Квантовые вычисления. Ожигов Ю.С. - 90 стр.

UptoLike

ВУЗ: 

МГУ | Москва

Составители: 

Рубрика: 

φ S
b
p(n) −→ 0 (n −→ ∞)
n φ
0
(x) = 0 X
0
−→ X
1
−→ . . . −→ X
t
a
ij
= δ
j
(X
i
), i = 1, 2, . . . , t; j = 1, 2, . . . , N,
N = 2
n
P
ij
a
ij
≤ t ∀i
P
j
a
ij
≤ 1
T
j
τ
P
i
a
iτ
≤ (j +1)t/N T
0
= ∅
ˆ
b
j
L
j
= T
j
\ T
j−1
P
j
ˆ
b
j
(j+1)t
N
≤ t
b 1, 2, . . . , N D
b
j
L
j
b
j
Eb
j
= b
ˆ
b
j
/N
φ
0
D φ
1
X
0
0
= X
0
−→
X
0
1
−→ . . . −→ X
0
t
φ
1
ξ = kX
t
−X
0
t
k
ε > 0 P (ξ > ε) −→ 0 n −→ ∞
Eη
2
≥
E
2
η
i 1, 2, . . . , N j
Eξ = 2E
P
i
r
P
τ ∈D
a
iτ
≤ 2E
r
t
P
j
b
j
(j + 1)t/N =
t
√
b
√
N
2E
r
P
j
b
j
(j + 1)/b ≤
o(1)
r
E
P
j
b
j
(j + 1)/b ≤ o(1)
r
1
b
P
j
b
ˆ
b
j
(j+1)
N
= o(1) (n −→ ∞).
P (ξ ≥ ε) ≤ Eξ/ε ε
P (ξ ≥ ε) n
G p
err
p
err
= 0.0016, N > 1 000 f ∈ G b
f X
t
=
P
j
λ
j
e
j
B = { j | f (e
j
) = 1}, ε
0
=
P
j /∈B
|λ
j
|
2
.
ε
0
≤ p
err
,
X
t
e
j
, j ∈ B p
err
f c
j
= j/N, j = 0, 1, . . . ; L
j
= {j ∈ B | c
j
≤ |λ
j
|
2
< c
j+1
} ζ
0
=
P
j
ˆ
l
j
c
j
ˆ
l
j
= card(L
j
)
|1 − ζ
0
| ≤ ε
0
+
b
N
< 2p
err
(N −→ ∞).
                                                                                          

                  
     
          
                    φ  
                     
                                           
                           p(n) −→ 0 (n −→ ∞) 
                                                                                                   Sb
                                                                                                            
                                                                                                         

      
    
                             % &  
   
           n '  φ0 (x) = 0   X0 −→ X1 −→ . . . −→ Xt       
              & a = δ (X ), i = 1, 2, . . . , t; j = 1, 2, . . . , N, 
                                                  ij     j  i
N = 2n          a ≤ t    ∀i   a ≤ 1
                      P                     P
                                   ij                                ij
                              ij                                j
      T    '    # & #    τ  #  P a ≤ (j + 1)t/N    T = ∅  
               j                                                 iτ                      0
                                                              i
b̂j     '   Lj = Tj \ Tj−1                   ≤ t
                                                           P b̂j (j+1)t
                                                                   N
                                                            j
           b # & #     1, 2, . . . , N     '      D
 b      # & #       #    ' '   L                 b
        j                                                                                 j         j
  $$   $       '   Eb = bb̂ /N        
                                                                 j      j
φ0  D        %&  φ1         X00 = X0 −→
X10 −→ . . . −→ Xt0    φ1     '      ξ = kXt − Xt0 k
              $ $$   $ &                    '  
  )""         ε > 0 P (ξ > ε) −→ 0                             
        
                                                                    n −→ ∞

                     $ $$    Eη 2 ≥
 2
E η 
    i        1, 2, . . . , N j            
                    Pr P             r P                       √     rP
                                                              t b
            Eξ = 2E          aiτ ≤ 2E t bj (j + 1)t/N = √       N
                                                                  2E    bj (j + 1)/b ≤
                    i   τ ∈D               j                          j
                r P                     r P
                                               bb̂j (j+1)
            o(1) E bj (j + 1)/b ≤ o(1) 1b           N     = o(1) (n −→ ∞).
                          j                                 j

             )  P (ξ ≥ ε) ≤ Eξ/ε      ε %   
 P (ξ ≥ ε) '            n    
                    '   )      $
    # %& #  G    )  p       '   
                                                     err
perr = 0.0016, N > 1000       %&  f ∈ G         b P #
               )      f    X = λ e 
                                                                                                               t               j j
                                                                                                                       j
 B = {j | f (e ) = 1}, ε =           P
                                                 |λj |2 .   
                                                                                                                               
                   j         0
                                          j ∈B
                                            /

                                        ε0 ≤ perr ,                                               
     X '     e , j ∈ B    )  p 
                              t                               j
                                                                                     P err
                 f '  cj = j/N, j = 0, 1, . . . ; Lj = {j ∈ B | cj ≤ |λj |2 < cj+1 }  ζ0 = l̂j cj
                                                                                                                           j
 ˆl = card(L )    

                                                                                                                               
     j        j

                                                           b                                                                     
                                        |1 − ζ0 | ≤ ε0 +     < 2perr (N −→ ∞).
                                                           N

Страницы