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Lecture Notes 3.F

# 9 m m ight b e r epresented a s a l ogical u nit o f

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Unformatted text preview: , terminate). t ransmission l ines). T o the t hese t state moves along o f utting p ieces t ogether. 0 If a = 1s tudy, cursorhings f urther, w e t hink theptop line, and if a = A along p iece ( see F ig. 9 ) M m ight b e r epresented a s a l ogical u nit o f i nteracting the bottom. w e o nly r epresent t he f irst i nput cursor site a s sM a nd t he p arts i n w hich f inal o ne a t t he o ther e nd a s tM. All t he r est o f t he p rogram s ites t hat a re Ifetween sM aalong a re c top, then nternal p arts bof M ,⇤ ato negate b (otherwise b it moves nd tM the onsidered i it applies + b nd M c ontains i ts leaving it nly sM a nd t M a re sites t hat m ay b e c oupled e xternally. r egisters. O alone). ¶21. In either case, the cursor arrives at the reversed switch, where sets the next cursor atom t. F. The f irst t hing w e d o is t o c opy ( using C O N T R O L L E D N OT's) o ur e xternal i nput i nto M . T hen M o perates, a nd t he c ursor g oes o n t he t op l ine i n o ur d rawing. I t c opies t he o utput o ut o f M i nto t he e xternal o utput r egister. M n ow c ontains g arbage. N ext i t c hanges f t o N O T f , c omes d own o n t he o ther l ine o f t he s witch, b acks o ut t hrough M c learing t he g arbage, a nd u ncopies t he i nput a gain. W hen y ou c opy d ata a nd d o i t a gain, y ou r educe o ne o f t he r egisters t o 0, t he r egister i nto w hich y ou c oied t he f irst time. A fter t he coying, i t g oes o ut (since f is n ow c hanged) o n t he o ther UNIVERSAL QUANTUM COMPUTERS line w here we r estore f t o 0 f 183 f coPY I i ~ NOT f I J Fig. Figure III.42: Garbage clearer. 13. G arbage clearer. 0/1 annotations on the wires show the f values. [ﬁg. from F85] ¶22. We can write it Ha,b (s, t) = s⇤ as + t⇤ a⇤ tM + t⇤ (b + b⇤ )sM + s⇤ a⇤ s + t⇤ atN + t⇤ sN + c.c, M M N N where “c.c” means to add the complex conjugates of the preceding terms. Read the factors in each term from right to left: (1) s⇤ as: if s and a are set, then unset them and set sM . M (4) s⇤ a⇤ s: if s is set and a in unset, then unset s and set sN and a. N (6) t⇤ sN : if sN is set, then unset it and set tN . N (3) t⇤ (b + b⇤ )sM : if sM is set, then unset it, negate b and set tM . M (5) t⇤ atN : if tN and a are set (as a must be to get here), then unset them and set t. (2) t⇤ a⇤ tM : if tM is set and a is unset (as it must be to get here), then reverse their states and set t. (The t⇤ sN term can be eliminated by setting tN = sN .) N F.1.c Garbage clearer ¶1. Instead of having a separate copy of the machine to clear out the garbage, it’s possible to run the same machine backwards (Fig. III.42). ¶2. Initial state: An external register In contains the input, and the output register Out and all machine registers are all 0s. s is the starting program atom. The ﬂag f is initially 0. ¶3. The f = 0 routes control through the reversed switch (setting f = 1) to Copy. 184 CHAPTER III. QUANTUM COMPUTATION ¶4. The Copy...
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