Квантовые вычисления. Ожигов Ю.С. - 52 стр.

UptoLike

ВУЗ: 

МГУ | Москва

Составители: 

Рубрика: 

kAk = max
k¯xk=1
kA¯xk.
G = −I
˜
0
app
U −I
˜
0
U
G
exact
kG −G
exact
k = kUkkI
˜
0
−I
˜
0
app
k = kI
˜
0
−I
˜
0
app
k = k
˜
0 −
˜
0
app
k = O()
G G
exact
G = G
exact
+ ∆
k∆k = O() t =
q
N
l
2
ν = t∆ =
P
j≥2
l
j
√
Nl
2
l
2
= O(
P
j≥3
) l
2
ν = o(1)
P
j≥3
= o(l
2
) ν
q
l
2
N
o(1) ν = o(1)
G
t
= (G
exact
+ ∆)
t
= G
t
exact
+ O(t∆G
t−1
exact
) = G
t
exact
+ o(1)
G
t
exact
G G
exact
G
p
m−2
(λ) = |G − λI| I
p
m−2
(λ) = 0
p
m−2
(λ) =
1 − λ −x −y
1
v
1
−y
2
v
2
. . . −y
m−2
v
m−2
x 1 − λ 0 0 . . . 0
y
1
0 v
1
− λ 0 . . . 0
. . . . . . . . . . . . . . . . . .
y
m−2
0 0 0 . . . v
m−2
− λ
=
(−1)
m+1
y
m−2
v
m−2
x 1 − λ 0 . . . 0
y
1
0 v
1
− λ . . . 0
y
2
0 0 . . . 0
. . . . . . . . . . . . . . .
y
m−2
0 0 . . . 0
+ (v
m−2
− λ)p
m−3
(λ) =
y
2
m−2
v
m−2
(1 − λ)(v
1
− λ) . . . (v
m−3
− λ) + (v
m−2
− λ)p
m−3
(λ).
p
m−2
(λ) = (v
m−2
− λ)p
m−3
(λ) + y
2
m−2
v
m−2
(1 − λ)(v
1
− λ) . . . (v
m−3
− λ).
−p
1
(λ) = (λ−1+ix)(λ−1 −ix)(v
1
−λ)+v
1
y
2
1
(1−λ)
                                                                                                    


                   
  #('# %!  )'   
     '    &  $   '                         
                                                )      
                                                                  
  $  $ $ $   

                                                   kAk = max kAx̄k.
                                                            kx̄k=1

   )    '  G = −I                            $  & −I U    
                                                  0̃app U                                0̃
  G            kG − G                                                               − 0̃app k = O()     
G   
         exact
             '         exact
                            Gexact
                                   k
                                     
                                      = kU  kkI0̃
                                       
                                                   −  I
                                                      0̃app
                                                            
                                                              k
                                                              
                                                                = kI
                                                                  0̃ −
                                                                     '
                                                                         I0̃app
                                                                            
                                                                                k
                                                                               
                                                                                  = k 0̃
                                                                                            G = G                 
                                                                                                                  P+ ∆
                                                                                                               exact


k∆k = O()   t = N
                           q
                             l2
                                       & $                     &    
                                                                                                       ν = t∆  =
                                                                                                                 j≥2
                                                                                                                 √
                                                                                                                     lj

                                                                                                                   N l2
                                                                                                                         
         P   '             l                             ν = o(1)    
l2 = O( )                                 2
        j≥3
                                             q
 P = o(l ) ν     l2    o(1)      #  # ν = o(1)   
                   2                           N
        j≥3
    Gt = (G                t       t                   t−1          t                     
                   exact + ∆) = Gexact + O(t∆Gexact ) = Gexact + o(1)
   Gt                   '  G  G                                      )
               exact                                                                        exact
     

                                                  
 $     G         #     $ 
  p                      I      &    )      
         m−2 (λ) = |G − λI|
pm−2 (λ) = 0   $          

                                      1 − λ −x          −y1 v1 −y2 v2         . . . −ym−2 vm−2
                                        x   1−λ            0     0            ...       0
                       pm−2 (λ) =       y1    0         v1 − λ   0            ...       0            =
                                       ...   ...          ...   ...           ...      ...
                                      ym−2    0            0     0            ...    vm−2 − λ

                                           x     1−λ     0           ... 0
                                          y1       0  v1 − λ         ... 0
               (−1)m+1 ym−2 vm−2          y2       0     0           ... 0       + (vm−2 − λ)pm−3 (λ) =
                                          ...     ...   ...          ... ...
                                        ym−2       0     0           ... 0
                         2
                        ym−2 vm−2 (1 − λ)(v1 − λ) . . . (vm−3 − λ) + (vm−2 − λ)pm−3 (λ).
                  ) 

                                                   2
                  pm−2 (λ) = (vm−2 − λ)pm−3 (λ) + ym−2 vm−2 (1 − λ)(v1 − λ) . . . (vm−3 − λ).                           

*    
−p1 (λ) = (λ − 1 + ix)(λ − 1 − ix)(v1 − λ) + v1 y12 (1 − λ)  '                                     

Страницы