Method for solving an electronic structure problem based on hybrid digitized counterdiabatic quantum computing

Abstract

The invention pertains to quantum computing. Specifically, the invention refers to a computer-implemented method for finding the ground state of a molecule with a quantum processor by using a quantum-classical Variational Quantum Eigensolver (VQE) method with the ground state corresponding to a Hamiltonian of the molecule, the quantum processor comprising a predetermined quantum circuit for producing trial quantum states for the target Hamiltonian operator, the predetermined quantum circuit comprising parametric quantum gates associated with one or more parameters to be optimized, the method comprising: - providing an initial Hamiltonian operator, - computing a pool of generators to construct parametrized entanglers for the quantum circuit, and - applying the quantum-classical VQE method to optimize the values of the parameters of the entanglers for finding the target Hamiltonian representing the ground state of the molecule.

Description

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nr nn m nr vnnnnm . rxm mn mmnnnnmrwr. r rn, mnnr m,nv wnn rr mr-mmn m rnn rn nm nvr nmr r n nm- rn mnn m , m w rn rrnn r r nmr rmrn r rmn nm nmrrr nmrrnnrmmr rnmr mnnrr, r rmn mz.nrn wnr mrrmr -rvn mmn, m mr wn : -mnnn mnrnrnrr, n nr rmrznnrr nmr, -nnnrrnnnm-r m mnn rrnmnz vrn rm mr. mnrmmnr,n rmrnnn r rnnrn. n nnm r, n .. rnrmmm nrm mmmn n. mn n nr mnnrnnmnrmn mrmmnr wnmnn: r r n nn nr rn nmmn, nxn n .nm r r r , rmn. n,. ,nrnnrrmrrn n rnmrm. ..nrn,^rr^xrr rrm.,nrmrmnnrnmrrvr n n.nmm nnrm m mr wn nrnmmn: .mnrnnrmn n nvnm mmrrmnn w r . m nmmn,. rm. w n nr- v n rmn r x nrn m’ .nn. r mnnrv, w rr- rr.r, n rrm-rv n rrm n m rmr rnrmnn m. r mz n-r , w nnnr -nr nn.n n-r , nrn rr- rrn mnnn nrn vrn, mnn r mnn ^^ / . mnnnn nr, xnn m rrn nv wrnnrnm rmn nnmrn-nwzxrmnn.rn mnnr- .nwnrmn rmn-- mn m . rm rnn mnn, nr- rmrm m nrmrmrnrnnrrr.mnrxmnmn.n,- mrm n nrrrm w rmrzr nz n rm rm rnm wr r .n,vnrr . ^^0, nr r nw1n2r=mmvnmrznrmrzmnrrmrnvrnrrn1m3!z3!43!∗n, wr ^^∗r m rmr,n n .. ^^m^^ ^^ ^ ^^ ^ ^^ ^^ ^^r 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mmmnnrrzmnnnn:xnrmmr, wn rrrm: w mnn ^^ m mrrm ^^7, nrnnxnnnmrnv: . rr ^^80!#9:n rnmrm. ^^7,nr rrnnnrnnnrnrrr.: nnvv nnr rrnrmrmrr_ vr^^nnrr .: vrv nrr ^^80!#:rxm r nrmrrznr.rrrrmm ^^7xnnnrnrmmrnrm r nn n .. vnmm n .m m. r nrrz n rxm vr rnnrznnnnr xnnn mmrr nmr , rrzn rrrm r m mnn. rrmn mr n w mnrrrnn xnn w nmr .n m nvn x w rrmn nmr r. n, rrzn nrnrrrmn nn rnrn , , nrnnr wnwmnnnr nxr mn mrnmnrn vrn nrn m rmn nmr r r. rn n-m .n rrnn mz n, rn rr- nrrmr n-r , nrm nrnnr m-nr nn, r nn rrnn n xnnn rrm n v n r n wx rrn ,- r rmnn. ,nxrrrmrn-nrn wvv wn rn- nmrrxmn, n wvnn nn n nn rxm n r rn wvnn, nn n r rmnn rmrzn n wrnn.n rn r rm, rmn m mnmnrnrr mrmrmnnn n nzn^ ^wrnn;r<rrxn-n vnr nn;<>?r w- nr. n- n m nnr nrn rrn nr rn rn wvnnv wn rnn n w r rx n v wn x mr m . w- nr rn ^^, ^^, ^^,r ^^nr wvnn-nvrnrxmmnrrn mwn.rrnrm wr, n n-r . -r n rnvr rn n nmm .. n mr nr-mrnrnr wxnnrn,mnnnn ,r.xm,nrmz nrnmmnnm, wmrnn r rmwr w rnm rn nvv rm mnn w rv m nrm r mwr mnn w n nm n . rmwrn r nmr rwr. rm mn rrr, w mn m nr nrrrn nm wr nm r n mr,..r- wr mzr.rr, nv nr vrn nmnvr. nn r nrrmwrnrnvnn,nrvnnnr rrrr mm,nrr rvmnrr-mn.mn m , vrn nmnnvmr mnrrm n wnrn vrnrn. mnn. n rnrn nm nvr n rm n w nr mnnnr ^^.n n vrrnnrn, wnm m r wvnn ^ x n v mn rnr rn nr. nrv n rn vr nrn n mvrrn ^^n rmrnr ^^, ^^^^mm^xr :w ^^n^^n^^ ^^ ^^^nmrmrz^^ ^^ ^^ ^^n^.^m.wvn^ x n v mnn w r r.nzrmrmrr:rn ww:nn rmr ^ ^^. n .. .rrmrmr vnn:nrn r wvnn ^^ ^^^n nm : rn rmrz nmr ^^ ^^.^ r wvnnvn w^^ ^^^ =rrmnrz ^^ ^^^^ ^ rr-^^ ^^,^^ ^^n^^^ ^^ nr rr .rx^.n^^:^^ = ^ ^r^x n v mnn:. mz r^^ ^^ ^^ ^^^^^^nrmr: mzn rm rmr.nr:r mnmzx n vrrxnnvrnnmvr^^mm^^.nmnm v,.n rmr ^^ rxmmnnrnmnrrm.r ^^ mnmz x n v, vrrnnrn vnr rmrz nz,nmn x n n n nn m rmr mnmz nr vnnrnmrnnn wn r –rrrnr, xxnn vr. - nnx vrn vmn mnnm vxrmnn.rnxrmn mr n, n m w mn : - -vmznnxrmrn. v w r r n nrrrnnx nn vmmr,nnrz mrrrmn. rmrz mnnnn n rmrmzr, w n x12n v nxx n ^^0rn rn ,vn nvrn w vnrvnrn-.nnr r vrn.n m nr nnz. nv rnrrrm,rrvr r m n zmmnnnr,rvnnnrrnmr-vrnrmrrr, n ..n w m nrrnmm vrrn.rmrn rrnrn v n r mr ^^, ^^ = ^^n, ^^w, ^n^, ^^ , nm wr ^^, = ^^ ^r^n⋯r ^^ ^wrrr ^,^ n nrmrr m rr.r rrn rn rm@vn nm nnnrz,, w rr ^^ r rn nmr rmrz ^ ^ ^^ wwrn ^^7r nr vrr ^^7nr .r :n v nv •nrn rnnn r, w nz r mn m nnr.r mrmnx nrrn n r rmrz n-- mn, r nn • n r , w nr rrn rvvrrnn n nz mn rn n vr nrrnn w r vrnrmr rvvr v nr.rrvvnnrr nrrv n wrvrv. r •rrvn r , w m rw nz m .rmnrnrrn,mnmn,rnmn w nrrrr wn nrnnrvvrm nnr rn rrm mzn. n nmr mr n rnr n mzrnvr, mnn rmmrnrnr rnnnnrv nvrn mm. vrn • v-rv, wv-mm -rrwrnnz vzrn rnmn.nvr rn, mnn rrn m rmnr r mnn.n, nrrnn n n rmnx n nr. mn r rn nn nm .. r mnmrn nrnrnrrv--vr.mnx, mn, rxnnn rnvr,rmmrznnnrnnrrmn mrznn nnn.nrv mzr mm. vrnrmrn r r nn nvrn • n-vrv-rv-v-, wm m-rrnz vrn nm r r rw nz rn. mnnrn,mnmn.nn rrn m r rr nnn ^^n, mrxnrrnn r rn n n rn nrnnrn.rmrn mzn rrm.n mzrnvr, vvn rnmrmrnrn mnn r r rnnnnrv nvrn mm. vrn v m r mnnrnrrv,m wn n n mrm r-nnnmrn,vm. r-nmmnnv.nn nn nr r r v n nmmn n nm rvn, wnrmnmn ^^r n rnrrmrnn ^ ^ wrvmrnnn n ^r, wm v. n, mnnvrnn m ^, w^^ ^^ ^^A1 = − ^^ ^^ ^^0 +nw rr^^mnnn ^^ ^^rvnr =r-^, ^^ =. nnnr n m rmn rn ,rr n r r. rvn w, rm n.wvr, r.vn, n v n, n rnnrv, n , mxrnrnnwn n.nrrrv n rn rnvnn,, rm ^n^ nrm. n rm ^^ rm mBCv n,BCmnn ^^ nn ^^A1rn mnnn rm r rnn- rvnwnnn@ ^^@ ^^@ ,nwrn ^^@,mxmm -vnn nn. ^^ wrn.nrrm, rmrr,w.r., ^n^ =n nmm .. wrm, nm rn ^^B-rC= ^^+^r^+,n +⋯+ vnn ^^ zD^ xr^D. wrn ^^r nm ^^ ⋯ nrnrn nrrr, rrn-rrrnm. nnzm v nx. w nr r r nrmnwnxrr n: nrrnrm n mnnwmrmn ^^r, ^^̇=^^^^.17,8⋯+m, A^^A1,r^^vFAv1,⋯nnnn^^^− - rrn m r n rvnr r ^7n nn n rn. n mm - ,n r r n n nrrnn rrv nvn,n v rnrrrmn nrr r nz r- r , nm, n nrmwr • • = =: :vv nn rr rr nn nn nn ^^^^+== ^^^^A,1, ^^F^^A1^^ , ^^ + A1^^F^^A1n ^^G=•A1+mxmmr vn nrz rnrr, wr^n m m- mr xm rn, rr.r, rr n .wvr, rr r mnnnr nrm,rr nmmnrmr nr rnrrrm nmr nrrn mmr.vr , rm n . r- m nmr rrn nrr rr,n n r-r n rr nrrnrmnrn wnrr mrvv rnrrmr.n rm. nmm .. nr mnnrrrvvrrnw rnn nrnn n nrrm nnr vrmrnmzrmnnrwr n nrr, rnrr mn rn . rnnr nmnm v, x n v nrnn ^^ w rw^^^rn r ^^ ^^^ r r^^ = ^ ^^ ^^ ^^r^^ ^^n^z^^ ^^ ^^ ^^^ = ^^ ^^ ^^^ wrrr-rnr,rrnxmnrnznrm rrr-w:rn ^^ ^^^.w r . r n rnrn nrr-n m ^^ ^^^nn . r nmmr,n mnn ^^ rr, ^^!"n n n mn0wn ^^r . m rnrmnnr mnn ^^#%n mmrw / .n r r n n mn n r v rn m rmnnr mnn, r rvvnrr ^^7n,r nn w r vrn rmr ^^7^rrr rn rvvrrn, vn ^ ^^rx n v mrnrvvv v , nnn r- ,nn r. nrrr n nrr wn xm,nrnmmn, rr wrn nnrrrvvrrn.r nz, n rvv n vv rn r rvv v n rrn n ,n n.n rvr n n n r-n r r , r rvv. wrrrm r w r nr n .. nnzrmnmr-nnnw n mmnr nrr rm , r- n- r n, w . rnn r rmrz vrnrm n r nnnr n nz. n . rmrrznnn-r rrnmrrnrnr ^^.nrmnr- r vnrnrnmr rn.nrrrn ^ ^^. mmnnnrrrrrwnnrnvr n m nr rn nrmnx nzn r nr m n nrw8Gn nr rrr m rn,m,nnn.nrrrnrm =v. ⋅nrrr.m,nv wnn rnmrmrr-mmnn m rnn rn nm nvr m w rn rnm- rn m rnn mnn nmnm,r rvmrnxr rmn nmr rr nr r rmn nm n v r mnnrr, nr mrr r mrn rmr nm w m mmr mz, rvnnnrn: n nn mnrr, n nrr nrn -z rmrznnrr nmr,n nnn vr nm- m mz v rmrr .nrn nrmnnrn wm rnvr wv.rrnnmr-nnmr mn. rm mm-,nrrv mmnn-rr rr.nnnnrnm mmn m nvnn, n nm- nnn w nrv mn w nmr r n rrmnnm mrrmrnrr rrrnrr, nm r n mnrrn rrr rn ,nnv nr w n mn nmm .. r rmrn rnmnr v nr mmrr rmr nm r r, rv mn mn rrm nm nm- m rxrnnnmrz vn nrrmrnr. ,nrmrrnmmn, r r n v rmr rmrnm rr rmnn vnzmrnrr nnm mmrmn. x n v mnnrm rrm n n rrmn mrmnn m n mr r nm n nnnr m r . nvv n n rn nrrn , . rv mnx mz v rmr. nm- m rrnnnx nn vm- mn mnr,m, wnmr rrrm mrmn rmr rmr nmr.n r r r nrrn m,nr vr nn nnr n mz v rmrr rrn. nnmnnm mrmmnn,n n nmznnvrr rmnrn rn nr nm m. nnrnmnrmn m nvnn, nm- m n. r. w rn nrr rnrnnnrrnr wm-mn. mr nnvnn, n-rmrrx.n mrnmrnmmn m nvn nr rnmnmnmn n, rnnrr wnrnm -r- .n v znnrznrmmnrm mr-m nvnn,nr nrr r mmr. n n wnrmr:rnr ^^rnnrm nr ^^0. nnnn ..nr mmmmn m nvnn, mnnrr rrnn rrrnn m n r r m w rwmrn,v.m nmnrrnmmn .nnmrnmmn,m m m nv n, m rn wmn,r m m,nnn n2, m,2,.nr m. nr r rnrrnmr wm-n r m nvnn, m nn m , m r m mm-z m .rxm, m r m r nn rn₂, mr ,rm m r w₂,n mr . m v m nn mr n:₂nmnnwrrnnmm w w m m rr w w .. m, ₂n nrmnw rnm w m m, m,n n n mnn rnm w r w . . m. m r wnrrrmnnmnmmn m nvnn, nmr n m . r rrn nmr n-r r mnxmrmn nmmmrnrn mn nvnn, rn n mr rrn rmrz wvnnwrrnnvrnn.r w n nmr rn,rxm, m wnn ,nr rwn xm.,mn-5nrrr. rm “ w rmrz wvnn m,r nr w wr mrn vrn” mn n vr rmrz wvnn mr w mrn. n, mr, r,r,vr mr, n rnrnnmnmmn m nvnn, rmr nm mr mr v n,.n rmr w r nnm nmm .. nnrnmmmmrn m nvnn, nrr rm mmr rnn ^^!",. ^^#%. nrr nrm rrr nnrnmmn, m nvnnmr wn : . n nrrrm n mmr,mrn nn rrm-r wrrrnnvn mmnrn,mnnnr mnn nnnrrr,nr rmn n mmr m n . rnnnnrnnrn,r nrr rn r rrvv .rrn rr- rrnr rnn nrr ., .rvn r rmrzn r n r ,r.mrvn rnrrrmrznnrn rn w nrr r rvvrr, wn vnr, v nrrn w.rmvnnx rnrm vnvr rmnnn, wnrmnnmvzr rmr,nr .. wn mrmrrnnmzrrrn r .rmrn rrnn mn .n ,mnvrnn r mr r m r rmnn nm nr nnnm nm mnmzn r w mnnrr w nmr r r rrn, wnrnnxnr n v nmm.nnrrvrvnnm mnrrmr,n mnvnn rrnr m r rmnn rr w mnnrnr wnmnmnrmr mnrmznrn.nr nmm ..nnmr nv,rnvnrn rr r nm- vrn m r rn mnnnnnrmnnrnrn r wnvnnnrr.vn vnrn n,mnvnnvnr rr,m mrnrrvwnn :r nm- . n nrrrm n mmr,mrn nn rrm-r wrrrnnvn mmnrn,mnnnr mnn nnn rnrrnr-rr, rm n n mmr m .rrzn nrr n rnr rnn rrnrr rn r rr vvx nn vr,nn, wr rr- .rrn rr- , .nz,n,rvn r rmrzn r n rr.mrvn rnrrmrznnrn rn w nrr rrn n r, w nrz,n w r rvv.rmvnnx rnrm vnvr vrmnnn, wnrmnnvmrz rmr,nr .n. w mrrmr. mzr rmrn rrnn nrrnrmnnzrr x xnnn n n r ,nrnmmn m nvnn, n mmm nrmrmnr ^n^!", ^^#.%. nrr nrm rrrnnnmrn,vrnvnn rr r nm- vrn m r rn mnnnn rmnrnrn r wnvnnnrr. vn nmm .. wnvnnrnnmnmnrzn rwnnrmr,rwnmn:r, w m .rrr n nmrmrrrm n ^^ , ^^m.mr,.., nrm . rr!"#%rvvz nrn rnnn, wrnrrrr-rn r r r n x n v . rn .rr rr- . . r nz, w r rmrzn r n. . rn wn nrrnz, w r rmrznnrn w r rvvrrn.rm , w r n .m vrnxrmn vr. mnnnrnrmnrrmn. w r .vr wmr rmmrz.r rmrnrnmrrn:mmn m nvnn, w nrr - wr rn-rrmnrrm m.rrm rn n n rmn wr r-r, nnrrrm. - mr rnrr,n rm. n mrr wr r- m rr mr, w rwrrnn -rrmnnrnv mr rnnmznrrn wr r- nnn mr ^z^, wn.rrrnmrr, nn nrr rn m nr- rnnn. mr nr - -rrmnnnrvmzrn. rn,nmznnrrrrnn wrrn r-- nmm .. .rrmnx n wr r- r n rmn --r--rrmnnrvn mr rnnmznrrn wr rr znn.nnn, mr- ^^ ,- wr nnrr nnn mr nr rn m n r . r- mnnvnn.n mnvvr r nnnn w wn rwr .nmr rnr rnr n: n: nmnn nmnrmn, r n rmn . rrn.m: mn nrn nnrrmnm mn-nmnn:nr.nmmn v r ,nnn-n r nn mnrmmnr.: n nm r rrn,v n,n . r r: rmrz-n rmn::rnrm vrnmmznn rmr.n wn, rwr rrrmn vn mrr rr-: . . nrrrm n mmr: mrmwr:rrnr.rrx.m,nr-rr nnrrmmrrr ^m^n , n m n rm.!"^^#%. rrzn : rrvwvr: nrrnrn.,nnn nrrr-r rn rrrn r nvv m n rmn rvn nrr.. .rrn rr- : nmm .. rrrw-r: nmrnrrn..rn nn.nzn nm rr- n. r n. n r nz: rnwr: nmr r..r nr rnnr . nrrnn r rnm,rznn-nn rrnnnzr. mn. n n nz:nrnwrn:nmrnr..rnrnr.rmnrn r rmrznnmnwn nnrmmn n m.-nrnnnrrnr..mn x n mnnnnrrn: rwmr:nnnmnr r..rn n. rn x n v rmr. nvv rrmn rnmrn w r vrn n r n nm m.rmn n. nrmrn mzr: rwr:nmrr r.n mrmn r mz rmr rmr,mn. mnmz nrr.r rn mznrm.rn r : rrwvr: nmn r r. n v n,r wrn m..rmrrm mzr,n rn rn. ,nvrn nrrn,r mxmm nmr nmm .. r w: nrnmmn m nrrrm r z rn rnmrvvmnnrr-nn. n nrrz rr:rmm.nmmnr r-w r m rvn rn : n nrrrm n mmrr,n.., xnrmr. nrrr rm nmr rmmnr ^^!", ^^#%.nrnmmn nvnn, nr nznnrrrrrm wv rn rrr nrmrm. r:r rrnrznr nrrrrvvrn nrrrnnn, rnn rr- rrn n x n v . wr :rrnnnzn rr- . r n:.rrmnrn rnnz, r wn. r rmrz n r:n n nz, w r rmrznnrn r wrvvnrrrrn. nrm ,r wrrrmn. w rm:rrrnrvmn x n v mnn. mz .nrnmmnn,rrmnwvr vnrrn nmm.nvr m:rmzn mrmzrrnnvrnr.mn .. nn-nm w rmr. rn nn rvr nm .. :wmrm rnnmmn nvnn. rnwnn rm n. m nvnn m mr mr nnmnn. n rm. rzmnmnmr.v nrr nnr- .,.n. m nr mrxxnn. nnrm rnm:mrwrr-.n z nr rmr- r r .mznnrwr m rwr m m v,rxm,nrm r :rwr- z nr rm. . rwr m r m- n r . . rwr m rnmxnrmnn r . . rwr m r mnnn r . rmmnnnrwr m. : m w , -n nr rmnrwr. rm rn. rmn r rv nn:nwrrmrv. : rm rnnmmn nvnn. wn wn: : :rmnrz nmnrz., w r n : rm: -mz.. nmm .. wn rn r,:rnnnrnnr wn r nz. vrnrmr, nr nnvv w n . rrrm -, w r nr w r nnrv rn n. nr r wrrnr n . rr rnmr nr , mzn n. , z nmr ,r m'mn m rxm rn nrn:wmn nnm-nmr r. r r nvr m . r n w rr-n rnnrrmnm r rrr nr . nm n r rnrr nn r r nn r nnnnn rvrmnrr nrmzr n- mxrmn vnr r mnnrrrrrm, wn n.mrrmnr. rmr. r mz vrn nr mnmznnvrrnwnv. n nmr rn wr :m n r r r:nn wr m n r ^^ ^^^rn m n- . vrnrmr ^^ nnnvn r rn mn. w.nn ,nrnrrnn- ^^ wr nn ^^ ^^^r rn. vrnrmr

[0002] nm .. x m nnr,wnrxmn, n mmr, m nnw- nrr r rrn m n rrnnn nr nmnmnnnmrrn-nn-rrn rr-nn. rxnm mnrrn m nn mnr-mmn m rnn rn nm nvr m mrmnr wr nm- mmn, r nvv: .nrn 2 mnn r m • • m:r-:. , wr nr-m n. • • r:. • • rn mm:.nr-- m:.r:r ww- r n. -rnr-rnmn,n wn w nr - nrr :.nrm - -n v: rmr: ^^ =^. ^^ =. ^ - mrmr: , -..-^+, =. - -x -rrrr:-nr: - . n.r: -. rr - rr rr m • • m:r-: , wr nr-m n. • r:. • n:.. nmm .. • •rrmzn-- mr:r ww- r n. • mnrrn r:. v rnr. -rnrrmnn,n wn w nr: - :.nrm - -nnr m vr: , rmrr:m, .r: ^ ^, =^ ^,^.=. ^^G= ^^I=, ^^+= -^. ^^.= ^^G= ^^I= . , -. ,. , - , -. , -xnr: . - r -. rr -rrr:-. nr: -.- rr rr m • • m:r-:. , wr nr-m n. • • nr::. • •rrm.n-- mr:r ww- r n. • mznrr :n.r. -rnrnn, wn w nr: - nr-rm n:.nrm-n vr:r,mr: ^^,=^ ^^ = ^^ =, , , ^. G ^^I = ^ ^ ^^ ^^ ^^ = ^^+ =^ ^^.-^G =.m^^I = ^^Jr=-m^^K =,r:.- , ... -, . -, . -, . - --,, -.. --,, -.. --,, - - -.x -, -. -, -. - - r-nr: -nr. rr -rrr:. : -. rr rr nmm .. 2 m • • mr: - , wr nr-m n. • r:-. • n:.:. • • rmmnr-- m:.r:r ww- r n. -r rnn, wn w nr: -nnr-rmr: n:.nrm , ,, ,, ,, , , , , ^^ ^^ ^^ ^^ ^^ ^^ ^^. G, , -n v rmr: ^^ =^ ^^ = ^^ = ^^I = ^^J = ^^K = ^^L = ^^M = ^^N = ^^+- ^^ ^^ ^^ ^^ ^^ ^. -, . -,, ,^, . -, . - . -, . -, . -, . , . -, . -, . -, -, . -, . -, . - . -, . -, . -, . -, . -, . -, -. -, - - -xnr: -. r -rr- nr: -. r rr rrmr:.r m rr n mnn nm r mnr mn mnnrrr- rr. nn nr-,nrrnmnrnmrrn-n: rr m n-rnn rrrnnn. r mnn, rrnn rrnn mnn, m n- rv .n mnnrrr m . nmm ...rvnn n n rrmn nmnnnrr: rr n mrm, n, rr- m . r,nn.mnn nrr nrr n n :mmr,n rn nrm n. nm rn. rr rrnrrrr-n: :nzn rrn nrr-n . rn:nz:nn- r n. r : nnnrrm nrr. x nnx n :nmr r mr. mz vn: mnnn nz. nnr mmrr: v ,rrv rrnnmznzrmr.rvr : . mnrrnrrn nrnnvr m .rn ,

Claims

nmm .. . mmr-mmn m n nmr rrnn rn rn nrrnnnm- rrmnnnnm nvr m w nmr rmrn r rm m , nm r r n nmr rr nr mrn rmr nmmnnr wr, nrrrmn nmr m mr rmr - -r mz, vnnmnrn:mnnr nmn nrr nrr, rmrznnrr nmr, -nnnrrnnnm-r m mnn rrnmnz vrn rm mr. r.rnnnrnm-nrm, w.rn rv n mnn rr m. rrnn mr, wrn n nm- w r rr,v mn w nmr r nnnn rrmnnm mrrmrnr rrrnnrvnmn r r mnnrrn rrr r nm ,n r w r mnn r rmrn rnmnr v nr mmrr rmr nm r r, rv mn rrm nm nm- m mn rxrnnnmrz vn nrrmrnr. , n.mr rrn m, wrn rn nrrn mxmm wvnnwnr mnrrnnvrn.nr w rmrznmm .. r.nnrn n m , wrn rmr nm mr mrm v ,nn w.rn rmr w r nnm . nrrrnmrnnnmrr w, w-rn. nm- m .rn mr wnrnnrnnmnnr, wnrnnnnrrr n m w r vrnrmrrm rmrn rnrrnr.n .nnrrxrnnn v mr, wrn r mnnrr rrn rrnn nvr n w w m nv,.m nm .mr rrn n, wrmn n,m wrrn rn rmrnrmnnmr r rrn nmr nr r m . nm m.r, w mrn rn nrnr m rr.rrrmnn rr rr, r rr m r nn mn .wnmr-mrmrn m rn n m ,mrn : vn r nm- vrn nmnvr . n nrrrm n mmr,mrn nn rrm-r wrrrnvnn mmrnnm,nnnr mnn nnn rnrrn,r rmn n mmr m . rrvnvn nnnrrrnn, nrr rn r r .nrrnnmrrr-r, rrnr rnn nrrnmm .. .rnvmnr rr, rmrzn r n r nr.mrvn rnrr,r wmrzvnnrrn rn w nrr w r rvvrrn v nrrn r r, n nzn nm.rmvnnx rnr vmnvrmrnnn, wrn mz rmrr n nmr r mr x n vnm,nnvr .. wn mrmrrnnmzrrrn r r.mrn rrnn . m, wrn nr !. nrr nr rm n mmrn ^^rmrrr n mm r rn." ^^nm#%mr-nmvmrn m,mrrnrvnwnr:nm- rn . n nrrrm n mmr,mrn nn rrm-r wrrrnvnn mmrnnm,nnnr mnn nnn rnrrn,r rmn n mmr m . rrvnvn nnnrrrnn, nrr rn r r .rrn rr- rrnr rnn nrr ., .rvn r rmrzn r n r ,r.mrvn rnrr,r wmrzvnnrrn rn w nrr w r rvvrrn n , v nrrn.rmvnnx rnrm vnvr rmnnn, wnrmnnmvzr rmr,nrn .... wn mmmrmrrnnmzrrrn r r.mrn rrnn m.rnrrnr r rrrmr mnvnrm rrn .m .rmrmrxrrmrm .mrr,rrmr mrnnrn w, wn m r mr rr m n m. mr,r-r mrr mrrmm mrnnrnn wm, wnrx .

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