Lecture Notes 3.F

# If 1 na detects 0i then it leaves b alone 14 ccnot f

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ter |a, bi: Aa,b = a⇤ a ⌦ (b + b⇤ ) + aa⇤ ⌦ 1. You can write this formula Na ⌦ Ab + (1 Na ) ⌦ 1. That is, if Na detects |1i, then it negates b. If 1 Na detects |0i, then it leaves b alone. ¶14. CCNOT: F writes Aab,c for the CCNOT operation applied to lines a, b, and c. Aab,c = 1 + a⇤ ab⇤ b(c + c⇤ 1) (exercise). This formula is more comprehensible in this form: Aab,c = 1 + Na Nb (Ac 1) . ¶15. SWITCH: One of Feynman’s universal computers is based on only two logic gates, Not and Switch (Fig. III.40). If c = |1i, then the “cursor” (locus of control) at p moves to q , but if 182 CHAPTER III. QUANTUM COMPUTATION Feynman 524 O a sMiNoT01tM s =b+ I sN t tN I Fig. 8. C ONTROLLED N OT b y switches, Figure III.41: CNOT implemented by switches. 0/1 annotations on the wires show the a values. [ﬁg. from F85] I n t hese d iagrams, h orizontal o r v ertical l ines will r epresent p rogram a toms. T he s witches a re r epresented b y d iagonal l ines a nd i n b oxes w e'll p ut t he o ther m atrices t hat operate on r egisters s uch a s t he N O T b. T o b e cspecific, it moves to r. f or t his l ittle s ection o f a C O N T R O L L E D N OT, = |0i t he H amiltonian t hinkingnegates s tarting atprocess. It also of i t as c in the s a nd e nding a t t, is g iven b elow: H e(s, t = s ' a Fig. III.40). ¶16. It’s also reversible) (see s + t *a*tM + t *(b + b *) sM + s~va*s nt- l ' a t u q- t ~rs u + C.C ¶17. The switch is a tensor product on |c, p, q, ri: ¶18. ¶19. ¶20. ( The c.c m eans t o a dd t he c omplex conjugate o f all t he p revious t erms.) A lthough t here s eemcpo+ r ⇤ cwo +outes ⇤ q ere pwcr ]. w ould p ossibly q ⇤ t be t ⇤ p r [p⇤ c h + ⇤ hich p roduce a ll k inds o f c omplications c haracteristic o f q uantum m echanics, t his i n ot so. I f t e ntire c omputer s ystem s tarted i n a d efinite s of or (Thes bracketedheexpression is just theis complex conjugatetate fthe ﬁrst a b y t he t ime t he for reversibility.) Reada the till i n s ome d efinite term from part, required c ursor r eaches s, t he a tom is s factors in each s tate ( although p ossibly d ifferent f rom i ts i nitial s tate d ue t o p revious c omputer right to left: it). T hus o nly o ne o f t he t wo r outes is t aken. T he e xpression o perations on (1) q ⇤ cps:implified b yc oare set,t he S * I unset them utting set S . N . if p and mitting then N t erm and p and t u = q m ay b e ⇤⇤ (2) rOc pn eed p ot b e c oncerned inot set, thehat o ne r oute is set c and r. ne : if n is set and c is n t hat c ase, t unset p and l onger ( two c ursor s ites) t han t he o ther ( one c ursor s ite) f or again t here is n o i nterCNOT: o s cattering ishows CNOTny c ase b y t he i nsertion i nto a cThis is the f erence. N Fig. III.41 s p roduced i n a implemented by switches. hain o f c oupled sites, applied to o f c a, b o f a sequenced f s cursor t he controlled-NOTa n e xtra p iecedata hain andny n umber obyites w ith atoms s, t s ame m utual c oupling b etween s ites ( analogous t o m atching i mpedances i n (= start...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online