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1
2 a) Dutsch-Jozsa b) Grovr s c) Shor s
3 3 PD I Mchal A. Nlsn and Isaac L. Chuang, Quantum Computaton and Quantum Inormaton, Cambrdg Unvrsty Prss
4 N N log N L [=(999)] NN N N+
5 d V (, y,z ) dt m y z () ( t ) U( t ) ( ) t t t t U( t ) I!! 3! 3 () U(t) UU * I t U ( t ) U( ) ( ) ( t ) U( t ) ( t ) ( 3t ) U( t ) ( t ) n U U U n n U'
6 z I> ( t) a( t) b( t) a( t ) b( t ) z I z I I> I Z = a A a a a A * a a * * a a * * t t t t U( t ) I!! 3! 3 UU * I
7 (NOT R U R U U R ) b( t ) a( t ) t b( ) t a( ) t ( U R U R U R U R k k R U X(I X ) I U U R R *
8 (controlld NOT) 3,,,,,,,,,,,, U CN U CN, U CN, U,. CN U CN a a a3 a4 UCN a a a3 a4 N n U CN * UCNUCN I
9 NOT b a,, a b AND c a b a a b b c b Controlld NOT NOT a b a b a A b a b a A b c XOR a b a b a b a b c B A B
10 X Z Y Paul matrcs adamard gat U R X Y Z y z sn cos, sn cos I
11 adamard gat y looks lk a squar-root o NOT gat, though s not a NOT gat. y y
12 y z sn cos cos sn sn cos X sn I cos R X cos sn sn cos Y sn I cos R Y y Z z Z sn I cos R, y, z
13 A NOT B A NOT A B A B AB A,B A,A B A B, A B,A B B,A B A B B B, A,,,,,,
14 a b c NOT NOTcontrolld controlld NOT a a, b b, a c b c c a b a b c c c a b a b c a b NOT NOT AND b c c b,c c a c b c c a b
15 NOT3 NOTcontrolld controlld NOT a a b b c c U CCN a a, b b, a c b c c c a b c CCN CCN
16 a a b b c c d= d
17 (U R ) (U CN ) UCN a a a3 a4 ( >, >, >, >) a,,,, 3 a a a 3 a 4
18 b a d y K y ) ( ), ( ) ( ~ b a y K y,, ), ( ) ( ), ( ) ( ~ N y K y * ) ( ~ ), ( ) ( N y K y ) ( ~ ) ( N y N y y U adamard gat y y y ) ( ) ( ) ( ~ y y y N y
19 n j R R n- R n. j j n j R n- R n-. j j n j n R. jn j n j n. j n R jk jk jk jk jk jk jk p k j jk j k R jk jk
20 j R R 3 j R j 3 R R Stp R( ) R( ) p Stp 3 R3( 3) R3( 3) Stp 4 Stp 5 R(3) Stp 6 3 Stp 7 hjk kjh Stp
21 Quantum algorthms Dutsch-Jozsa algorthm Grovr s algorthm Shor s algorthms
22 Dutsch-Jozsa algorthm ( ) :, U, y, y U y y () U,,, Walsh-adamard transorm
23 Dutsch-Jozsa algorthm n n U y y () n n,,,, n n
24 Dutsch-Jozsa algorthm Dutsch y ) ( y U 3 U 3 3 3
25 Dutsch-Jozsa algorthm n :,,,, constant : () s constant balancd : () s hal and hal Msson : Judg whthr () s constant or balancd. n n U y y () 3 n n, n n 3 n z z n z
26 Eampl: n= n n (,,,) (,,,) ) ( or (,,,) ) ( (,,,) ) ( y ) ( y U n Gt () s constant. 3
27 Grovr s algorthm () N= n N- N N n n G G G G n n N Phas n
28 Grovr s algorthm () G n n Phas n ()= n P n n n I I I k k k k k k <>
29 Grovr s algorthm (3) 4 n n=
30 5=35 5, 53, 54 m n n N Fn m mod N Fn n mod5 N=5, m=
31 Fn n mod5 N=5, m= F = 5 F = 5 F = 5 4 r= F 3 = 3 5 F 4 = 4 5 F 5 = 5 5 F 6 = r m r m F 7 = 7 5
32 Fn n mod5 N=5, m= F = 5 F = 5 F = 5 F 3 = 3 5 F 4 = 4 5 F 5 = 5 5 F 6 = 6 5 F 7 = 7 5 r= r m r m N=5 r
33 F n n (mod 5) F F F F 3 4 F 4 F 5 F 6 4 F 7 X (n) Fn n mod5 Y n (mod 5) 3 3
34 F n n (mod 5) F F F F 3 4 F 4 F 5 F 6 4 F 7 X (n) Fn n mod5 Y n (mod 5) XY 3 3,
35 F n mod5 X(n) n Y n (mod 5) 3 3 n (mod 5) r=4
36 Shor s algorthm () : X 3()r= , :,Y X ()r 7 7, ',k k
37 Shor s algorthm () ()r=()=()=(4)=(6) ()=(3)=(5)=(7) ' ,,,, ' X4
38 Shor s algorthm (3) kk=, n r, n r, 3 n r, (r-) n r n=3k=,4r= kk=, n r, n r, 3 n r, (r-) n rr 7r= 7 =Xk=, 6, 3, 4, k 7 7 4,4,,,, k 5 k k r=5%
39 ()=k, k=,,, N-k y U U y, U y N, p( N),, y,,..., N k () k ( ) N k ( ) k N N U k k N=, k= U k ( ) ( k ), U k bk, bk, bk, N N N=6, k=4, g ( ) 4. g k 4
40 .. 3. # S N # #3 #4 #5 #6
41 n
42 ono
43 (n) n T t s T () t s
44 T? t s. (Kz) 7 K
45 QED NMR :, STM,...
46 * Vandrsypn APL Vandrsypn PRL Vandrsypn Natur actorng 5 Chuang Natur 9 Dlt NEC Vandrsypn PRL 99
140 120 100 80 60 40 20 0 115 107 102 99 95 97 95 97 98 100 64 72 37 60 50 53 50 36 32 18 H18 H19 H20 H21 H22 H23 H24 H25 H26 H27 1 100 () 80 60 40 20 0 1 19 16 10 11 6 8 9 5 10 35 76 83 73 68 46 44 H11
7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6
26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
ac b 0 r = r a 0 b 0 y 0 cy 0 ac b 0 f(, y) = a + by + cy ac b = 0 1 ac b = 0 z = f(, y) f(, y) 1 a, b, c 0 a 0 f(, y) = a ( ( + b ) ) a y ac b + a y
01 4 17 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy + r (, y) z = p + qy + r 1 y = + + 1 y = y = + 1 6 + + 1 ( = + 1 ) + 7 4 16 y y y + = O O O y = y
( ) x y f(x, y) = ax
013 4 16 5 54 (03-5465-7040) nkiyono@mail.ecc.u-okyo.ac.jp hp://lecure.ecc.u-okyo.ac.jp/~nkiyono/inde.hml 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy
2009 IA 5 I 22, 23, 24, 25, 26, (1) Arcsin 1 ( 2 (4) Arccos 1 ) 2 3 (2) Arcsin( 1) (3) Arccos 2 (5) Arctan 1 (6) Arctan ( 3 ) 3 2. n (1) ta
009 IA 5 I, 3, 4, 5, 6, 7 6 3. () Arcsin ( (4) Arccos ) 3 () Arcsin( ) (3) Arccos (5) Arctan (6) Arctan ( 3 ) 3. n () tan x (nπ π/, nπ + π/) f n (x) f n (x) fn (x) Arctan x () sin x [nπ π/, nπ +π/] g n
4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx
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(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n
. 99 () 0 0 0 () 0 00 0 350 300 () 5 0 () 3 {a n } a + a 4 + a 6 + + a 40 30 53 47 77 95 30 83 4 n S n S n = n = S n 303 9 k d 9 45 k =, d = 99 a d n a n d n a n = a + (n )d a n a n S n S n = n(a + a n
3 m = [n, n1, n 2,..., n r, 2n] p q = [n, n 1, n 2,..., n r ] p 2 mq 2 = ±1 1 1 6 1.1................................. 6 1.2......................... 8 1.3......................... 13 2 15 2.1.............................
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LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University
LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University 2002 2 2 2 2 22 2 3 3 3 3 3 4 4 5 5 6 6 7 7 8 8 9 Cramer 9 0 0 E-mail:hsuzuki@icuacjp 0 3x + y + 2z 4 x + y
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1 8, : 8.1 1, z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = a ii x i + i
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, 1 ( f n (x))dx d dx ( f n (x)) 1 f n (x)dx d dx f n(x) lim f n (x) = [, 1] x f n (x) = n x x 1 f n (x) = x f n (x) = x 1 x n n f n(x) = [, 1] f n (x
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(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b
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![(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y](/thumbs/98/136512264.jpg "(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y")
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EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
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