Download PDF by Rosinger E.: Basics of Quantum Computation

By Rosinger E.

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2) | | | | 00 > 01 > 10 > 11 > −→ −→ −→ −→ α α α α | | | | 0> 1> 0> 1> + + − − β β β β | | | | 1> 0> 1> 0> This leads to the third component of the device in Fig. 1 which this time is a mixed classical-quantum device with three qubits as input, while its output are two classical bits and one qubit | ψ2 > M1 a1 M2 a2 a1 , a2 , | ψ3 > | ψ3 > Now the measurements M1 and M2 made by Alice will give her the bits a1 and a2 , respectively. This is precisely the classical information which she has to communicate to Bob.

One such case is with the term no-cloning used in quantum computation. What is in fact going on here is that, quite surprisingly, quantum computers do not allow the copying of arbitrary qubits. Thus a more proper term would be the somewhat longer one of no arbitrary copying. 39 40 E E Rosinger Yet in spite of that, plenty of copying can be done by quantum computers, as will be seen in the sequel. In order better to understand the issue, let us start by considering copying classical bits. For that purpose we can use the classical version of the quantum CNOT gate in Fig.

Im , j1 , . . , jm ≤ n, with i1 = j1 , . . 9) || U − Bi1 ,j1 . . Bim ,jm || ≤ ǫ It is further known that a generic set of 2-qubit quantum gates B : C4 −→ C4 have the above universal approximation property. In other 37 Basics of Quantum Computation words, this property is valid for an open and dense subset of such quantum gates B : C4 −→ C4 . However, when one is given a specific 2-qubit quantum gate, it is not easy to check whether indeed it is universal in the above sense. Let us conclude with a related result, and its proof, which can offer certain additional specifics, Deutsch [1].

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Basics of Quantum Computation by Rosinger E.

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