The Toffoli Gate

Find the output of the Toffoli gate acting on ( 1 , 0 , 1 ) (1,0,1) .

(1,0,0) (1,0,1) (0,1,0) (0,1,1)

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2 solutions

Matt DeCross
Jan 19, 2016

The Toffoli gate maps ( x , y , z ) (x,y,z) to ( x , y , ( z + x y ) mod 2 ) (x,y,(z+x*y) \text{ mod}\:2) . Since ( 1 + 1 0 ) mod 2 = 1 mod 2 = 1 (1+1*0) \text{ mod}\:2 = 1\text{ mod}\:2 = 1 , the output is ( 1 , 0 , 1 (1,0,1 ).

Spomer Brian
May 27, 2019

Very simple algebraic transform of x,y,z coordinates -- definitely not as complex as matrix multiplication.

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