W e w ill r epresent t he c o n t r o l l e d n o t b

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Unformatted text preview: he o ther l ine a ' = a t o r esolve t he a mbiguity. W e w ill r epresent t he C O N T R O L L E D N O T b y p utting a 0 o n t he c ontrol w ire, c onnected w ith a v ertical l ine t o a n X o n t he w ire w hich i s c ontrolled. T his e lement c an a lso s upply u s w ith F A N O U T , f or i f b = 0 w e s ee t hat a is c opied o nto l ine b '. T his C O P Y f unction w ill b e i mportant l ater UNIVERSAL sQUANTUMith E X C H A N G E , f or t hree of t hem u sed o n. I t a lso upplies u s w COMPUTERS a ..... 179 o b ,,, o SUM ^ CARRY F ig. 4. A dder. Figure III.38: Simple adder using reversible logic. [fig. from F85] Quantum Mechanical Computers 5 11 ~CI 0 b . ..... SI s'- - -l---b b' SUM c' A C d=o' (3 = 0I C1 C ARRY = d ' F ig. 5. F ull a dder. Figure III.39: Full adder using reversible logic. [fig. from F85] ¶5. ¶6. ¶7. s uccessively o n a p air o f l ines, b ut w ith a lternate c hoice f or c ontrol l ine, a ccomplishes a n e xchange o f t he i nformation o n t he l ines (Fig. 3 b). I t t urns o ut that c ombinations o f j ust t hese t wo e lements a lone Primitive operations: describes quantum logic gates in terms of a re i nsufficient t o a ccomplish Fa rbitrary l ogical f unctions. S ome e lement two primitive l ines is n ecessary. W e change the state w e c an “atom” (twooperations, which h ave c hosen w hat of an call t he i nvolving t hree state R O L L E or O N T R O C O N T system D C“wire”).L L E D N OT. H ere ( see F ig. 3 c) w e h ave t wo c ontrol l ines a, b, w hich a ppear u nchanged i n t he o utput a nd w hich c hange tLetters near the beginning iof oth lalphabet (a, b, c, a . .) are used ). data he t hird l ine c t o N O T c o nly f b the ines a re a ctivated ( . = 1 a nd b = 1 for O therwise c ' = c. I f ,t he t hird l ine toward theetend 0,p, hen e vidently iprogram or register atoms and those i nput c is s t o ( t q, r, . . .) for t b ecomes(which1) o nly i f b oth asequencing a nd t herefore s upplies u s w ith atoms 1( c' = are used for a nd b a re 1 operations). t he A ND f unction ( see T able I ). In this simple sequential(a, b), n amely only),one 1), a nd (1, 0), all give at a computer, (0, 0 (0, program atom is set T hree c ombinations f or time. t he s ame v alue, 0, t o t he A ND ( a, b ) f unction s o t he a mbiguity r equires t wo b its t o r esolve it. T hese a re k ept i n t he l ines a , b i n t he o utput s o t he Annihilation operator: For a act). T line a, f unction is t he c arry f unction c an b e r eversed ( by itself, i n fsingle he A ND the annihilation operator is f or t he s b it defined:um o f a a nd b. ✓ ◆ 01 F rom t hese e lements i t is k nown t hat any l ogical c ircuit c an b e p ut a= = | 0i 1| . h t ogether b y u sing t hem i n c ombination, a nd i n f act, c omputer s cience 00 The annihilator changes the state |1i to |0i. Applied to |0i, it leaves Table I the state unchanged and returns. the zero vector 0 (which is not a meaningful quantum state). a c It matches |1i and resetsb it to |0i.o '...
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This document was uploaded on 03/14/2014 for the course COSC 494/594 at University of Tennessee.

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