diagonal ones. num_qubitscSU-n[R"S5UlX l[R"S[R S9Ul[R"S[R S9UlUR R5Ul URR5Ul [R"U[RS9Ul URR5UlURR5UlURR5Ul[R"US4[R S9Ul[R"US4[R S9UlUR'U5Ul[R"UR(R*[R S9Ulg)z~ Initializes the internal structures of this object but does not set the matrix yet. Args: num_qubits: number of qubits. r)r r dtyperrN)npempty_mat_dimzeros complex128 _temp_g2x2 _temp_g4x4copy _temp_2x2 _temp_4x4arangeint64_identity_perm _left_perm _right_perm _temp_perm_temp_slice_dim_x_2_temp_slice_dim_x_4_init_index_matrix_idx_matshape_temp_block_diag)selfr dims l/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/unitary/aqc/fast_gradient/pmatrix.py__init__PMatrix.__init__s8mHHQK  ((6?((6?--/--/ ii288<--224..335--224#%88S!HBMM#J #%88S!HBMM#J //4 ")<)>Q  DI IIdii %r,r(returnc[R"X-[RS9RX5n[R"US-S4S[RS9n[R"SS[RS9n[ SUS5H>nXUS-2XDS-24USS2SS24'UR R5X$S-SS24'M@ U$)z Fast multiplication can be implemented by picking up a subset of entries in a sparse matrix. Args: dim: problem dimensionality. Returns: 2d-array of indices for the fast multiplication. r rr) fill_valuer rN)rrrreshapefullrangeTravel)r(all_idxidxbis r)r#PMatrix._init_index_matrixCs))CIRXX6>>sHggsax'ARXXF GGFq 9q#q!A!a%iU23AadGSSYY[CQ N" r,layertemp_matdaggerc UR5upEnURnURn[R"U[R"UR XPR S9SUS9 U(a([R"X@RS9ROUn [SUS5H8n [R"USS2XS-24XRS9USS2XS-24'M: X`R SS&g)a Multiplies ``NxN`` matrix, wrapped by this object, by a 1-qubit layer matrix of the right, where ``N`` is the actual size of matrices involved, ``N = 2^{num. of qubits}``. Args: layer: 1-qubit layer, i.e. the layer with just one non-trivial 1-qubit gate and other gates are just identity operators. temp_mat: a temporary NxN matrix used as a workspace. dagger: if true, the right-hand side matrix will be taken as conjugate transposed. outraxisrFrr N) get_attrrr/rtakerr conjrr:r9dotr! r'rArBrCgmatperminv_permr-r( gmat_rightr?s r) mul_right_q1PMatrix.mul_right_q1W %~~/Hiiii RWWT--tIPQW_`>DRWWT799 q#q!A "AAI& 8P8P!C11u9 " 'r,c UR5upEnURnURn[R"U[R"UR XPR S9SUS9 U(a([R"X@RS9ROUn [SUS5H8n [R"USS2XS-24XRS9USS2XS-24'M: X`R SS&g)a Multiplies ``NxN`` matrix, wrapped by this object, by a 2-qubit layer matrix on the right, where ``N`` is the actual size of matrices involved, ``N = 2^{num. of qubits}``. Args: layer: 2-qubit layer, i.e. the layer with just one non-trivial 2-qubit gate and other gates are just identity operators. temp_mat: a temporary NxN matrix used as a workspace. dagger: if true, the right-hand side matrix will be taken as conjugate transposed. rErrGrrN) rIrr/rrJrr rKrr:r9rLr"rMs r) mul_right_q2PMatrix.mul_right_q2wrTr,c 2URnUR5upEnURn[R"U[R"UR XPR S9SUS9 US:a@[SUS5H.n[R"XBXS-2SS24X8US-2SS24S9 M0 OUS-n [R"URSX45[R"URU SU45SS55 [R"XCRSS5URSS5S9 [R"URU SU45[R"URSX45SS55 X`R SS&g) ay Multiplies ``NxN`` matrix, wrapped by this object, by a 1-qubit layer matrix of the left, where ``dim`` is the actual size of matrices involved, ``dim = 2^{num. of qubits}``. Args: layer: 1-qubit layer, i.e. the layer with just one non-trivial 1-qubit gate and other gates are just identity operators. temp_mat: a temporary NxN matrix used as a workspace. rErrGr Nr rrIr/rrJrr r9rLr0r7swapaxes r'rArBr-rNrOrPr(r?halfs r) mul_left_q1PMatrix.mul_left_q1Vii$~~/Hii RWWT__dHqV^_ 91c1%taa%il3QY\9JK&!8D II QN+R[[9I9I4QRTW.9Y[\^_-`  FF4Q+1A1A!R1H I II T1cN+R[[9I9I1d.9Y[\^_-`  &r,c 2URnUR5upEnURn[R"U[R"UR XPR S9SUS9 US:a@[SUS5H.n[R"XBXS-2SS24X8US-2SS24S9 M0 OUS-n [R"URSX45[R"URU SU45SS55 [R"XCRSS5URSS5S9 [R"URU SU45[R"URSX45SS55 X`R SS&g) ay Multiplies ``NxN`` matrix, wrapped by this object, by a 2-qubit layer matrix on the left, where ``dim`` is the actual size of matrices involved, ``dim = 2^{num. of qubits}``. Args: layer: 2-qubit layer, i.e. the layer with just one non-trivial 2-qubit gate and other gates are just identity operators. temp_mat: a temporary NxN matrix used as a workspace. rErrGrYrNrrZr[r]s r) mul_left_q2PMatrix.mul_left_q2rar,tmp1tmp2c URnUR5upVn[R"[R"XFSUS9USUS9 URUR p[R "XR5 Sn [SURSS5HQn X;U S-2XS-24U SS2SS24'U [R"UR5U R55- n MS [R"U 5$)aC Computes and returns: ``Trace(mat @ C) = Trace(mat @ P^T @ gmat @ P) = Trace((P @ mat @ P^T) @ gmat) = Trace(C @ (P @ mat @ P^T)) = vec(gmat^T)^T @ vec(P @ mat @ P^T)``, where mat is ``NxN`` matrix wrapped by this object, ``C`` is matrix representation of the layer ``L``, and gmat is 2x2 matrix of underlying 1-qubit gate. **Note**: matrix of this class must be finalized beforehand. Args: layer: 1-qubit layer. tmp1: temporary, external matrix used as a workspace. tmp2: temporary, external matrix used as a workspace. Returns: trace of the matrix product. rrGrgr N) rrIrrJrrr0r:r9r%rLr;r) r'rArerfr-rNrO_gmat_ttmp3_sumr?s r) product_q1PMatrix.product_q1s$ii( A t4dM &&&!q#))A,*A!a%iU23DAJ BFF6<<>4::<8 8D+}}T""r,c URnUR5upVn[R"[R"XFSUS9USUS9 URn[R"UR 5UR R 5SUR 5S9 XRSUR5-n[R"[R"U55$)aC Computes and returns: ``Trace(mat @ C) = Trace(mat @ P^T @ gmat @ P) = Trace((P @ mat @ P^T) @ gmat) = Trace(C @ (P @ mat @ P^T)) = vec(gmat^T)^T @ vec(P @ mat @ P^T)``, where mat is ``NxN`` matrix wrapped by this object, ``C`` is matrix representation of the layer ``L``, and gmat is 4x4 matrix of underlying 2-qubit gate. **Note**: matrix of this class must be finalized beforehand. Args: layer: 2-qubit layer. tmp1: temporary, external matrix used as a workspace. tmp2: temporary, external matrix used as a workspace. Returns: trace of the matrix product. rrGrrZ) rrIrrJr&r;r$r7r/rsum) r'rArerfr-rNrOrhbldias r) product_q2PMatrix.product_q2s$ii( A t4dM%%  dmm113!O b$)),,}}RVVE]++r,cURn[R"X RSUS9 [R"XRSUS9 UR URSS&UR URSS&UR$)z Applies the left (row) and right (column) permutations to the matrix. at the end of computation process. Args: temp_mat: temporary, external matrix. Returns: finalized matrix with all transformations applied. rrGrN)rrrJrrr)r'rBr-s r)finalizePMatrix.finalize$soii __1(; **<"00"11yyr,)rrr$rrrrrr&rrr r!r"N)T)__name__ __module__ __qualname____firstlineno____doc__intr*rndarrayr1 staticmethodr#rboolrRrrVr_rcrrlrqrt__static_attributes__r,r)rrs6 S3S0&bjj&  &'''RZZ''@'''RZZ''@#&#&BJJ#&J#&#&BJJ#&J # #rzz # #PRP]P] #D,,rzz,,PRP]P],B r,r)rznumpyrrArrrrr,r)rs#ccr,