Квантовые вычисления. Ожигов Ю.С. - 51 стр.

UptoLike

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МГУ | Москва

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P
j≥2
l
j
/N =
˜
0 = (
√
1 − , X, Y
1
, . . . , Y
m−2
)
T
q
l
1
N
=
√
1 − = 1 −
2
+
o()
˜
0 ≈
˜
0
app
= (1, X, Y
1
, . . . , Y
m−2
)
T
O()
H
0
H
0
U I
˜
0
m H
0
U
U =
1 0 0 . . . 0
0 −1 0 . . . 0
0 0 −v
1
. . . 0
. . . . . . . . . . . . . . .
0 0 . . . 0 −v
m−2
.
I
˜
0
I
˜
0
≈
I
˜
0
app
= V
−1
I
e
1
V V V
˜
0
app
= e
1
V
−1
I
e
1
V
˜
0
app
=
−V
−1
e
1
= −
˜
0
app
V
V =
1 X Y
1
Y
2
. . . Y
m−2
−X 1 0 0 . . . 0
−Y
1
0 1 0 . . . 0
. . . . . . . . . . . . . . . . . .
−Y
m−2
0 0 0 . . . 1
,
V
−1
=
1 −X −Y
1
−Y
2
. . . −Y
m−2
X 1 0 0 . . . 0
Y
1
0 1 0 . . . 0
. . . . . . . . . . . . . . . . . .
Y
m−2
0 0 0 . . . 1
.
I
e
1
=
−1 0 . . . 0
0 1 . . . 0
0 0 . . . 0
. . . . . . . . . . . .
I
˜
0
app
= V
−1
I
e
1
V =
−1 −x −y
1
−y
2
. . . −y
m−2
−x 1 0 0 . . . 0
−y
1
0 1 0 . . . 0
. . . . . . . . . . . . . . . . . .
−y
m−2
0 0 0 . . . 1
,
G = −I
˜
0
app
U =
1 −x −y
1
v
1
−y
2
v
2
. . . −y
m−2
v
m−2
x 1 0 0 . . . 0
y
1
0 v
1
0 . . . 0
. . . . . . . . . . . . . . . . . .
y
m−2
0 0 0 . . . v
m−2
.
                                                                                      


                                           0̃ = (√1 − , X, Y , . . . , Y              √
                                                                                   q
   '  P l /N =                                                         T   l1
                                                                                          1− = 1 −       
              j                                                1           m−2 )     N =                  2   +
                j≥2
o()   0̃ ≈ 0̃app = (1, X, Y1 , . . . , Ym−2 )T    O()      ' 
&          !     H 
                                                       0
              $     H                            
                                                                0
     U             I0̃    m              H0  &   U  
    $ 
                                                                             
                                                1    0      0    ...      0
                                            0 −1           0    ...      0   
                                                                             
                                   U = 0           0 −v1 . . .          0   .
                                                                              
                                            ... ... ... ...             ... 
                                                0    0     ...    0 −vm−2
 $  &  I                                         I ≈
          −1           &
                                0̃
                                                             #    −1         0̃
I0̃app = V Ie1 V                   V                  V 0̃app = e1                             V Ie1 V 0̃app =
−V −1 e = −0̃            & V
       1        app
                                                                                    
                                                                                  
                                           1        X Y1 Y2           . . . Ym−2
                                   
                                         −X         1   0   0        ...     0    
                                                                                   
                                V =
                                         −Y1        0   1   0        ...     0    ,
                                                                                   
                                         ...       ... ... ...       ...    ...   
                                         −Ym−2       0   0   0        ...     1
                                                                                   
                                           1  −X −Y1 −Y2               . . . −Ym−2
                                   
                                         X    1    0    0             ...      0   
                                                                                    
                            V −1 = 
                                         Y1   0    1    0             ...      0   .
                                                                                    
                                         ... ...  ...  ...            ...     ... 

                                                
                                         Ym−2  0    0    0             ...      1
                                                                       
                                                                      
                                      −1 0                     ... 0
                                     0    1                   ... 0 
                              Ie1 = 
                                     0
                                                                       
                                           0                   ... 0 
                                      ... ...                  ... ...
*        '   &  
                                                                                          
                                                 −1         −x −y1     −y2   . . . −ym−2
                                            
                                                −x          1   0      0    ...     0     
                                                                                           
                      I0̃app = V −1 Ie1 V = 
                                                −y1         0   1      0    ...     0     ,
                                                                                           
                                                ...        ... ...    ...   ...    ...    
                                                −ym−2        0   0      0    ...     1
                                                                                              
                                           1     −x −y1 v1      −y2 v2    . . . −ym−2 vm−2
                                  
                                          x      1   0           0       ...       0          
                                                                                               
                  G = −I0̃app U = 
                                         y1      0  v1           0       ...       0          .
                                                                                               
                                         ...    ... ...         ...      ...      ...         
                                         ym−2     0   0           0       ...     vm−2

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