out f const in .NET Printer code-128c in .NET out f const

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out f const using visual studio .net todraw code128 on web,windows application QR Code 1 [(. 0 + . 1 )(. f (0) . f (0) )], 2. (11.38). whereas if f is not constant out f not const 1 [(. 0 . 1 )(. f (0) . f (0) )]. 2. (11.39). Note that in t Code 128 Code Set A for .NET he two cases the rst qubit states are orthogonal. If we apply a Hadamard transformation to this rst qubit we have.

UH1 UH1 out f const = . 0 (. f (0) . f (0) ), = . 1 (. f (0) . f (0) ).. (11.40). out f not const Thus, a single measurement on the rst qubit determines whether or not f is constant. Applications of entanglement The Deutsch al gorithm is, obviously, very simple. A slight generalization of this algorithm by Deutsch and Jozsa [23] has been implemented in an ion-trap quantum computer containing two trapped ions. A much more involved algorithm is that of Shor s for factoring large numbers into primes [17].

We shall not review that algorithm here but refer to the reader to specialized reviews of quantum computing. We point out again though that Shor s algorithm has been implemented, on a nuclear magnetic resonance (NMR) quantum computer [18], in order to nd the prime factors of 15 = 3 5, a demonstration of the algorithm and obviously not a demonstration of the power of a quantum computer. Unfortunately, the NMR approach appears not to be scalable.

Another important quantum algorithm is Grover s search algorithm [24].. 11.11 An optical realization of some quantum gates There have bee n many proposals for realizing the quantum gates in quantum optical systems such as polarized photons, cavity QED, and in systems of trapped ions. Here we shall discuss all-optical realizations of some gates based on beam splitters, Kerr interactions, and optical phase shifters. Two photonic modes are required and these form the basis of a dual-rail rail realization of a quantum computer discussed by Chuang and Yamamoto [25].

Only single photon states are involved and, to make clear the mapping of the dual photon states onto qubit bases . 0 and 1 , we start w ith the realization of the Hadamard gate in terms of a 50:50 beam splitter, as pictured in Fig. 11.15(a).

The input mode operators we take as a and b and the beam splitter is chosen to be of the type whose output mode operators a and b are related to the input ones according to the transformation. 1 1 visual .net USS Code 128 a = (a + b), b = (a b) 2 2 (11.41).

or, when inverted,. 1 1 .net vs 2010 code128b a = (a + b ), b = (a b ). 2 2 (11.

42). We assign the computational state 0 to the input product state 0 a . 1 b , that is, we take 0 . 0 a . 1 b , and similarly we take 1 = . 1 a . 0 b . From the Code 128 for .NET rules developed in 6, and letting UBS represent the beam-splitter transformation operator, it follows that.

UBS 0 = UBS 0 a . 1 . 1 1 = (. 0 a . 1 b + 1 a . 0 b ) = (. 0 + . 1 ) , 2 2 UBS 1 = UBS 1 a . 0 b 1 1 = (. 0 a . 1 b . 1 a . 0 b ) = (. 0 . 1 ) , 2 2 (11.43). 11.11 An optical realization of some quantum gates Fig. 11.15.

(a Code 128 for .NET ) Designation of the input and output modes of the a 50:50 beam splitter in a dual-rail optical implementaion of the Hadamard transformation. (b) Optical dual-rail implementation of a phase gate.

(c) Optical implementation of a dual-rail 2-qubit controlled phase gate.. where we have dropped the primes for the states after the beam splitter. Clearly, this device provides a realization of the Hadamard gate. We wish to make it clear that, despite the appearance of two photonic modes containing either the vacuum or a single photon, those are not the basis of the qubits.

It is the product of the states of the two modes that map onto the computational basis. We are still dealing with a 1-qubit gate. The single-qubit phase gate can be realized by placing a phase shifter in the a-beam, the operator for this device being UPG = exp(i a a).

It is easy to see that.
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