From 9ddfc13688fd05bfa25a49cd8a85f8609a12ec72 Mon Sep 17 00:00:00 2001 From: Benjamin Neumann Date: Thu, 30 Jul 2026 18:21:07 +0200 Subject: [PATCH] vault backup: 2026-07-30 18:21:07 --- .obsidian/workspace.json | 8 ++++---- .../Anhänge/Pasted image 20260730181449.png | Bin 0 -> 14026 bytes .../Anhänge/Pasted image 20260730181941.png | Bin 0 -> 28770 bytes .../Discrete Fourier Transformation.md | 14 ++++++++++++++ 4 files changed, 18 insertions(+), 4 deletions(-) create mode 100644 SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge/Pasted image 20260730181449.png create mode 100644 SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge/Pasted image 20260730181941.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 46e17ef..518d5d4 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -216,6 +216,9 @@ }, "active": "25f5b25d5eca7203", "lastOpenFiles": [ + "SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge/Pasted image 20260730181941.png", + "SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge/Pasted image 20260730181449.png", + "SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge", "SS2026/Quantum Computing/Introduction to Quantum Computing.md", "SS2026/Quantum Computing/10. Discrete Fourier Transformation/Discrete Fourier Transformation.md", "SS2026/Quantum Computing/10. Discrete Fourier Transformation", @@ -234,7 +237,6 @@ "SS2026/Quantum Computing/7. Quantum Circuits/Quantum Circuits.md", "SS2026/Quantum Computing/8. Ket Notation/Anhänge/Pasted image 20260730102318.png", "SS2026/Quantum Computing/8. Ket Notation/Anhänge/Pasted image 20260730102312.png", - "SS2026/Quantum Computing/8. Ket Notation/Anhänge/Pasted image 20260730102305.png", "SS2026/Quantum Computing/8. Ket Notation/Anhänge", "SS2026/Quantum Computing/8. Ket Notation", "SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md", @@ -243,7 +245,6 @@ "SS2026/Quantum Computing/7. Quantum Circuits/Anhänge", "SS2026/Quantum Computing/7. Quantum Circuits", "SS2026/Quantum Computing/6. Composite Systems/Anhänge", - "SS2026/Quantum Computing/6. Composite Systems", "SS2026/Quantum Computing/1. Introduction/Introduction to Quantum physics.md", "SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md", "SS2026/Quantum Computing/3. Quantum Systems/Quantum Systems.md", @@ -261,7 +262,6 @@ "SS2026/Datenbanken und Informationssysteme/4. SQL/DQL Data Query Language SQL.md", "SS2026/Datenbanken und Informationssysteme/4. SQL/DML Data Manipulation Language SQL.md", "SS2026/Datenbanken und Informationssysteme/4. SQL/DDL Data Definition Language SQL.md", - "SS2026/Datenbanken und Informationssysteme/3. Relationales Datenmodell/Relationales Datenmodell.md", - "SS2026/Datenbanken und Informationssysteme/3. Relationales Datenmodell/Relationaler Kalkül.md" + "SS2026/Datenbanken und Informationssysteme/3. Relationales Datenmodell/Relationales Datenmodell.md" ] } \ No newline at end of file diff --git a/SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge/Pasted image 20260730181449.png b/SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge/Pasted image 20260730181449.png new file mode 100644 index 0000000000000000000000000000000000000000..dc09b8d6c4c2a4cd643f56908898d1dba55e288a GIT binary patch literal 14026 zcmb_@byOQ)-)CD26bMq>DaGC02~M%%?hXZtd$HiIMM`jYEm~ZQyB2p+tVn=t`g`7I z_uX^eJ-d5$|41^KjNG}C`<;*7NL6K7bW~#07cX9*%gaf9eDUHH5WXDy1_}P&C>7uV z|9I*8QC9Lr^#th={L5==2_=aaFY4ma9!(M9-%*_9bX{M(!07w?dO74&Y5`w~?Ix|` zrtW0r=4txb@`dbYOUqBLHcoCvns4B{@Jh%_NoaT(o#iOmkmzR}*e8ai>0RgJ6GddS zN4x`QCrC^AnoAHe5BI)eGiW3zUWr!qGDYQkZMty|zUZZ@fAbz)X1AzM10RGcLOwe6 z(y|SO9--JBN~0P;`3owEZ`ayq^Y+k={b!(;vVZBZ#?e?^(vnZWyQCz=l8M{EJtk43oOc3Bew!_uQuRscK=T)_w;DgSkntieE7 zt}*r^)d1Gh82jIIxXzkz^#5HNm+Ui(_@^adpaCrSFMaH2=+Xb$51$wx_;=$zW^QKC zzuIW?pWA3<E!OjJs@wb5~2(K7vbW+mZ!~Z)r86 zV12w+exs>d=LC5Uf|rZGMVnRIbAYBrQD&^+GjSn3h1XaFti-pthjf<|#k=Y_d+)?L z8Zb_^k)oo4*9wqMsYw2)q3su-mJ9Jth};h?CP)yRmAGfbmpv1giaCNMaz${E<_}6H zJS#}jw;sW7_O#xv1R+9)gI!dDk}C2gEN^?IbTz>ag(s^W&Y1S}j(RpVOsZPU<117K zOdBNhp9Js9tz0T4)HG5&_3}G;$oIhX(u6e*OEsBO=Zvc7JT4v!7ch^SNLPWFitXs= zi2yu-qKJLE`}oD^9_XK1C8xzF-si@khd9c?s=*O=yS>falcnkdT96;9jU+%mcF*jE zFBPWr2vF!7Z*6%$RoRB-q$ch z@^+(aCu>!rLsSqMZ};f_^4Il%WNeqQEj0BsCn!4~T+1h#X4Di43Z(V{+N^%UQ| zz4?Q=dkK`L#l9{6R8~8R&;D5?7}vF|J_vv$|LK;4=&*8wL2W&J-7{;MxF#tff^Ds7 zkbA-d2pT}#zqxyDz>}LvKM1{L`dP!kUj^)}f5==8u6KQ0-pfFdVdbkC){GW6sVssJgIyl zCEB8@b#h44HGVGsg5X9-K4<}E()V?l*h`=z9zCW0c%4Q*5_AYfUC~~L7++6|eEu~- zS+VAi{?j;o@yJbJitls_-F2WwD7`#dI}X{iJB4+Ji4_gv&NKhbdOJ3)_PDqoYhrrM zCL+BB@*Y&p-#v)kr4gtUKub8Ct_Bl~Pj3xEJ1C8Q=Ei>_`hNWE#2ZlPAtJJ=0!Xy9 zUZ%)k3OD5;0sE?k__PBYI{`e#;%5n&?wDuJqb%Bzu^+zb3)+b#M|x!(8Fh#MQARxW z$N8CqeaTH$Oh3HIH;q1fKM>{$&P%!4JY1*3nHPHY4+{@yJu@!+O%4#kg(Ratbw%|i z?W^2BX#lT)QzNau>l!P7R^#b=3>gYvr%^ zHf14TP{+s6W=pU_Fzadd#7Zg4kxdt;>hrRc^$V|Vk1gRvFe78*0k`{N5YuSjmkDK} zc{=<|dm0VtrP)MWbbtQv=W88UA^L#|tDe2(+#hBgU!IgjJ?FC4?$+8C#lFw?Yaw{; ze{_F$pEReQg=1XtCuID7rOZla?|9D3 z-qq-CVF0va*w=$Qu|jm?g@Zg{I*w013;gmiUF7L7S0Ue3ADvss_{FI^ual#)m8dBm-?L%dJ( zVbek0VrlUjbm!?{ia9lXj1@;K-#5MT^RSm|I3%<;h>FEx(t*S=R0OOm_Lhgp_%TJ; zmQO{$+P2RCU3 z5NG$EYt)N}lLX_Cg)tKetvAYjEkG8Fx0Zb6#4=DXQnV#%%J_9ECvB@w_`FG`!%~n1 zTBvCD`n!(bUw55wbxL~o=Y2n76)W$EgjMB{qQ0}!(62K2tqx{3-v0Ss9T3(_rwACa zl}pZ9I0A3VER=4wPz@v)ixv%IQ+^{W3=92uW0?|NDt3A0Kf^xmiIzNY!3d+{Ajy+U z58e)V$38(!&)78|vt4rzBIExG>1(Fzl=!xwHcWIFYWrrEIK@dTyZ1omp6we+dqBYe zbFm@eZAh6ugTwpPB<%PdZp)k;WS|WyWxH4hK-Y}^zNPl*^>etX7C~uVXZGH{}BcKdeCdcH5|oynbp9YDvI1K8M{ck-i>5T#V%Y zggeFUuSc~r!88D-a#aaS1Ez9n@CY zBV0R;BN`}G|6zb@FSHNU&H7$Dq<^H544_t-(B!3nwwyW;tqIl3>pD-(Dk>YMe zE_LU4GlND*O&dk|y&F(H)SQ!e=c1w$u5KH%r~S?+WfjjxNNK72E+iKct&9G8^u@yH z)C|**_x=OhC_kN%vcFGh1!^N-pT5k_kf9;nfg9RQ_@+;QE(?ydcID4y_jlUqd7-HVrQb0#8nR2f)K0xH&)J{(eBhq)dmWXp%A$(wo( zSl<$q>n;ydDFr9*6f%?fXhx>8k4F+kkDV%{iaPD&`xWb zEcI{`U}XXg!u!~w@kWEV$iru=$DglpDw#+88m-LlPvVZS>l1;c#+M7hj@;rI4Gm)p z5hWRg%@W$iUohP>>TkE7JN8aAgd@E+Vxv77<4a8Xoj7+m7Cl6KH|~d@o|N!`y=zC& z6sDqR8!IwA4!Rjwu5W=(KbKy7^|OLR3hDt66QWAV6cZ9>qFd5k zBxpPqTWO6YIPHxLZM@$>uY*m;784JQa+Oo9ivujX21a73hLMkAsU(kW8oNmd{#eu# zH;Q+tS?i){Yzi{)=^go)$znA|t6fZ-uN7Nsw9RZ`{Bqb0PvcIEI}%iajK>y3{Gv^C z;x0JRjpFK=ffvm*CGO*{h%Ox5&fvXpOPb4oP(tDdt%2>kRLisEWrF z;7#QdF6y*`a>4ASYmW{}L6VEl9@DLgUD91DGTdw*nzs8x8L~z92H)-j{aAfoSg(cx zTcVY@4-Ga5**8l1Xt`?0U8~84=%=w*Uq?U_BLoQ^tX^NpVN7sEFw{AFPp?KiHK*lO1A3FY#dgJLWT=$q-(g9=p*(B zio_PQQDH2Xm`Wm0(yFSoh;-5e`5WWwbxHAd8{tm{fzvo_rWc&Vq$Cm)oROzpAKpDY zTV&gkqLe_Sx`wx9yU4XYhX#Zi$d%sB!|shswl7##ZbCa0(*-DRZx?j{N=-**?BS#? z)8U=!5)v%n`s#u<4RP-=d_3X0%+s=v4S6a(C7FsJE8YF)YN(|SOPvX zQtkx>GfXi1hWfoPqT8ShC}p*{EmT6ng1_ z_9qX;F}@2@Kp&!i;Kira9L5 zSzw7!#leTL+DoyxNtSFl!i(;bTc?SGjC`#nK-X4-;xk@i;MQpTsWY^e7nQzp&a|@> zxapMlEG}(X1$tO@zUm|`hmy7CCNDaX(3C0)5}TR-K)P0ng0bg>#cHLLG-g)TJ4DS} z?0=?d&Sa)io-Pi&CMD^dB|r5Np75z9hX&XWR**l;O$0K6+pP1NN(wGI;x5ln?d;vV zbNr5aJ1X*(tC_qNJ4WxK>CC&O z)H|5D8^=YLjzrc?m zTv9$P8~z^ZtAIWk0+(sNFORDMrsHM?Yz`Fb=P_B4C!rg#Q_bRJ&3d;cxtE3^o1Kie*(KT;+t#j4C`!k~%FxDsbejF0jU>Gp4`vd@ zWyr{O0G+eVbG7J7S9Rs>tJ)R;1VA^?5{@dFZJqCXM(wblzdE^%kNj@$At7TVOUAap zP5k{<|6;cJ-jLAKtetw(i*wY+j&tH9>HBd3!eLCKi>%P2_=ojegNEjTHDS1dbhws# zY;P+*h6}v5GS4ffFC93a#075q3dYPyQwj5|!FXvv&iO+aw1O z%}Tt6!r}v4KYjWhobP6GtVG*TS+Y+Oo%h>7_Ir-O9#?gg?nCm)TyqA=NOr#}fy^hb zV4r?^4&3Yrax$+BY~Wum`rYU$nK!!&fn}P=A|mfM`1=dNDW_~qDOh8qo^v_p7Wpx| zk(4b+FLreEbbfct^Cfif{R}9`;u1UC3dBz5~agc7M)eg-So#0!U0{w zcH(h!f~RdWxoxp{FzcBxTiY956S zdzwOzxAvAUkdd*1_}Us@PoD-?JA|uvaBdpTqAdmaB8#C~!O*fb-Vgi~Q0I81luu#E zsWSr3mKwP_Hr1)BBG+gC*Ow%T$^ zUi&gKW)<^im38S!o`Iu-GOW9LEos z=4-&*8+Tn_675H2#1mqpCl@!=cTK|4_g&-@EhXp>-CV$thB%25MBN`bf4Q2{KgB6Q zr>H%RLGs6zY+lXucC{3w?wqSnuX64Fb)VY^ao`Djg;yep+1M1!& z*PnZ!-29r-tRKbu)~}2eeYu`x@|3i*kCPK~hQ7J+5U#0V4Bd+GqAsRN9Rv}<2OZojMf;zdU`m)x=A|UwQR5a=jma;XnH-WDG)9mooR@}I*`?Wewk$&GF>QS3XJV)Ji zbVLy)mjUG>%#$r?WSLKgSghNbvnI%<(5hD#9@LhOk}RamJ9|j9I9)A8%?_m|v$r#uLA`t(zx3w&k9ro25brC0zo(6+ zB(+yPk4K~07`Y4h;5OsuUJf?@_;L?XaO=b=;e0K`ps}$z37Q zFx(Fr7yS>SK;&#z&Dl`$3~@JGLBpg>Tvq&HN8uynd^c~+QCyDqZNM5fJ*Hosvuzk< zC(%Z=_^NI1GtGkgprH4~IQ!!Z$``?276S}qu+xs4t1V7%e3kI*!MwZ6TsoLxoPJW- z3<=cN<01S56{st14*Y?xp6)e;l1jLDg0dKj=@z|;zp6|?G7lf?UH?-GvUOLHxZ#2c z`O+bZJ*jTNj$^#k%P#Zx10s-1eXo!LO zz4Gv6M)@Y;vv3?~z@^~Vjk1RzhKJ;FUwJQ4o8G4>Dc3p0*L?beL?XGu_PIsFk zHpvhc!dcs{z0FZ^JQM*QxSJT2R3tf13X(d-y`+((e7UC+V=c@}HIDo>Zn)T6V_R~I z1mtU;X-=%#poMs^XS%UXI-dekq7sxzrM!1YABdM4GhIwO#RvJf=Zg91a3-`;ZQM_PFOxqyPtL~*fEz^J#z;xA9UlFj6e zc#>gGT=*4AmO#2M_jvS@<4rb?$?I+Ib?-zKP3DQ-ah0v`xHIz^ITu}9%qP?h8&%#} zv*FvH5hXkVh+pGyIQG9w2~&is?`H_(sEhXecpiMSv5>sw-g1SKO9{~dvO2xKv63{f zu=-Hrmm?kTr&gb~u-TOvtGXw_bsZM@s1>TiVS*~_B=$6)z7>LCFK6TOv$Oyq6F>UC zI)Wg%3jg^COo%pgYdfvtN0A(gxu}ct;3^ir+e%xlZYe^`tft&E_wC1R9?{}$s4Yp9 zRN%aknV^UlCH2V^b!h9`_tVllE+$IpS5BD$=KX81r4EINJo%>|jZY|)Eto#K43a|R zuY>uVr>rvs;D54|x=e@b;^>~ysMvb5cDRgZdj%{)WE_36)@E=EZ;8b{|@zlL4sWXbKsveC}zZCe(IAkKf z`O+Tj!Ea*k5YV&bje8S@YjkLvfd@DLtX(}Sqfle!xRj+pbEbmDCUeYmI*6PSW94m*09Z*p#Cv#|=c zThd1bAD;x>jS4lGuBodo+2lcWpC#}c&8DSv)xg5_?Sg8u+P$K5>|YoHy)BtFd1{mal3%f+ev zHi(89EE`2VP1iVnB!kD@Lk6&1JMZUk^Jy49B02M34%g_R1g2hvyvLOe!GU6gV8jT~ za0iOWUInn!>R@$Q7I?9f7O!{qnnmT^BF)YJptDez$V~;WjTUq`=H0IT_O<2`ap(0i z3~TG_JDC5q=r28OezO+ht15F2hn$09lS6{23K*$-?;H81E!$OvG=LwG!Z1T>kQ&N1`O%)!;G|cce7EjcaFszo)ckJ!tmpzeqJ3r5O zom_bJRyQUJ$`RE6X3g3XS1a?-@7siK^kv*9B zs&WyOlhQjzD+=7yK!88X6E9;Uz}vE!p#&0{aqg30K)&f+nUBvrr2GyE_&GBT#!mFP zA1{FEk^-M7^P8Xe`;X6k^uv(YV!yKUIBa+r$D+q9;`_!2Tp+M#CpwSw!{^3;yn+M{ zOI`~Mvj{DVoF!+`q=dsh@67Cn1hFbiTl*g->|bm%@3Ok@v-%HeU=KCwo0k5EUGljl zD!DR~REi<>M3Y6VF}VP@zLyV;h*Z3Ldk#}3q=w3qbx6|9;w=0VAiI zgb{{pnUc;a3N4dY=-IX91ew;uORRyDOl01VAVJZLQ8OFiX9=(TD9++)n$hvR8{G_!eOUGW-tId4Wd2(N;!o$x>wf*Uyj zSne5Ln+0UG;mo?v#XaBZjo9(*6c_}1G#=lNCgkFb%!b8T#VaoF0*OdoEVt>_ z3WI5d9}K)q*{@7pvfhD0Csq9f9yP8_6U|)*XC59uJj((abpHP5SPJ+I0lZ(M1p|CY zTBf~HLh^UjmK#jE-5Xd4xzXSIMQsc5t=6i{UhWNTI!_Ed1U{f-1wwD{pxwF8SI|vZ z0AXlH=4r3=)ysP`hGDVFf~!HPi?sKDaLa|Wq%o)ywUckYm8zyGWiSb5uYT&}>D;Ysg$s zy9)^aaO{y~K!I(3qE0^K&GE_Vle;Sa~ zyhFR6)!#cX836XRS)Hsr)0xgqGUnHSv|_J>-w99tkCxoaDg=U(y3D) z9LT_vf3CCOy?K{BoIa!5^xoOLhA2*hds?ZPu}b4L_QT4mrqhm*UZ|?9rDsYf91CW> z`dcH?y!Zpl@*3$d=Nhkl=OzXW3GHe*Pq|powG+^?gMf+f%wa>s-*(xDho7sXH(9PQ z{L$C>?_*|&`h7k_O2H=n2J_G9wlHp|c z10J$I_7z6ziMQgId^N)kcLN^f7)S;5S{1kIxTx!i{jc2*Q8v%rYVqW7cc3B&uBhT zC{dj4p{_jrx^%^?a>t8;BS7xfoyH(L*6>jrlJj@Z`u_lOnI1EnYOh+Y=q??irK!)T z3X>CiS;af9XsMb^w8g?Y@t3Nahzf9wIY@@EzBKu_At0j3CM@8SI@+KJ;wXp;c7!|> zR83Fc{rjiD1nAXX0L}pcYbJ@N#yRfv-J4&Pu`BD?qhbfDUOEz#+LDfnvOCn=2rmzi zY37VDi&W|T1R;Rkl=qpr^w~&JCmyHYnEnY>y5D6hZs)j9!OPy~nn*>3-WoIVo6_$S}V(|2t}(fKzc`sz&Qd6g&R_-0bD5{Mr4F>GK#0Zuzq zySfPHvQ5W+(p?R{_|4Sze?IK ziX+V!b6AgW(cM_hjHP=^;ujDQzYmdJV=|SJVj#|?UY12}6LQQ2>IUWSng%4ml6D`# z{KU5qMhFW?`9!swGdKGu zdkx%aiMAfcx5cmz% zlilTjM?lZgFb+C{va=^<1*77HB5SsLhu~?^{1i1^)_j+=*0bY`cOZ7>EmHUCc(i7K z6&`RFl(o%Aq9@8iU)@E1GaaBK0maijObI2VNu(ANi~O5#Or+S<1w=k%!jApg9y-!8 z>LKtv^VfcZ{sd1eiFTmVC^zA?N!9)Ux1?#G1PrcALtsC>V070QcH3uhf&q|4*6agf z4e78yYasu*Ad-F+w@M~jJ(a9lBO>~PF`L+D@~43`t4WM3oRntC~J()JB!(gJqK^y1fAE=~gG_~yRx<~g+#`Vl_+TWnqo zku$3WelG0-cic<~mA)&%1$SdyWx|V^vRTA$=T6LsI?swL8%{_yDW!kUVra2}?AB%%05{X)1XMvI-l4Ju7Pc9voj8xan*$Dx^* z;wwe4FogSt!44;*OFmK;9X#XEi5*f@-@fe0-OiWpW0M8Xu9sw^Jzf+9@;f8VDfce% zm*09(`^bXi2*Pl5XOL>i2S%AM)6 zpY!Flw8NJ(ip6O!lJaO*Zpew;Q#}M+R|L%c%@NNj_;GqGsfdp7Vd5{9v96zq31*fl z^7h!6O-nXl-Kmz&u;Zrx@c|VB~7PpHRg zUoVK9@yk`r1xOJ}7<}9+YK>x_xwVMOOT1?{+?2QxESWPw7i8BO(xD^*>FVs$gI+Z} z<_Ko43RX^DFBr(2D3R%nyNNXeg%uCBJHToYt6l=7AvwW z4ah!Mcq+@?;;N1l^+}`{dCVx!-VL%Ecc%xP0s=|Af2Y@|_vc>06?fFWAS%*A+4&%; z&WE{B{0Q^!8-N=BX=Z)F!5#4u+x9zcvtKlMX}IzQ5ha_;ZxDAwCBzT}49$3SiY+6U zJsOW0bF@t7QHu3&-n&p$_*tQtb6<*R(}K+W!Pw0o-Y zrF&f0Y^}4A@*zqY5T_eO@Pbcfmx8@(_QU&PKASHW6Vv$0JpwjPNWVp!)Y{4T(~W4h zS%g2K5dB!L2Hz`gS3@LWA?OD?^e6H^xc9ha9t*3(jJ3v95XiI1aN^SO#V*~Wyjrhe zsUD5*RdjZF8&1UeUqmsaH6X>9q^27!1gY*R0bqm{OJ?Emn6wF5Qb9zUiazcQt$4b$}$6-ky8W%md^L8Nx#k6oI zMMjveO}3eLXrMEykqUwKYaeGp{IiOMPpw!mTbi*^J-1=Ty??}Lj0?-_?eA){B=kW zQ(9P-YV_E7-5W*6cLW+{!sPGST~e1rKS%Kzj_0*G6?m?MkQsXZdbWRrJfn(3%+Z>1 z$JmXQY#?@}-6Q}$!*R`N{^LAPJItB}W|PPRk6+J0q@`n1w{Rf~pE%2>QGq4;DqXV_ z6EN5EVQWeBJGnPp67D&sSJXjm=z|n^&ILawzuJqVC2PReS&@n2j$|{;@YJ09^Wkt( z4x46G>Yy=PxjdFyzVM`!50~|CE^DO=(cTzHW6q;%xs1!yGrp%#i_QG&-PWfPH~a3urJg_Ky)6k6ut(O`i7ya+y;C6!kvymEtYg+j{3GlPJ-=2Rn;# zI39nu59j}ocw~F?BshN0Qi9duH)y~$QEF2Tx7oa>U|wtE&y(znGD|80H}TqCJ@zSs;U z%%2o{9P1tnwE72*es6v}`6UMTY1<-Szg?H3co6&dq^ifQNu~SY!v253_J2Wq_%0d$ f#k{CY80Kz$4Boq+SB~(hW-sKWm8GgBO@jX$L`XQc literal 0 HcmV?d00001 diff --git a/SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge/Pasted image 20260730181941.png b/SS2026/Quantum Computing/10. Discrete Fourier Transformation/Anhänge/Pasted image 20260730181941.png new file mode 100644 index 0000000000000000000000000000000000000000..01621a06d08e2ecbf000359f4512b2933b5cd30a GIT binary patch literal 28770 zcmce-WmH?y*Y4ZmuEC4DQ=mX`f_s7#cP~YX6o&%A-CY6&Qry}S+)HsNRv*$t> zXoz>>?(S6(f1bN*DFUBWkG|MJyg;#&QI~o4tS$lj&H@$j8q-zD!2Q`Xyq>4u=igmm z)`&NWJmmE~v|VgHye!;oo+-N7*f_h}yLg!DVjzaN{8E;a(eXAtXfv~CTv=HW2AOTI z!N>b9EwTLS7&<0NxJI!2>yWm(WpR!hdAtqLKfoM@%?J6(ElYV`M(0=;XQM0b6O(!p z3t1`)Q)n-ahC5f_zDv56;Ih}oxgq+R_LJ-C_9O3EXSznTvYchI*LAJ{W1NCO^8R_p z7fD`%mYG=F(Omb<+{Dt^#a5ADNZhGr@~z1*7JYTqNHFLkRT5p2< zfRX~Pn#u4~_kV_F zehv#G_|N39vFZPfFC`@f{v3Ue+V4vpc;^>Rfj&!(IOy|PMo7F0hy+!o^jW}C$T1T# z^VNd>w?g!wiUn>D$#m$W24PSR?HXBgN2Av%XlD1gW;MtIGyr4cA%WWJkk`y__iL(j zUz*!u!R|<<_(B>)D;0&Zx6TyNtB}bqxYFclF2wMcgCln1gV%_W(|8w`a94$Yi?bK` zgA`1`t1tRAl~ya``m5t(lNC3N?tb^}yzu$kdk$DHXenB3^&-(fr5x5%zbf*N5^5#0 zNfqMK-xJEs;~(VR)(&aYSeYL0#^gvKVM|ccf#J0_B+G16UAnbB^Q?w!N(-nT`TccvNe%I8i=8aRbzA}- z==r?aifL7tFMBTz#!n4N*rcNBiwzlm8&KcQl~mEJ!H)>FWG09veH@GOcS>6;0GPmu zkuyB=0dKGzfV6u2nE<$iN9jjdpGwLZrHK9X@^k1QRM0^&2)Xg=w0^)&;nzaxAEJqHulw9quCrZ_%a(!% zx5-XA)0q{H0khgx1%_&}pa}mdy@mmvmPnPzPy8%kJ1HjmfRMq;=ig>|rYw>>=l5dr zE;Oox3QkE?5WzdY{ff2nBOeMz<#e5fC@i&^H|}2 z)5fuIdMY|x8Gd4+XdE-I%WTzM9Fuzs<7OXUdDtGB1u9d&&x;yzANCCV=tv0E`I{9N z=#|O@`TI-3_6G^R!l4G4qNbKA5{D2&6w8yYm&UZ5b0uK7l21sMRi zg*!(fF}bQtB=&=jdV;@Ax80Agq368s(Xazt5j;>~pQo|581XHenqx1A5I8l^#Aj(K zS{K`QNx47fl&V)eCddW(I}vi-{>b_&ANf0P6zs7)PT`Zr%&g@Bnt;i8q39dd?Yy@E zXX95w%?quDqOcLpfrG|B=$1+`Z;w4YsEIti4K6(OLI@%T$LUCq)Y()Br+*H3b&C~u zOU5p@VSBNY8^4%mdnXv$_`^ngDHTn5kT_;@^rm3Fk&QaeX020H) z|M1?;99p;u@>i%9CV_9LjH%5XG=dmY9+ENlyn>B*Vx7p}n_P?G?pB8JXVC~uhGpb= z{tl?@#HcQ@cH>(%E&N=X;irUw$`chl3jP38&YPiA?x04-oInXqn^UGq*;D)wZXG~$ z*dR|lTFznuEU>Yub|D2X!n*yOibb{xAMyehWmKE=bnJ&%Dl@A2{%mGA+AAt3JwQX( zEHMxBgS(5w)4gkg78UM0Wx!z2Vsh!ijKlh(618e`sjFR;C@kop@V-mN!q#K?L&qD7 zVG6c3cd#M*g>l+?e7U4H6gDZI_fGO+;(ut)Pv)fj!XVbc&qULcxffUGfLK|lSG@G_)( zHkJIYu&2M(&h%`R=f|mXf$FJ`9DNG>fgY~R_D~Ww-%#WsKe6S7y8Z))RWt-V8+Y%_ zg1_fUF3TwOcKk=QJO9NxPnH}#AUdCkJ{7cs-qb`uo2Yqz$Sly_va+)mJW^BmaA?6*guD&YE;F0m1yXf1A2{)oLn#$MI%tWV} zSZtL_-z>M{p8xTrXik<1ED7ls`$dt~@jUMm?~ECJIut9G^^Y-~N#h4x@)n-OIEL7P zhHEp9;O**8ZxD_sjAxe$EwAY0A${u}ogmuDf5+zSFM| zokGRFh>qLMe}3-p`-t20HDVsMhW(>DLx?i;&LB28|1CMYuJ79#Zu*_h)cZoMe!M#o1Z10@B$NPl}1H~TA z*F37!KP5Oza?y@uQBw!6>wL83Z->`}Plb$+y=qKe^<4GxuD7x6khqZqNXMdZR6NaAU%g@l>60rMB1AXdZ z`;FRyD));2c-_vVjgy>YEsEeaRSDceg6Xp=7qO?I*$XE7DsW1uY; z6EHCI+b10uKi{Y+`XncLxj40@E;1o{`zv_HUAu&^sU{pvA$U8gcN0l{jsg`v%^{wR zaq8{iA7{V7&$3HwU_8$@lKmHtz4{e_8CaO*i$Rf7Drwz*IqPjAU7-HDm6ngf&}w6J z5mDp`covRym`TBp)(dF%U+qfgs=T%KoY$!qUEY4`uQqY-a#81L|bwfi|26+rH z$f%xxa`uNY5TlC4%lYJ5L24-RnbJO_nA$$XbtlU!w2@b5{BAO}K#ye#9dDpr(1TZ| z`y6eQIzauU<6a&&3V7w6cq~jd%9BNlH)2v~SUxOK3$ru%!hi8c*0XQ7$+7Mg}20r^52f3AwSV-C8pd zSD`@|O@8dYwOsp|!n};RZLcLUZhXc-yn>HqQR7CZ4>w=S#iVuL=%SpfD)?ajh}ye$;7u)Jh_w$$ z4prn3W5>$@d!@6H-P|83Zjvmy+Y1py{ef+SPVUZH*trGIQRw!Ycyk7$TC_!P!ou<3wpQBeYbq_A` ziXHuec?k}v5_KNSMh(Z^OX26=W|3XLFM#@CGR(&GR-BEgci3Jw#c7P!-O#G7 z&b%PSCz>E+HGm*xIJwP-?_fiTb-Jb334uz2&2_i&%<343wdbOArBO|*KY)b<7-}g2 z&o51y!a#T4Q`!<>(?O%i&tm*3F=g?Ih{_>iKIgqaZ|YyA=a3{YCm-;kc zvp=dv88nKD76Fvei)854(#aMKP*&3t0xvv`&`N-w?T0io^ ztU39!B!2&S;_tCe{}pBKu`ai5fkRQLK}~wdryrt}L&R5K?cCY!DWeFn%szFlvspn9 zfm{h1_KcW(scgtf55@@lImI}3+(+p66{1ZmUjkjh%|hYjf%Lko0T>03dy*$F}R9as47X8j+3}A#nsYPN@axaeEl_a(S9#i(G%fE3P2g^HEkTC|&!WgAE;D zKr;WKfDAH4453O*89PdxtCs(`G^^s#2yfB`A=}@3cuvN)bq z3(R3Eb&;k=h+H(qZng&_1qd@FOkyA>@BCQzTj;o~B~df1S%1dbC<*|HVm**YGQHa=!a-Rwc*ABS?&isqt60sV1BGp~<)CZKr8-(s=o*n665bl&^Lv=FO{AUy- z$9(}jI^=;3LH{hpHa9aq`NZ>1KjotA(oNcQ5Wz~{DbpLgM%&5!sFRvM)u(@qD+u1U zLFMPe$#hb&zbV^?8+ePK_DWw{QGfANuPl?Tdu`}__!-?!68+qZa@do)FG61bsAsk% z=EBI`b!N_=J@d=du9@ayN33t7u2P%xx|fXTZc6E^IP;s3fx9V?KIlZj8i zfrg;ttf-=F8H=So13rjUZs0e9c%6`)(>*jSO9dmeFp?Xwi&$lxk+URhj`Yo)Yd1bK z)-lK~jWEb`Fp~V^i45{V?L(x26{R57xc`B44!&I+p^TlVU02`%v_4zWqJbt#EO|pO zx42V*%*Jqk&%3v6Ti35bHsEb><6$J3^Y2AXfLN0MNQ#7^cPtW_LtQ6-<(IBsj_-Rb z>wG984FXHgZR5_5%AjY?d``0d6*55}NSjp`^x5!oNVFTYa|X<*PmuJGK6@gSUKrD9 zfd56Ec+|pIAiurP@_E0hhm1Ujm1e2Y58y%)HW^+9zo)&Epd3yT`>vO5JBqOA9=A#> z5AO6&kKSZ-i}_hc`+T$&r=c#~k|bMHtkDG+clr2Ni6&mB%smpp-ny;{`=j{?ypsfW z*DukN<(OMeesXq7xbF;d&3=_IvvUDx9md~;$nQeNUwkP3x&ktHRbKzr_7-~L&`W&l zso%iDfnKk6pyb=V*W^cfmZtUBIJw`~+EOM%PTTqo(Z)G3?u}dG=#;pM?54>Z?(X?w zQ9G!DO#AbxEWAn?;*r@|ytBTp(=dV|m?eX6uG9R&%gf3{-YX;#@gC@48d7To=H!5Dd2I^Rl=r>RIM9*QO=%tKKY) z1~MH0KS>V8eEr&N)xB7bnj%9aQuc#^e^e2S3yxqrEUT}UF^Ypf_-7j!g=++KGh)9Y zw5NGZ6GqA{QD{(M@G|l1a%t-y_C`}ss}o6@E^=vPTU8OIWYAsPr{E1<`Imkofcc#b z16iLDg=Qs8J1<=f(B*>a)SVDt=|N_#tNZf# z>if*8`tG~bT7qoLf8D=slGoN6Fd8!2czw&|E`7$CSCep z=eKUHfAG&$d~c7>yV>3aw4Yz4?#&wN_KdK|^n3QdF}8n9P>uWl4eRa}f!mG2gKt-X zoE$4mOJ*h_F}vd`g?b79NRgVq=Tc6XP`nNq4mp0vQe;qO%dxTEkLfK!1jajML=3jK zzrJpX&@X>1y8XfQezPkRTv+LybRSW4E5>{@>rNsl+%N#)Tqq@~e1O}^lz5oD$qam- zIHI3)z*Kz%ch2V=WJG|#&B3dkuyN}aq!rS-JZKQaowh20hH^EK|2S;Cd&#H9K5R~s zm?xP9@+)D*Y`=q;B!2e7_**B*#?w69J@3|mu(*?AP9nCU>W|qE*nm$wCM`HLTr)FekjZMRaN$H#MBxf)kWK2b-`h(cFmNSR404zex_= zl|k)K88|$7Zx3$LMefVuv;BiIjY{&yC1VF~@s)`)X|vWoHj;09aQRc*?%b(A2$kl%iXP$P zE)tu^Rqj;6i0rfT?t#m#eb(qbh3nTyF!?9~r_l^NraHRYPF=+)C7g z5ea2qjmL&<{-N#jXqBAbJ}^aLhFIw>-8c21%@=jSW~YzkJ%&PsQaDReCR4&EZ0+xm z|I-6%-UOc%v~@o=9TgVB_{@C%N)C`a_=yrHyjKTqqof(2UUM6M zZ42GiM&+oIzMTLH6{CywPd;cezhCU2Y z7&qI1go{$l@Fk^3-R+0JiwoQnJ9uy(H2Y#f$8Iq$da`A)-9u3hnUc5%$pr)h`(4ce zDiF4|lWYVR#TNgl_H`>eHlO_i;s<@?+3?FmXD~T^bycRjJti*5xC8jkK!v06HOkWb z$FC%>cjB|4hutomDhtcd*}}?%LCc79$~@Y2v)QB0GOBR_{M761EfubPcJu?X9wxE%=WTQKVEOps6q$Zn_K$ zx>yDTF=qOX&McYHYUlQv)hs9y;>$WokhP&m`Z<`w(M-8XVUR&d(RnLKb!=98ZOiSq^feTo6JbcUo0h<-wFyr#Yk8#R;l zK9)(n$Q#4-d6HBXB@uLP-g-lSw?(_zjFa#2CJ5aGys`bz8h2u~%SHv`RvjWduv{Y6 zEJ7YFzUvF4U$ah51S*krt2D1*iE(?#+vSIyGK-HXS`FbXzE>U?H7l(kjGf=BwNt$^ z<3wdkc;PTzC}^YRJ;j>5u|+@iXyBrWMLpqJ$2Zzx8q1 zQAwUjAl4yOo05N|8Wvx0>NY9Oq`F@0R&lqNU2tBdm9HY5dZ{gnugW&=Wyce{>>27| z6BihW;bn{otbdVQGW7AbOCeYe$DkcTKu>15J*oDwQVO}758!!U|Knf^Y?K(H8X46D zA|)keejz!=f8KC{LA65R(!?6R)Q~g@6JrR1<{ul%rB1xU)7TJ?u-+D#9 z08kXPmnr;csK_mCBnY}mUe=E6+u5Y9gB8{N#IO|lctJ(I3&dP*!P?iwPSY$l76S}a z40==<@R8LIjP3GWh%qD@8oB};J>fLNFYTHhY5gS|I94J!(F@C}n) z4MQ(f3Fqs7wYX%`9_FJ4lra6IbbAwVPlxYbgX1^?NgpY$CI9s6U%?b#!Wys7soV=b zf9<0y_aQiB4OgENb=@{*JY}#s0^jR3_Wf&AZolnZ%?IOSH;wi{eh+5_U7JKn)Ypo8 zDg-HjW@Xg2dM~g+F+WAMmog%njD#zK+H$V}CQreva+Lr^W-*|dq)L%Z26*1T7n5>- zdH@$)5PD$7Cq~-|c21VqETBvFm1du`|G1|s{s}@y+|2I*M#2S0)Jd+t%L9-zmNfh7 z(Ctc|oy$D$FP+Uv4w}B3db-sGQ2+m`iHJ$z^!#^~&i~Z|4QVn#5MmZ~Eq==}vel0N z@o(x+L6qM+x))w1Y6I3UHP)mGVjF}g(Rud2W2MH%ySX0hrsFwH1YcGaI6u1MZcw9N zG^08eLr!AquTq7a^!G>yX~mxH@{yqK=7w^ZIO-{ePhKvDdHpV`&yFZs2VV;%V*OK8 zc{<1FA*1tuXWT#l>S|gkk?{XgvCx_14Hr04V=)t|-4Bbuev%H_L$>4bkVhnfz~C6L znQozYwYjtgwH_$*2h;;_uZ5M@^mn&)rm%8)<2Zu3u?HEU)Nx`BmBGc{K1Orh?jFldVYY-#}9KznKUmS^a$2+;tO8VxL6m>Xa5<2#QuG z%xL5)xUTV%O9xmdy~e;INhwCU8)(kn95O1bj-d=q3%-AS$G`#+^_+sJR)*f>h>AX` zD-7&17^|VLuP)mPvAvXKoLfkwI-hiGy-`GD2ULL7DfhHzX^1sZ*&`^gkYBY<0#(0- zXHfO+in{ETy3VXe=0B8w_HD$nkaN4+N!UID$LJBVrUW*ND7TJ0#9cLnVT>k<7YY}w6v0(Ur(Qk9I)4kes z+--bhvK0sH<@V5!qHh006Tl;#CKJ;x?nTLeHwX4sSXcNH8nu{;uURp`5T&%7220DM^J z4r4JE7^?OtLtt(gR^zPJorjdzxNr4Wi+)UK`zsEN@W3}DU1KF-`?Wb-gPxdB4cvKu z+_>jnfIeE(I_-As02Xf2&!M|Tm`B(p+-$T-8Wg=tOTvY1&XIG)`{n2bkV*80Erxf_ zpua8H+TdH6zeSbBJSyy3rwdhqzfi9Cj&k@eso3O)wptQ`?#vw6f|&Qryq83|n2}R@ zDV`pAxhr-EXe$m)-g8{7K}AiDfHrmgfylXnkHDze76@iItoomj@zTm5S&0PLP5G+( z6{%NP9|bE!!w80u>DcZI_ea4LzAVU23$kL|XJrUtT~K(V6MVrkoW;{hf{IWuoe(7R za?ZuqW7W&QQ8{;bR<8ZSr6;`y1a)UP;xSLoR!V(6WVmuB3`Re(7Sx#JV_!@$)svDD z*2T}TIz`-t>D;iw!PaX#7PZ&T+C^fl7g?c-GB1F*2ABB=Zs{|YYP#j)fOKh?JZ(cK zxjh^PT?aqx_FT4T%`rul0VW}d80n+)gfBDl^X2+6>FJ5;LAoU_BS2!IsNk#5@7vQ8 zi?ckaX(gx8iTIXy?rLy#(!ZmAE+{dYW_#DJX(yrJR#R*lIxYlfwRzId5UBk#dKVHh+c?NsRtw^DzpaiY-b7v zBGFF~RVP^fzQNcDbUd?CVxf=3r!r zF7FL=1hl9o_(hK!@@d=Q#iTnLY4RWbld;yTC|L~75dr+TJfva#@BC6i8vr4VMo!IeF0ld?iA(DMZe^y3wb=Fp495%ty!FHeN42fR)gVyTxl|X3lh^x-rlC#RH^w}CR{^3^^Qk~%{ zEj2=JB#IPEi3vurhvCz3*S+&4lbvy&tk<~xMO9u~d zJe4TyeA$+Hww~m-9xF1Ags8%f9RMhIj_Xb~qFMVT-YAb;!pqRG%3}wW`eyOYn}Hk9 z=p;T4^8M4f=xPq5Y$TC=kPN)XV6BNB;7J9Ul!dV}B4y67X-&}uJmrB#_p&eof!E*( zS(!nAUh&9QjcXpX0K=^UbJpm0Ha6L~H6p=gl5;^0G0&&B2d4osvgw~O*Fq2J8LGD( zNLXb)`dcWDida4Umk1Xm&{x#HtpN;jg@t6!vXO!> zs}f_fKK4a7VRlAO4ZtNjDUjaM(*Zka>8mq2JRcmyTki;&VNxLhy0sPLmNTdhVfm+- zsf&^nJgpglEP+_`>$IYLLgkj+d3S~Zy=#FP#qR6S`s6VFtxhrfr8}(NMl`T>!vyqI z2!n@I23Us#)<8NahBj5kQfY@*?uRxdulH%`Q7fcwyYOZnXaNoRI(JwUHdv45UK4#% zFY2a{1(4u|(|~LBp_luX+Q$ym1$XtqYd^siT4p3p-ePEOjmv<81ceuVY*p*MGwfed zv1D)iNj5p$rgu4^p*PsrGdI5@206dM=rfvDd7scn4q|;ht3nEp=Q$&*=Fe+yKC!{P zAj9^O@4)R1)Msg}6Ud#nB-VDwi{e33ew+pE39ee-`ngOD4#UZu5NzgNqPbrm;#;Ix zsil7Fuim7q7&(U}8wM|x`C-_TvuKKr=@%arFtk?TuSihwk#|61vO2Dq=%gI^s49Ng z?f2WKyWtSW%NS$AR0lP6MRdIH4Zw}r;#Kp`W*Qx8`uWR;`w{xD7X%Axv7sk)i>4OE8}n2>?ZyZHyoi0wTin(QgPVnBapOb^K2;jduHV843`lJ`?P=%v9H_zw zsme;-Lk52`WuO>n0IY>`q|4CadV3tOH%j=c4Q)N83?;tlrj8oT|1u@6rmAC|RUm$7 zM?E!9T{4d)5G}cHcVoNf7%SaNW`@C&4zLHnz{q%nqM2Nwqv%yiJ2sAYBHY=TZ+k*D zM=@XMIX9wI4LV|WT1pP9Q#68pYLQ*wjTzv6GcH2iJ}P4GBIpT4a}mQ&+kINA+_#z* zfRT&Ts=7L}>&sg8+A|<(_@!>FEY;g+)uJzXq4jUjM|W#=a4){b)z6*oa_kg}79>>O zyyz-ZSHwm*+IpuD%+v+q+-cqXokwjR@}VL)Jaeg}+kY0wc_($S|4@SBGy^>Uf*Vjm zw4XI2=fHz*H74&#3x@#GTxGaM#RAswLLS2VrR z{tjVafHUmR^6Z!0kJ#lCjyAi34PSlxz8O4tUST?w69(zOa`K&o`)}nJ|&tk_yQ2a zB=?1{{djoEibUpHyqVj^IzRrAIAe2(q&(kq_yT_Xy}5?CYQ?#&2*!siZFzy^sFW`b z?X(e-*C61vHrrSG(mAJ5off=LITHk89je&GeTO2@&QEO}4<9SR+^J+k_N~)U@y3b5 z9t1a$$`2;0FSil!t^LJe(7`Z6V=+M$i(mBd2z)Ga?<6w$xu*QS*^d*e=gkf(0w$uUFa^TeX9}{?H3+CKTIt7#gEvGMYef^Aw44MP z-jHEI4)dfS#^usY^4du}1B*WyqTMkImIyl}s$_=9T~`)BKfd@;#1K8*JdBI)>DP`*U2qhQ4L3MNb;qs(bDN%;=LNg>LCKT1xPua$Z(y*sWvj z#XJjIXGwhGrwC-3(JC9i00BbuPc@n&E3rD{J>n0M?X?^v_FvY&+cdUFW-l~GpGJc3N$4%X z1M)v5Wa8Fb21-ts6)%l&`;oDn;~&?yO51W0P*jEt?0mObh~JB$rpAYK5SO;HGN4!! zlzA*GT-Svxen9?WGbrV-#NK`Z%Eqn)t~JZ+tYm=H>aoDm-mYf#Sd@Us0+c=sb-@%~ zB=w9Sosdfvs@Eog^*2L^%F$TZOAiB4m+(%HKU4(|7IE0}uqSYN14TSQMxa7*?&4Sd zMY0Wny)F%uDh1*q34miSA!GZ$&ByEnIfq#?&eQUL;_%WYQ+}L>gdY(vH*~S@HImyt z)J5$&qTg5!w<+^fA=)PvwuqVkFb0R+8(+d}AKd;A+8CHbW?`>!Z=5*^Bmm+j((h#y z5q&jsqW2(hr51{SONA-B3C$px;uMcOk$O|xe0#R>sk@D)>G5z*1hxu?pM1@ugAO#MSj6;e!25Pbg?9`_ev-A<^ntT(l3(N*FOf;6b$n&4e1i z+yC->rNKo!)tX2L3$Sv7x)dQZS)oFVoAWZchfma#2_`u5MraSsPlfqGJaNcd>MyJLrCj z#+2?a<@UpFH}pKmw?gibt_)Y_4K|3yKspI7k}dBJ zkK*be37l%8`#+JoU#8jt1wgo?a`J6LNKVn^kpz7%ybE;@@H%IuWvslCcz{XJ2;! zT#1l)iAm+#Pbij^Ft_7xNiP@oy)xaInJ4Kkc}PB(s1PST`w-*Vu9 z{pNNoPQiK3&_7^fsW*>t(Vbf&i1;MrB0Oe4=(2(SBCiEl7w9m$L){^5Cn?jy|FW^p zy(wai{LV~5M+lt^y(&;y!~G8&%LyvN28nDC-8Vpw`)dcDIQ;_2O%4_+h`5%#DJDd; z((qAH@5AEr3E4kJC+?|@mf*!$@LQ5s)1F8WnGal$;DIt6D_ zW%pCa`}&(&$Na8{uEjXm>o+uwoLnS}fFVhdDi~o}vLNAKMz2XEP$G`6uEv??^Hl3O zoV6H3cr(9(jbZVGZyOK#rm-rb2#QB?7t8idi4WmIYfDN4*x-(%ki;f{R^`@Lqhn;@ zF)(I%QIGmNws4AH)v;@>al6r|RvN(%8tI0PEp%MIdEY2grv$HHH5(xP%kc}v)}Io) zwYE4-x0|&D(K42e-wNo`ez+~RNm0IRYC8^I_Hnu@FU)R zhdI(q79a@BOCS&SToxP8c%h>_C;oo?jNMi-I(ID{{iyJl`xq{rC>iQz#8og`3I;uY z6&aXW``QQjLurSqA6p_zi2sdyGk_K0J4`f6YL}|+G!#e*vM;W;>Gt{4oj+3iBF^z7 z2UZENIMB6-lK7<%H)$P8W;nN7;ghOm_31`zfK&6`)CCSq^S0Z8?I`6WOQgC}{}t%T zi|5`iuDvx7+G6mrC>y4**8RVk9(`T@ER6bL&%0qx$1z|vidc_NfZG2j2l1H4xcWa_ zlQ?ie&5zn-Gez75cFx15Z>6+M5iZL;`RxVW)ZRdU_!Pg=C^mb3s@n6J>X?({d9oF` zN%w@0CpAs_Ku@EHc92~D;`lLt4`w+wN9D2*mt?jdTC^jH&KoR-71eI_t>SizE@MOr zMSOqWo~3DM_#rMOWM7Ppjbm6Zf3Y+D;@k+Kb8(>{=OYZ3J^-`iFOUb9CwZ+F93p>y z@P%DypsKAtxj-rkT3>P{i=URpmHJu{Cw!gjbLtjR-NzpXgG@&<2-slti1Nh;b?Fdgu2(aiKD466Sup#(p1Dh!+WgZh;HL-pM=~1b^b#IZ)t+cz-MMP7EOoR3h6BN z&Oq(pB8q#m_|L;F95kW#-h!>`|+ z&CL=uZsAVlvx97h?0?4f9Y>0gy~%u7iQA$aH2b`dq+05#hq|Fe{WCcRZKKPIavQRd zdvX``Db2||D|)JBYKwtrK23QgbS4KYyR3c@Vow!`U*sk7IS+c2Qj;+#2i(TO7-R$d z()pgY6*qM$nDyJlds7*zI1`k;e*8nhqWHPjt61EFfg5k7!cD zR{hp(a+PsNS?d+ zgcQBL{E~P30=V#)kcqPLp1{@4Uu?x3m2pm~Gzv&NjLvwJ%ACtS zrIsZ@%H7=$#6=p86W@hLLO4h&%3b|&Bo$i+3WOv zJB!6V?w$adN8UhDpyH7ri1k=PU8a}0ZyEKiA7EO{}NslFZT`Pd2 z2>otyB}1WY=$A+GipKi+&Ug$>6JF0NY2V<2sYE8JZ?%EB*CMY^K!yWAa2{c)Yu4A= zlq6hu`25yct7bTgD%$3)Mvb_F#Lv!w9Ll~!bM$FOKC6gBMS4(3xJIf=w2j&*Rur7C zHvpmA3V{qp9(C!d~mnqxg;Y+!S&LCX*QC(@CfpxAdC4M9-V8o z_M>9X<)L;PrpCx9tFy3ylt>Y?^rH?vxKuvhovKlJdOChTc2svjsVE4t)}JC}pep zS{7~kxVIxp*M{Kkz7e1or`V2$QVjLjL?i@SENDr{xS?5M?G?G*$=^m!d0do`+s=8a zg{GqttT*QX&B?wD?KqU7#)}H>A;Rho6THci6P5p?!1CU00VR$OE`&6XuoB`wwr93; zhD44nu>Fi~nh1YeH^V#ohqBTni*MHeB6zV zdd3{WxFn+NBjXS!H1m(Vc6ak3t{_IKl;UYkhguk5`Xnx1L=+po({?72 zNm0&-o4UDS@6(hr{7)#Bd$y4Pz|Yh3{cVaP1`m`N`X|0J9(L^vW9I3uUq>kO8YOA$ z4sTy?s@mTl!?slH^?0smFuuXb8$sD>6nk#l(ngvI&#|l^L_@rB+Iqc@IGP1xrUq&; z11*J1JBeR1cKZwl{j&L6xQ|T;h>?&uSDc9t-M0HvXT*FKBU(t$*sTd4nJs@^Qn}`< zemmXv&6HE|V~uB?o~Zbtx_Po_LN6!tb`Levk7m&X`R47^J;ObG@Mry5SK0eznbS@Z z)i%y@W2Ff(Shr6$Nw-pOXk><3L^CMlvKq;68n}_NuVN_X1IT|}JHzq$`Mh=h7|*X- zvI9bFiBfFn;d|u6_;4=u*GnHtUJF4eXZ9n>Q$!SP)@gHK`-Zhb-2XAl{dRjtBx{wfacwTAJRI3^ta>GaKx z_-bA#*f?j>2{Hxc#SYUIXU4Kpo^AYo_&k=UwkL18xngL+_bA5)qkPd|&Vx{#r!7z# zq?brY=0D($3Q*zQ2Q6d762o@>Ti+f|`gTb)n&{LteLq32vxa+#a zC1fnac{iCGO!hOG(RbMq7ce1#c#O?4C>yEHRARv^&~XO zfnkejbiKt~au5f{H;2k#ean+vtR9b`zWR+kHRb|pQdx|S?SF*!z#xHU8kUrqWx_Vm zW{o|lx-+JAb%GcIUK8&iT3{=j-Z(xomRxZ@m1q2VJ*YGISjvWqu)CcHoe!&P9mDk~ z!l>}~J$%@Npe5Qwfp6&8P^#dt@uiZOO;zlT1UG9X#({k|KH?ZSpW9cR?4gfv6~hG| zecC@O8Warajj^I_wNFg`-Pp+oGD4ubT1m!XL;FxHTpi&C#6V1fhZQ#Znaz0$v@}&% zmGI&DONT4__V?z)<)8v`*JZO|tuA8#?V$knvizd)Ws-|7V47iHSXbnfvJ%YGDE9HO z3usXSIT66^H+7E{OM$aL9hTMA%b14wNlqH34*l^6En7QmlM=*`Pi87N91bj@vh)IZyy43xtJsN4*%@Vijg`! zx~I6?dK@w9GrO-y2@nzz`db!sQ+CYxWHO*am<)zBr7v^P?b@H6b|%nfXCAgcxA`S6 z9B7WSPiaNIDT(kISR4vUQs(%u3Ha!vvyzd%1n*X0#op7xkq|+;e+tr~!PCZ5kZm;V z#rFi0M1){Yf%`?{?iu29kALIYmhf5lqeJdAI0LuW{Q00Xe@!so4%()iA|oB39$fz>A!r2gy^fytM0+KRs)a!k!)P;D z)#nUwzx=$qltZsV>;*Fe0KSQPEACkCls}m@0)I&#J23YVO^2-<2eI+&y5$yrHU4&_v6anl6+I~DNJ6;2ra(A$=XiQqX;4BBalNvKYd)`?efPWHoj%_`f$s10Lf-H z8nYvG*(Ji)!;}m<3}Xw3qJ`VG>n7^eyRx*pT<%kr%%fcQB5ZgFIAn3iq{j*|TzCyI zEghu$4MRD{IuuAg;-12%6v2GeV@E~N_t6hs>|&G(H`=l&kVYyQCGF>{%_Ztl)^Ip4 z!f25x_CpsFN~(f?$`%wCw4&&7clydBesJ8YhK|n^4dwSgl@f^kvIsEaE`$(Uu&Cnd zoI8@PJTREjq=-x@VX*KVaMXe>K-4Huxqx2$pwzeFZ_!p z)VtBMWFJyT)v0f6NobV6A>+2CDK7vs&ADO$zbd&=&N{(YBW+Hjyo%yl74FW z2mLnzw$O+3j)z&~AT!pHIHY}9g!nlZVIj=kr!c=3UnNW;sLAfE9DM#VFm=1|p*!S@ zDclE+JZuao4EtmtShTo@+F>_p>nA2h1J;Sr zh;-9-L!M| zlQ{jT)Q7ApL61$Bu_tx0LQ4w0x?w!xqGmFOKC-2!ez>9rFN&2h3U4S#BpbK4U^X=5 zo1*`@u83(AbG+^7?_h$Zj6nhJG4~Ib9pBg17~Z^jqY(HoXm-sRD%FazbR>C~AjFUF zB-ry+Au?{&L!NLU*f_%G_agE2Jh3DLNSr}P(h!tNh^-mOUM!*)>whx9!Eu7TLIT#n zY9s~92A@cW!v7RW@Eo$HYcgoEIj!z@NH>N#lratJMncmLLXgHfyYIAYtdaG35vfWz`>C+jFr;Cl@NQCe&+llHFvQ~w zk^l&NzdFh{i;Li|@Dw$KQ$%$5-6yLAVDVXH=v9)`!yl>sg>Nq310S{%9@s91hUmoR z?wqL}F3mZ_qvB#;yP>7l;*7W3uNdn{_1$|C8$!PB^`xU(z#}neCmhJY_w#b+CRD6b zztF3DQ|^ft>jZXKzF?rLKF__jr+s5_uMu2N{$81xaEP^TMw?9tcsxO@pe48MqG$>p zKM(L|G4Y5Op9A23QTbfcQ`9Hs$J5nmGe@l8W>T^I-eQTPh~rQ~zyEt`M0s3)tX$;Q=Hr}Dawc6A8NgrJ`QY8sCygr$v!v=uIpq-QV zm@-Z#ERZ6Zkc>4q`>`*Ku&H>y1v~^KLa1ZQ`GxIoUQlcYSoC^$pl+hy^dPEuMs7`7 zwRNv~t&d53g>z|T%#HnqpIC^2-OWS>SRZXqJ~Iy4iWESo9N6asFQ0sos9|~Ocelbj z|D(6Bj*9YY+f|fKsUajKhHg=Mh7?2?q#Fc8kS>vKX%M7i21G__q=u9f0ck;y?(WX> z4F2Bld)K#4taZ*h-=D-hv-f^>-1l`|_q9i8nog`zsxMRSlkyK5DNts~Fw!T->!8Jh zev!@_b)xP2!8zQ<9Sa)gtjym4a(~$#>Zwv~0WNOae_wN^3z;QNza!LR`FAJB4OaIr zHSfn8Zjx`>gr5oH8{EAcJA(`c2xeNRW_5N^8;Ui2r)QCmmk>NOV0m+u;UXBbOh*cN zvZ}SgPp)l}KMt-)H9O6RZdB=%5kj8iAYsj>AK!L2UXb-h2+UsDC*U%97c}cuz$ABO zw$l2wzX(=Y-IYC+3!H<|FRgQC$kUDdai6w<&dtxVwER@`X}IOm7j)bafP$@K7M!E& zK2$YL#QQ-!!;K2B1+xn~#S{iH68{icQDp&Ao)BN^>}r^SCc@6k(PW%|l*^ihcZqsp zKOkVR7}sYq0I{T=!u9Ry5t|Fu5+1t8PQC^3H|q}ue}s^rr6w?6&HA`>vp_0Zj<@TxC_@qKB>Hkm2*Ya4~#j(+>$W?P&< z9KojGBO>jrFceL4_b|eL_N44?8ZGtXR>chNJ4OllS&HEi^wbaDr;f(?Ew!uFV{}e_ zkoB#)_2Rlpe#s~lc!)g>z>c`O7>1Nt!G9YJ<%JA#W4`Tr^r1}1s~8vWlNLF}$j35L z@&}~Fb+XL`LRj@qU)_~nhcs6=td0qQXo1i`G7L~kw8#AxnDLF|&QY{&xT{SyYfMwA z_ezO>^SDcHsLarT%~0eGbKs$)by5n6@C)uIfFgvmTMxX?TG1ji;xZm1OQ(>%d2}Y2iaxD+pezu_%-IPiL$~IVUEZ{pEPWZp2q9 zGRu$!F}{lO(ytkfHbOvLCxnB~WYvXB8H3LaKK$jV#?29NpiX|NufS{jE&aEgi_?N~ zBVI(w92bTvRuQdSla7@_VN?$gz7Tu^M4ZkG7%m~n3%6`ru8c}a?(^s#5BrP9@1U?E z`{gIhnaun}wtt}|nF8FwDIAKuNu=Eu30zNKi_YYheLi%bI+E7q2Supo)Y&SAx8WFt z-@-KyF1JnCprw$1mfLjs`5K5krHO$zw^V~Q54*kOOuzP(w5xzknL*YoYGSOeswjp~ zrcrsJu#CG<4OEx=TaojM73fp~90x+@cKm zHRJue<=!YmQMfk|oCOAx>r_Csv7A#bp2v3?GgRP6jh)CA>34c%E^_kXT=(bnihl(# zR7=kUjd3bHoYj}kZLvhMUJmA;OvBKzjYO6yEgA4nwt?u_@(G~QdYqtI=tth4R|I`4 z-hWNdsnzg{rz{xgT~84(@<6!tB3Qlj#}~tU;xZdD*(!P%GrWVrnZOd-83Ky}fin|& z*q#Y0;9#y30Byz``MwhFaVx@dd>G-NJ-bN_evL&52UJvO_1;W98d;A<*PGDX>HeR6w)^7`7b?l6C;NyhqLg$vEAqGdeM$MRLFNN@6Be=`uXD zdHB_mD)fo}KckJ9UEPNYPgJh%TjZU!L)3~-2_N+txdI!P%r0bG1uW&U8wLa|>4S^% zU#A88BxaS#pf+V}lQwNmgd@cgeb<#l+xRLhfF_9G=ImO9KU9Mv{kt4?U))}%t10j# zA6X2HI1M39^RP2(0kYXh&I&u?Efw0Ox0rGzgFuwHiLYnF#Z_WvL*1R{iZUT;M-lexWzk>|58iguUMMOIJqt7=QuODGI$^ zqw~Q3gZrj%BP>qGR?sl?!$0LS_hEJ889P_jx;iS2s-67X^rdj2( zVyDl(wlV9MnPk5ycR{IC2eI+(Y`cYr>A;7h0DxyooYqqwV)gm{!V8Mt_gFqdtxpy# zUp4XN*4wq}SDQK{sr$kxvj;<28w)P+GJpx#vtYJ`+95Lh9ecj{;dmSZ(}EX{FW$S`^e19)HXSzE*cGT#+Db$6B_hyPL*ynNbJ)Cc zwsp6bRWAMrFGzk+v^0Dw_QSc?_yu-K59^TERaeH}oJlu;W@$ zd_Nw@Zh;loAR!5{)P`(f6*7)Sbk<35P6JKHSPZ%CVXh(zVh^KVYcei{QJ4!)jZNH5 ze!30AUGv9WdOu421pAjKVP!ww*_eU??3_7Z@9Dej^uiLl;iZy&W1d8MJ)~ktXJs5W zz~&~=cVzLwaDHr8Mzf9AEq!COQ37@(+h6P1j-w|iG-mw2O4PzzxF4oG7Y1_Jg)croWV$R5{c%j+hyJZ)g;Sd46iv z<$z{ZoAyzd`PB4IsFFcte4-5vstT{=3~?^?$#?}w?J7lihILfsHYHopWoy4yradCJ z8hvNo1I@NDo<9i2qV;1qB*b6RpgeQO9C=HJ1#>CPHa@C?uJyvt^#{EW+|--Ly9haGERASJ^K95Dgqy7`u!Ibc&H&8 z`%V*}JJ&D5%HGH>f zxP3C{OyBYP)Z|NP($mCgROzzCpZB38zCxT8KWQeGL$cPjNE5g9F+Y3&MD>`77?Bq1 zA-Kz)y4yZAk;>O}JAdtMjuia7GINqrwLi(>w9{Oduv+)gA|;>0dy)n|(HjeEyf74< z?mS2blHe6+C&dwV^EB!}M35Dqac;x&r^MzIE!%RgXXEMo`E@(mfdfl# zDO3kw>`dKyv{WJwVQ)V|eMr2KUkUe$sog9iyx~MM#~`ls-~$cCTyT6!2BZCt-_n$H zF&o~2V)sU}pA@@L+}(w=@_z0f9u4-+;LnO$v+3)46D}qe+^Iq+67L4o_=Fv*8rx>@ z*Ga5Gl_ciDqrb8DwS!4|y-%ipXizSoklB|Phgk#PIH@#|VjCc$jA+3xVGpK``K7?6 z#qr3k2KHsa*p_BZaA1g*PDMKplll3fF=)B#NGqff7W&mP_o7ySpDfm_IAWCqniC%- za+L$ahR0xuDMB&1Ubkt#MNI?4mU(PygWoMwhP3m8U>OnI0+Ad52ZHZi1X zs7ZTNZZ^~!zbK%mfERGC6q6;Fi)L2saY0H=PWeQMG@+r6FMs*iSd`x@cn8p>Jd>;m zQNCWC{?7&Q@IRS#-y6f_#COexztB*LoA+jz`btpVZC~Or&RP2?H`(r zro&`-PcS8(7~kU~D5JSh;InK)vtd{UfIK{uBlr$(v(`xI#^;y5-~G(xd0Jb@*hOmc zMCbFM;y6}+L!S1j72$aJ{PyA~8pENiH9vS;R!;rYLFXM#mr#8EvPC9NFCA2HC5_^B#U)%!o@PQ5DIOTy5bz1jT$6#LP!H< zU%?Z<;~-2szS6nDZ=B3$H#RUV$t^O}m?Lt|e?TkZOt0Nuoqh~Z4;@bqbu4)3HF5yI z@BxiPaC@QZp)5(8HCVREMlX7Pxip3Jdt(1|G%KgpPbvK6V5sxJ{?=?HFS_UyZ{Ck| zhnNmcJ~q0;`Sg)Ko7sQHf8_4;1XOB6hKP;lrU=S`6i$yEM38bWh`A|Bjx_ie&-pyA zJYZn#jXvLAXNmT|*OdmX$Dil|fKMH=aFySk267)uz*-(}b%U1K4zM9P`gGeZ%WAe} z#k-_6O$7FMXQ8Y*S1~iuBt#J_>Xaa&uVC)6Epv>8FpGwe3r&=k&d172ji9R47B8L9 zN@M7QpIUPG2bTN%)dW<+_%`H;ebf|d=C~g!=VTfUD_+m7hD`hKgNgUuD0*{kP3>-%yJD*S4ckAXHtiM4vl$vgj+!>YO-{)Q7@0icM93YFlj{opX?_>Kljk7Ak zzu-#=P&gXm`Q@dVwUtgiY%RW+XVZv6AplX$Zg(Q-~ONd9+rZlKmA3Hx*kIo zS0@V`Mj>hk8QQRqrWdm1Cm~K608Ix#A4_kUlI6eD?N+_}8T`UNxL2I6i-6}I9L_kw zH+t(=b*CWCaWZlRm(5w?7aZoTeW4j@rU3ZuqKpB$1$%@HWjDT4ML_oF9k42qx0cKG@!E-1K?7r zVS))^ZjOQWXj9`J5j574BJLl1W<%Na^xlX0lQP%ZrV&6$l}je=$i9+u`2%qGgma@v zj*7lMtY7v-`|CDM{L~ccsX*uFDF*rH&2kE`xan8z#CbBzt+IBK#EVXt?7OWVA-SZ^ zUm^;DoTcF6%f3R;QK&qC{ZIf%3xP|wt9rT)9E_>i*d80bWU+0J&vb*9YQ^al;d^8s zbI0yc73dthVE*FUxNnh?js`OLtDn-bp<>DL4^I#R6KN!31+8!4&AQrVK2Z!CLu8U+ z4+YU+58FoA!?azp7yT|2#xb5>ieqE?%)`xm0p&NqNeX%x;Z(wWKgxJ&Du|ybOn3|g z=5ao_tD<>Of%ak$Dq*_riOhb~_J(N~;`S_H4=${&DL^0u0HgnW*v-j#1#xBjDAS~N z&siM7tvqXhdCFQXdR|oLAOlMbp9|_hPlRH;zn@6H2Nl$_##_3&=MB?A znBPg*iLKveiR#5^x8Et>cRnX4F%j#15#i3uhdP@@TEmm02np`PxsbVGn@Yq1i_g{8 z^kv;{_K^|@$}?>IZ~!6Pql?V`9xFuP0{h#ZC=m36GN#|W!$ovJpUL&QU&HaKir=nu zhu;}!w6uy%nv09;BtiN#;lz?RH06UE^QT6|`L_Th4eq}Do&D%~hT$S8{#70^Ze`PD z^|kv&zT{vC2|z0r9u#R3v|f;)p-Plx2R>pTW2Wh1^7+O2b+g|)>GPM@g(nNnsFNqj z^R~FCDBP0yR*>D|4eRFhikUTa%L{+a+>H@=zQHYteD#q;Ecw)O!^5fEL_Vn6;zbGr z8iM4n?jgoQ$kJX9i~!YF()*^8{jf_O-@!#|y8?6&^_%0{ML%Y*WXcPSyaZ&4QBRR(dbppl9ScuaUzztm}S$?c1Uh=Tj0LKH646ZeVgGo4x3LMa~(s}qi{B9`?v;-(wk zzJx8){T$5se1M1N1**RS01Qm|sh^9It^8<+O-fK1ClkeQ_1!?kzEJ2BMamPL=#+5z zlcw5I21RXGDNe+W1ZSo`_%oiu=B3*!DRFg%WmpCm;&GY5Q|3aYf7ot=-PZ64-6=qg zfd+Y5aiPfbpFs`qX8oQA)vudVgw!7^C)11mqOPuTQ70d-7nbCawB8?#3O`FF_TZ>8 zkSscvg|y}KBqn#IJasmd22!hGPujfby*B2Exv!k}uYuYm3^Z^W+ZG&m-5hxK4LZp_ z8=uTYIyCIq?w>q3J@t-6tQZal17vi{(+8bDRU!-6_MGrZH*rdAN~`S>o1VIh02Lv? z@^xVd$76C1;TZciHwdw7_UD@NqE1h!Qf&n@4ZnTStj}=#IVY9590zb0($@~C-D+<7 zhWA6N=u6=O+xXW=z-0dZ&9IT)gPNQV5`XXKQ0qZAVBwk--?@406H=greql6W z)P8G=7VuP8|MLq*)Yc!3i+G})Bz0)|lftaY9j4Fw?af%N<-kJjX@`P9uFT|n0Uclq z$UvjG=SqPjYxM$V`P}-yeH>(f)l__ZC)vReC(mA%X_RPi>aJH{hN$UFa;oiw?8PNy ztA?Pn&RYPgM%(Y-EYHEK*zlBegUL5hB&1$$hxw;rUJ;YET&f?}nZ*ZybqqqUwjLfK zeVlN&xW71MK?!Hehh(a4S6M?FcHm)K=ywV1Mhf^$WmB;CB+8Gkzw9lU{vj>+}GvFOeg~w_l8g)WL$wrbWsADO@1t>S*Y+=)BOM~J zc}g7?`oOYJ9e^rfvA&%3#%;p6+XW?TmMFJ{ekwS5d&0|Xzv_fpG*3DH(&%KmZY9gD zU#zrUd2A_6o%?esv4hCRbh8wJn*bw;`ay8$r@rp}62G$xwBP@V!?||G5iR~ApV9Cr zSgKRj?en`ear~~QD|rSZ3vYT4}BV_JREap&@+dn-dgI2(E z@b_W2lXTSui0$${AJA5w{iSgKkpp%aZNHk#+sMH3X_x>0PlT@iN7xK|nPgK`Y&e7z zxSZg30VQYl#}u+MSt0qv*kXeo;7lj_`wqx(fZqS*rGN%I)6|zrz3Zl9QY@Y%u=f zi;HGx)(@FKNBu|h(x$+KlL9(>jB(u`PzFVj%ffV<7o z(n}e}tvl2J;t6H-35w&^_-2P_P&#_vWOkFPlLK$hi+wlSBxWA4zQ2>_L0_-Kw#UWm z8xvrU9i7aEr;`FgZ|0bHI_}^f?w<@m02ImEfe-vLhO1x4(6zVDdQ-e#3p4fCnMg!n zL0>Kea4NG#8u8PjD|KS$r>Er6-U;KKU{B3P7+o3gNu%YgK(3%VFFX1#NBob=Fr|M)xM>Ey)$%0It#dGZ zcH+yAC>)ueCKA{~@kW!^C*brWR}e3?5}7Mb3qV%D97%B84pH~&gR;IhZ3p}IXAb-> zQ$N0=GGKVvlDorl!|OKchGpTo)kF{-V_n)X^D&$6hA{?w9=DDnA((Wa-@qgsF{eja zs??BkDU#td4RJ;w-1rt6IJkXBnbdRM2{z`OF|W=od<(5Ih4>`~mD$5Mp~gI&B%48_ z_PKA>0|WrFD5H4sufxGRTM@6VY_QZCEoBeuzg+yvBjyTZLNh&P?AH243wDkO$R7r6 zEe!{W7vB{;4H(uHcAM1GIOx9s_Jd{Y65@*UL)(6( zaE*;Pl3Y*S>|5SEO!-th9S19$nfIL~ZL>e3;sbJ!{O$!ebO@H>P?sZk+Oj9U%m)5Q zh-zrq(*g0f=1VM>v3e-xz6+f1@t&C4ec_;Kx7aRz?JmdZG4Q93@Ka>TXCTPg`B8b? z34QQJ%CbFO_cxBy2)@)a##Pk&Ea~V(G1=PL8$4i zyrJn)2eog&MtS)30|{x_y(c3W0%=<6zduCp|1fTxMq~h58Rfo9bfHqDTVqfs6~#Rd zIXOe{RU@uT6I0A_@i73jXPCbToIc?_NaarowHhUGuaWiUfp|^%*L`99swo>LCRk1Y znEBn^l}9ZTj@|Yvfn=8;T(rYJ{FIqaeuW%zXq_>S2kDV75hgaCeDefd9UtW9$*jCq zP~;(b%)GrMYde^704OegV3~&u($tduphGIb67lp%=XhmTvwi^X?3eQToi+*jp-)cf z?{YF|$LT~MvHB>a@}uNwTy@+5VgYTSbhUlp ztN?C;GX?72r0BhMtY-?9N6ZTHo2ge}hTtYGb)1)72P-WGFnCX#RzBdHvvV$1=(Gzl zVz|AhV#M_4%KP9lm2DdjUXitT>Xgfe=1yz7COL?K)fxQ^#X9K@@1#jA%=9^)Dw_eao`{Tb=9>?swfQsDThkLo?%uImSt z1POZ$_)YWk!59-ygd@0~1msCMbS{%`b*ZDTGRaB-+dXzP)||Pd(U%(sOTSN2@cFLt zS+u;-QdVWs%cXSdaL@U^W|I)VG|LprB6=33#=EhVB4Z+n&s_Yr`eykqLYnyZ_R+HC z*lWOgYDqtpo{1$eCLv#(xD6YZOP+qQ1h7NoQfLgHQdk5OR)m$&tIJ?zOqb7 z+J??p0$8zB%4`lSKaOUaCl~7lcMHy#T;U9|P2kC|-;Q>7wa>305fDOY;En%TS z9fUWda^PZEX8t*TCXoI!^H<2_-Sa9QUXB&2?LD{)#?^89d9ob0scvV0EB`C&6k9?Fz(4^T^vUs4{(vhL#|a%{Bn< z+=oJeACH}@eTGJ~`BHRIWc4cbWmZjgDGtu)vpYxL93qa|5e20B2VpB8@xZWB0hG2c zE;ny504ZK<&o`N9!0jWy=GE<(;YL?uRft{-12uZX363nuqwhXXK!uNrOn^Gu)YlfA z;+VX|xMeth^9FL7?-b-;FCXO!lg^tVqguV;A~t~)EXlLiQPNL;9QS9g(j}?G%kh%P zNcuegeoO^NL!*COQ zZUNg|$o2IcV=^OYh*#0e)hA{%sHsoV*CZN-?4zmA;RF5r zLKEX0t7sjE6Z%ZIi;yuAnA6%ToqD?ylQW6wW)ZK)olS>S6JF_N75;q4y1N6Qs+GWn zR=6$&51sLEZR@p#U@&YsQ?>(!6xjDFnMa3LQRFO}$ut$Jps6~+!b4ITGeu`j=oPv= z0~#{tra`hx^99eR4kI!!Nj7=JleSV`>$Sm5V})6<&O&8uSEuwt*jS~hojzD<5MI>3 z-&J2K{e127bKY-;qJb6cL%zAPM&RbjukaGNL3;O;7gpKfw-z4LE@j}^{q(QWpkB?v zWdas%PrL)nCk@ae$pBhy{2=$|UHl@`Pu^TW(1wQV!v;5awYqWjOd$v`KQw*at^1Lm z_@Ahj`PyfA6rcZC;*G=o6xs)CgqRg20ISRo(-hI|rip5>a(G+U`Q5P$BCsz&U;k`< zH!hET6YF-_va-(=i^e*E6JI5( z(_DAc7?|1POtT0J6{T?}=M^kI>D{rT6azL*Qtsg5yN|gznrxV}McOrYXkP%XUcCJQ zbx0XK0keMYj{>~Bx7`-j6MCcZ7(Jev_x$WraX9s-VqOtv3oeYE9RQ3BC>IHuvI*|R zcKopc;LUD;zb5SrRud}1;}2SG7j5}Z=R^;t$S$|R3C(yvLpdkK+L(?3&lfF3qvxsQ z5$SL5x80e<7eh*ZCCeX;Ts<|rh{c)Ma*!RI8Zw)($gC5zm>9^@?g!L}C@2sBOY^Yv zMV999=A7fTzvTg$ZHmqmQ<&Aqzdv3m!c8y_pIg2rR}wA190N+W4Cpd|%@6BuW=V3l z%3-|JPdSnjFk!;{{}}B9aF3W0^xgmD);jkJk{q(B%PW)FrYnXkX(#5JyY6<-*WUH{ qoW^y83$mcIc62)OziZ&dbxHR3agBWC2f!78x1Pv9lPiXr2L2CWoyBzk literal 0 HcmV?d00001 diff --git a/SS2026/Quantum Computing/10. Discrete Fourier Transformation/Discrete Fourier Transformation.md b/SS2026/Quantum Computing/10. Discrete Fourier Transformation/Discrete Fourier Transformation.md index e69de29..e151415 100644 --- a/SS2026/Quantum Computing/10. Discrete Fourier Transformation/Discrete Fourier Transformation.md +++ b/SS2026/Quantum Computing/10. Discrete Fourier Transformation/Discrete Fourier Transformation.md @@ -0,0 +1,14 @@ +A mathematical technique that decomposes a function into its constituent frequencies. + +## Definition +![[Pasted image 20260730181449.png]] + +The transformation is a process that takes a periodic vector as an input and outputs +the period of that vector. + +![[Pasted image 20260730181941.png]] + +## Construction + +We will now model DFT as a quantum circuit. +For this we only look at N = $2^n$, DFT applied on n qubits. \ No newline at end of file