# LaTeX2HTML 95.1 (Fri Jan 20 1995)
# Associate image original text (scrambled) with physical files.
$key = q/{_inline}$f^-1${_inline}/;
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$key = q/{_inline}$3^a,(rmmod,91)${_inline}/;
$cached_env_img{$key} ='
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$key = q/{figure}labelkeyesfig{figure}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$O((logN)^2+epsilon)${_inline}/;
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$key = q/{displaymath}U_-pi2|0rangle=1oversqrt2(|0rangle+|1rangle);,{displaymath}/;
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$key = q/{displaymath}(x^r2+1)(x^r2-1)equiv0,(rmmod,N);.{displaymath}/;
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$key = q/{figure}label2bitXOR{figure}/;
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$key = q/{figure}labelQTOFF{figure}/;
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$key = q/{_inline}$n_m-1gen_m${_inline}/;
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$key = q/{displaymath}longrightarrow1overqsum_a=0^q-1sum_c=0^q-1e^2piiacq|c;,f(a)rangle;.{displaymath}/;
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$key = q/{_inline}$rmgcd${_inline}/;
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$key = q/{displaymath}arraylclf:a;SPM_amp;rightarrow;SPM_amp;(a,j(a),f(a))nonumbermboxFANOUT:(a,j(a),f(a));SPM_amp;rightarrow;SPM_amp;(a,j(a),f(a),f(a))nonumberf^dagger:(a,j(a),f(a),f(a));SPM_amp;rightarrow;SPM_amp;(a,f(a))nonumber;,array{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$f^dagger${_inline}/;
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$key = q/{_inline}$f(a)${_inline}/;
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$key = q/{displaymath}U_pi|0rangle=-|1rangle;,mbox~and~U_pi|1rangle=|0rangle;.{displaymath}/;
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$key = q/{_inline}$U_rmXOR${_inline}/;
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$key = q/{displaymath}|0ranglelongrightarrow1oversqrtqsum_a=0^q-1|arangle;,{displaymath}/;
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$key = q/{_inline}$N^2leq=2^k${_inline}/;
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$key = q/{displaymath}longrightarrow1oversqrtqsum_a=0^q-1|a;,0rangle;.{displaymath}/;
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$key = q/{figure}labelswap{figure}/;
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$key = q/{_inline}$logN${_inline}/;
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$key = q/{_inline}$O(loglogn_1)${_inline}/;
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$key = q/{_inline}$|0rangle${_inline}/;
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$key = q/{_inline}$|1rangle${_inline}/;
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$key = q/{figure}labelCOMP{figure}/;
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$key = q/{_inline}$loglogrk${_inline}/;
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$key = q/{_inline}$|a_k-1...a_1a_0protectrangle${_inline}/;
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$key = q/{_inline}$epsilon${_inline}/;
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$key = q/{displaymath}|aranglelongrightarrow1oversqrtqsum_c=0^q-1e^2piiacq|crangle;.{displaymath}/;
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$key = q/{_inline}$(0atop1)${_inline}/;
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$key = q/{_inline}$|ttqrangle${_inline}/;
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$key = q/{_inline}$|beta|^2${_inline}/;
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$key = q/{_inline}$rmprob(c)${_inline}/;
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$key = q/{_inline}$|a;f(a)rangle${_inline}/;
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$key = q/{_inline}$|a;0rangle${_inline}/;
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$key = q/{_inline}${x^a,(rmmod,N)}${_inline}/;
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$key = q/{displaymath}1oversqrtqsum_a=0^q-1|a;0ranglelongrightarrow1oversqrtqsum_a=0^q-1|a;f(a)rangle;,{displaymath}/;
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$key = q/{_inline}$|Arangle${_inline}/;
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$key = q/{_inline}$overlineA${_inline}/;
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$key = q/{_inline}${x^a}${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$|Brangle${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$2^k${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$f(a)=x^a,(rmmod,N)${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$91=7times13${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$1r${_inline}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}longrightarrow1oversqrtqsum_a=0^q-1|a;,f(a)rangle;.{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$a,(rmmod,b)${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$|a_k-1...a_1a_0stringranglespace${_inline}/;
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$key = q/{_inline}$delta=sigma=tau=0${_inline}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}|0;0rangle=|!downarrow,,!downarrow,,ldots,;downarrow,,!downarrow,,ldots;rangle;,{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$r^2leq=2^k${_inline}/;
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$key = q/{_inline}$AoplusB${_inline}/;
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$key = q/{figure}labelfig10b{figure}/;
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$key = q/{figure}labelfign{figure}/;
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$key = q/{displaymath}arrayrrrrrrrrrla:;SPM_amp;0,;SPM_amp;1,;SPM_amp;2,;SPM_amp;3,;SPM_amp;4,;SPM_amp;5,;SPM_amp;6,;SPM_amp;7,;SPM_amp;ldotsnonumber3^a:;SPM_amp;1,;SPM_amp;3,;SPM_amp;9,;SPM_amp;27,;SPM_amp;81,;SPM_amp;243,;SPM_amp;243,;SPM_amp;2187,;SPM_amp;ldotsnonumber3^a,(rmmod,91):;SPM_amp;1,;SPM_amp;3,;SPM_amp;9,;SPM_amp;27,;SPM_amp;81,;SPM_amp;61,;SPM_amp;1,;SPM_amp;3,;SPM_amp;ldotsnonumber;.array{displaymath}/;
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$key = q/{_inline}$2^k-1${_inline}/;
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$key = q/{_inline}$f(a+r)=f(a)${_inline}/;
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';
$key = q/{_inline}$|!downarrow,rangle${_inline}/;
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$key = q/{_inline}$X_n${_inline}/;
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';
$key = q/{figure}label1bitcircuit{figure}/;
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$key = q/{_inline}$|~~rangle${_inline}/;
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';
$key = q/{_inline}$e^2piiacq${_inline}/;
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';
$key = q/{_inline}$3^6equiv1,(rmmod,91)${_inline}/;
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$key = q/{figure}labelTOFF{figure}/;
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$key = q/{displaymath}f(0),,f(1),,ldots,,f(q-1);,{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{table}[thc]tabularcc|cccc_inline$A$_inline;SPM_amp;_inline$B$_inline;SPM_amp;AND;SPM_amp;OR;SPM_amp;XOR;SPM_amp;NOT,_inline$B$_inline%0;SPM_amp;0;SPM_amp;0;SPM_amp;0;SPM_amp;0;SPM_amp;10;SPM_amp;1;SPM_amp;0;SPM_amp;1;SPM_amp;1;SPM_amp;01;SPM_amp;0;SPM_amp;0;SPM_amp;1;SPM_amp;1;SPM_amp;11;SPM_amp;1;SPM_amp;1;SPM_amp;1;SPM_amp;0;SPM_amp;0tabularlabelTRUTH{table}/;
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$key = q/{_inline}$|Adelimiter;SPM_quot;526930B${_inline}/;
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$key = q/{_inline}$2^2^9+1${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$|25rangle=|11001rangle=|!uparrow,!uparrow,!downarrow,!downarrow,!uparrow,rangle${_inline}/;
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$key = q/{displaymath}underbrace1,~atop1,~x,~atopx,~ldots,~atopldots,~x^r-1,atopx^r-1,_rrm-terms~underbracex^r,atop1,~x^r+1,atopx,~~~~ldots~,atopldots,~atopx^r-1_rrm-terms~underbrace~atop1,~~atopx,~~atopldots~~~~_rrm-terms{displaymath}/;
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$key = q/{displaymath}(x^r2)^2-1equiv0,(rmmod,N);.{displaymath}/;
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$key = q/{_inline}$A.B${_inline}/;
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$key = q/{figure}labelFANER{figure}/;
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$key = q/{_inline}$(1atop0)${_inline}/;
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$key = q/{_inline}$10^12${_inline}/;
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$key = q/{_inline}$U^-1=U^dagger${_inline}/;
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$key = q/{figure}labelBENN{figure}/;
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$key = q/{_inline}$rmgcd(n_0,n_1)=n_m${_inline}/;
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$key = q/{_inline}$2^3times7times13times71${_inline}/;
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$key = q/{displaymath}f:arightarrow(a,f(a));.{displaymath}/;
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$key = q/{_inline}$rangle${_inline}/;
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$key = q/{_inline}$U_stringprmspaceXOR${_inline}/;
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$key = q/{_inline}$~~~~~~${_inline}/;
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$key = q/{_inline}$protectrmprob(c)${_inline}/;
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$key = q/{_inline}$n_0gen_1${_inline}/;
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$key = q/{_inline}$rmgcd(28,91)${_inline}/;
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$key = q/{_inline}$U_-pi2${_inline}/;
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$key = q/{_inline}$rmgcd(26,91)${_inline}/;
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$key = q/{_inline}$stringrmspaceprob(c)${_inline}/;
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$key = q/{_inline}$k_BTln2${_inline}/;
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$key = q/{_inline}$cq${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$O(exp[(lnN)^13(lnlnN)^23])${_inline}/;
$cached_env_img{$key} ='
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$key = q/{_inline}$28times26equiv0,(rmmod,91)${_inline}/;
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$key = q/{_inline}$rmgcd(28,91)=7${_inline}/;
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$key = q/{_inline}$k_B${_inline}/;
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$key = q/{_inline}$12${_inline}/;
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$key = q/{_inline}$|ttarangle${_inline}/;
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$key = q/{_inline}$n_m${_inline}/;
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$key = q/{displaymath}U_rmXORequivleft(arraycccc1;SPM_amp;0;SPM_amp;0;SPM_amp;0nonumber0;SPM_amp;1;SPM_amp;0;SPM_amp;0nonumber0;SPM_amp;0;SPM_amp;0;SPM_amp;1nonumber0;SPM_amp;0;SPM_amp;1;SPM_amp;0nonumberarrayright);.{displaymath}/;
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$key = q/{displaymath}f:arightarrow(a,j(a),f(a));,{displaymath}/;
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$key = q/{_inline}$j(a)${_inline}/;
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$key = q/{displaymath}Boplus(A.C)=left{arrayllcA.C,,;SPM_amp;mboxfor~B=0;SPM_amp;mbox(AND)nonumberAoplusB,,;SPM_amp;mboxfor~C=1;SPM_amp;mbox(XOR)nonumberoverlineB,,;SPM_amp;mboxfor~A=C=1;SPM_amp;mbox(NOT)nonumberA,,;SPM_amp;mboxfor~B=0,,C=1~;SPM_amp;mbox(FANOUT)nonumberarrayright.{displaymath}/;
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$key = q/{_inline}$2times2${_inline}/;
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$key = q/{_inline}$qequiv2^k${_inline}/;
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$key = q/{_inline}$q=2^k${_inline}/;
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$key = q/{_inline}$|Bdelimiter;SPM_quot;526930B${_inline}/;
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$key = q/{_inline}$|!uparrow,rangle${_inline}/;
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$key = q/{_inline}$x^requiv1,(rmmod,N)${_inline}/;
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$key = q/{_inline}$d_m${_inline}/;
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1;