Answer / kangchuentat

QUANTUM COMPUTING - ANSWER 32.6 : (a) H | 0 > + H | 1 > = 0.707 ( | 0 > + | 1 > ) + 0.707 ( | 0 > - | 1 > ) = 0.707 ( | 0 > + | 1 > + | 0 > - | 1 > ) = 0.707 ( 2 | 0 > ) = 1.414 | 0 >. H | 0 > - H | 1 > = 0.707 ( | 0 > + | 1 > ) - 0.707 ( | 0 > - | 1 > ) = 0.707 [ | 0 > + | 1 > - ( | 0 > - | 1 > ) ] = 0.707 ( 2 | 1 > ) = 1.414 | 1 >. (b) A qubyte = 8 qubits. When n = 8, maximum amount of classical bits = 8. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.

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QUANTUM COMPUTING - EXAMPLE 32.4 : A system of linear congruences consists of 3 equations : X ≡ 1 (mod 2), X ≡ 3 (mod 3), X ≡ 4 (mod 5). X has positive values. (a)(i) List the values of these equations from 1 to approximately 40. (ii) Find the first smallest value and second smallest value of X. (iii) Guess the third smallest value of X. (b) Let X ≡ Aa (mod Ma), X ≡ Ab (mod Mb), X ≡ Ac (mod Mc). According to Chinese remainder theorem, X ≡ (Aa x Ya x Md + Ab x Yb x Me + Ac x Yc x Mf) [ mod (Ma x Mb x Mc) ]. (i) Show that Ma, Mb and Mc have the greatest common divisor of Ma x Mb x Mc. (ii) Find the values of Md, Me and Mf if Md = Mb x Mc, Me = Ma x Mc and Mf = Ma x Mb. (iii) Find the values of Ya, Yb and Yc if Ya = Remainder of (Md / Ma), Yb = Remainder of (Me / Mb) and Yc = Remainder of (Mf / Mc). (iv) Use Chinese remainder theorem to find X.

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