Квантовые вычисления. Ожигов Ю.С. - 83 стр.

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МГУ | Москва

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˜
i
j
k
, i = 0, 1, j = ∅, 1, 2, 3, k = ∅, 0, 1
j
˜
i k
j = k = ∅
˜
i
j
k
=
˜
i
˜
0
1
0
=
1
2
(|000i + |010i+ |001i+ |011i,
˜
0
1
1
=
1
2
(|100i + |110i+ |101i+ |111i,
˜
0
2
0
=
1
2
(|000i + |100i+ |001i+ |101i,
˜
0
2
1
=
1
2
(|010i + |110i+ |011i+ |111i,
˜
0
3
0
=
1
2
(|000i + |010i+ |100i+ |110i,
˜
0
3
1
=
1
2
(|001i + |011i+ |001i+ |101i,
˜
1
1
0
=
1
2
(|000i − |010i−|001i+ |011i,
˜
1
1
1
=
1
2
(−|100i + |110i + |101i−|111i,
˜
1
2
0
=
1
2
(|000i − |1 00i− |001i + |101i,
˜
1
2
1
=
1
2
(−|010i + |110i+ |011i − |1 11i,
˜
1
3
0
=
1
2
(|000i − |0 10i− |100i + |110i,
˜
1
3
1
=
1
2
(−|001i + |011i− |001i+ |101i
U
rest
:
˜
i
j
k
O
¯
0 −→
˜
i
O
˜
0
j
k
.
i
j
k
˜
0
j
k
˜
1
j
k
O I
˜
0⊥
˜
1 O⊥I
π
3
h
˜
1
1
0
|
˜
1
2
0
i = h
˜
1
1
0
|
˜
1
2
1
i =
1
2
O
U
rest
C
8
N
C
8
U
rest
A
rest
α
˜
0 + β
˜
1 −→ α
˜
0
j
k
+ β
˜
1
j
k
U
rest
−→ (α
˜
0 + β
˜
1)
O
˜
0
j
k
A
rest
−→ α
˜
0 + β
˜
1,
δ
rest
∆
∆
                                                              


   )           #  #     
  )   #    $        ĩj , i = 0, 1, j = ∅, 1, 2, 3, k = ∅, 0, 1
                                                            k
            j           ĩ   k    
            $         j = k = ∅ ĩj = ĩ    #  #  # ) 
                                                         k
                   

                                  0̃10    = 12 (|000i + |010i + |001i + |011i,
                                  0̃11    = 12 (|100i + |110i + |101i + |111i,
                                  0̃20    = 12 (|000i + |100i + |001i + |101i,
                                  0̃21    = 12 (|010i + |110i + |011i + |111i,
                                  0̃30    = 12 (|000i + |010i + |100i + |110i,
                                  0̃31    = 12 (|001i + |011i + |001i + |101i,                                     
                                  1̃10    = 12 (|000i − |010i − |001i + |011i,
                                  1̃11   = 12 (−|100i + |110i + |101i − |111i,
                                  1̃20    = 12 (|000i − |100i − |001i + |101i,
                                  1̃21   = 12 (−|010i + |110i + |011i − |111i,
                                  1̃30    = 12 (|000i − |010i − |100i + |110i,
                                  1̃31   = 12 (−|001i + |011i − |001i + |101i
               $                           #                   # 

                                                                                                                    
                                                         O                 O
                                          Urest : ĩjk          0̄ −→ ĩ       0̃jk .
         $    $   #     ' 
ijk      '                 0̃j 1̃j    O I  
                                                                      k      k
     0̃⊥1̃  O⊥I        π        h1̃10 |1̃20 i = h1̃10 |1̃21 i = 21 
'           O        #    
                                                              3

  U       '   '           )   
            rest
     N 8  $
C  8
       C                $ '  $       $                
    )    $    &        '  '
       U                      &   
                                                   '  
                                 rest
#      $
     &                    #            
 &     A          $ &     &         %

                                −→
                                    
                        rest

                                                                                                                    
                                                j           U
                                                                                   O          A
                   α0̃ + β 1̃             α0̃   k   + β 1̃jk −→
                                                              rest
                                                                   (α0̃ + β 1̃)          0̃jk −→
                                                                                               rest
                                                                                                    α0̃ + β 1̃,
      &               )  
                      ) )    
          )           
    &         #       
                       &               
 '     δ               $       
                        rest
 ∆         )   &  &   '     
  )   $       )              
) #  #    ∆    '                

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