By Matthias Homeister
Quantenrechner versprechen ungeahnte Rechenleistung. Quantenverschlüsselungs-Systeme sind sicherer als alle Alternativen. Theoretische Informatiker überdenken die Grundlagen des Rechnens neu - die Forschungen zum Quantencomputer haben die Informatik verändert. Dieses Buch führt anschaulich und auf Beispiele gestützt in die Grundlagen des Quantum Computing ein. Alle wesentlichen Ergebnisse werden detailliert und intuitiv dargestellt. Der Leser erfährt, used to be er von dieser Technologie erwarten kann und wo ihre Grenzen liegen. Das Besondere an dieser Einführung ist, dass keine speziellen Kenntnisse vorausgesetzt werden. Alle wichtigen Begriffe werden umfassend eingeführt, ein mathematischer Anhang stellt benötigte Grundlagen kurz dar.
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2n − 1 ✱ ✉♥❞ ❞✐❡ ❙♣❛❧t❡♥ ✈♦♥ ❧✐♥❦s ♥❛❝❤ r❡❝❤ts✳ ❉✐❡ ♠✐t ❜❡③❡✐❝❤♥❡t❡ ❙♣❛❧t❡ ❜❡s❝❤r❡✐❜t ❞❛s ❇✐❧❞ ❞❡s ❇❛s✐s✈❡❦t♦rs |i ✳ ▲❛✉t❡t ❞✐❡s❡ a0i . . a2n −1,i , s♦ ✇✐r❞ |i ❛✉❢ a0i |0 + a1i |1 + . . + a2n −1,i |2n − 1 ❛❜❣❡❜✐❧❞❡t✳ ❲✐r ❞❡♠♦♥str✐❡r❡♥ ❞✐❡ ◆✉♠♠❡r✐❡r✉♥❣ ✈♦♥ ❩❡✐❧❡♥ ✉♥❞ ❙♣❛❧t❡♥ ❛♥ ❞❡r ❖♣❡r❛t✐♦♥ CNOT✳ |00 |01 |10 |11 |00 1 0 0 0 |01 0 1 0 0 |10 |11 0 0 0 0 0 1 1 0 ✷✳✺ ◗✉❛♥t❡♥r❡❣✐st❡r ✸✶ ❙♦ s✐❡❤t ♠❛♥ s♦❢♦rt✱ ❞❛ss ❞✐❡s❡ ❖♣❡r❛t✐♦♥ ❞✐❡ ❆♠♣❧✐t✉❞❡♥ ✈♦♥ t❛✉s❝❤t✿ α0 α0 α1 α1 CNOT α2 = α3 α3 α2 |10 ✉♥❞ |11 .
3 ❡r❣❛❜❡♥ s✐❝❤ ❛✉s ❞❡♥ ❆♠♣❧✐t✉❞❡♥ ❞❡r ❜❡✐❞❡♥ ❇✐ts✳ ❆✉❢❣❛❜❡ ✷✳✽✿ √ 1 2 |0 + |x1 ✐st ✐♠ ❩✉st❛♥❞ √ 3 − 2 |1 ✳ ❲❡❧❝❤❡ ❆♠♣❧✐t✉❞❡ ❤❛❜❡♥ ❲✐r ❜❡tr❛❝❤t❡♥ ❡✐♥ ❩✇❡✐✲❇✐t✲❘❡❣✐st❡r✳ ❇✐t 3 2 |1 ✉♥❞ ❇✐t |x0 ✐♠ ❩✉st❛♥❞ 12 |0 |00 , . . |x1 |x0 = |xn−1 ... x1 x0 ❦❛♥♥ s✐❝❤ ✐♥ ❩✉stä♥❞❡♥ ❞❡r ❢♦❧❣❡♥❞❡♥ ❋♦r♠ ❜❡✜♥❞❡♥✿ R= ❉❡✜♥✐t✐♦♥ ◗✉❛♥t❡♥r❡❣✐st❡r 2n −1 ∑ αi |i . i=0 ❉❛❜❡✐ ❜❡❞❡✉t❡t |i i = 0, . . , 2n − 1✿ ❉✐❡ ❇✐ts ♥❛tür❧✐❝❤❡♥ ❩❛❤❧ i ❣❡s❡t③t✳ ❢ür ❇✐♥är❞❛rst❡❧❧✉♥❣ ❞❡r s✐♥❞ ❡♥ts♣r❡❝❤❡♥❞ ❞❡r ❊s ❣✐❧t✿ 2n −1 ∑ |αi |2 = 1.
3 ❡r❣❛❜❡♥ s✐❝❤ ❛✉s ❞❡♥ ❆♠♣❧✐t✉❞❡♥ ❞❡r ❜❡✐❞❡♥ ❇✐ts✳ ❆✉❢❣❛❜❡ ✷✳✽✿ √ 1 2 |0 + |x1 ✐st ✐♠ ❩✉st❛♥❞ √ 3 − 2 |1 ✳ ❲❡❧❝❤❡ ❆♠♣❧✐t✉❞❡ ❤❛❜❡♥ ❲✐r ❜❡tr❛❝❤t❡♥ ❡✐♥ ❩✇❡✐✲❇✐t✲❘❡❣✐st❡r✳ ❇✐t 3 2 |1 ✉♥❞ ❇✐t |x0 ✐♠ ❩✉st❛♥❞ 12 |0 |00 , . . |x1 |x0 = |xn−1 ... x1 x0 ❦❛♥♥ s✐❝❤ ✐♥ ❩✉stä♥❞❡♥ ❞❡r ❢♦❧❣❡♥❞❡♥ ❋♦r♠ ❜❡✜♥❞❡♥✿ R= ❉❡✜♥✐t✐♦♥ ◗✉❛♥t❡♥r❡❣✐st❡r 2n −1 ∑ αi |i . i=0 ❉❛❜❡✐ ❜❡❞❡✉t❡t |i i = 0, . . , 2n − 1✿ ❉✐❡ ❇✐ts ♥❛tür❧✐❝❤❡♥ ❩❛❤❧ i ❣❡s❡t③t✳ ❢ür ❇✐♥är❞❛rst❡❧❧✉♥❣ ❞❡r s✐♥❞ ❡♥ts♣r❡❝❤❡♥❞ ❞❡r ❊s ❣✐❧t✿ 2n −1 ∑ |αi |2 = 1.