Computing, quantum

Alice applies this operation to her photon 3, and after that the three-photon state is changed to the following 

There is a superposition of four three-photon states in the last row. Each state shows the state of Bob s photon (number 2 in the ket), at any given state of Alice s two photons. Finally, Alice carries out the measurement of the polarization states of her photons (1 and 3). This inevitably causes her to get (for each of the photons) either 0) or 1 (collapse). This causes her to know the state of Bob s photon from the three-photon superposition (1.25)  

Then Alice calls Bob and tells him the result of her measurements of the polarization of her two photons. Bob has derived (1.25) as we did. 

Bob knows therefore, that if Alice tells him 00 this means that the teleportation is over he already has his photon in state / If Alice sends him one of the remaining possibilities, he would know exactly what to do with his photon to prepare it in state j) and he does this with his equipment. The teleportation is over Boh has the teleported state (f), Alice has lost her photon state f when performing her measurement (wave function collapse). 

Note that to carry out the successful teleportation of a photon state Alice had to communicate something to Bob. 

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Atomic-scale devices already projected pose design challenges at tlie quantum mechanical level. The framework of quantum computing is now being discussed in research laboratories [48, 49]. 

Preskill J 1999 Battling decoherence the fault-tolerant quantum computer P/rys. Today June... 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

Fig. 12.15 Schematic representations and truth tables for reversible primitives CONTROLLED NOT and CONTROLLED CONTROLLED NOT, used by Feynman in his construction of a reversible quantum computer [feyii85. ...

Two properties, in particular, make Feynman s approach superior to Benioff s (1) it is time independent, and (2) interactions between all logical variables are strictly local. It is also interesting to note that in Feynman s approach, quantum uncertainty (in the computation) resides not in the correctness of the final answer, but, effectively, in the time it takes for the computation to be completed. Peres [peres85] points out that quantum computers may be susceptible to a new kind of error since, in order to actually obtain the result of a computation, there must at some point be a macroscopic measurement of the quantum mechanical system to convert the data stored in the wave function into useful information, any imperfection in the measurement process would lead to an imperfect data readout. Peres overcomes this difficulty by constructing an error-correcting variant of Feynman s model. He also estimates the minimum amount of entropy that must be dissipated at a given noise level and tolerated error rate. 

Margolus (margfiOb] generalizes Feynman s formalism - which applies to strictly serial computation - to describe deterministic parallel quantum computation in one dimension. Each row in Margolus model is a tape of a Turing Machine, and adjacent Turing Machines can communicate when their tapes arc located at the same coordinate. Extension of the formalism to more than one dimension remains an open problem. 

A wide variety of proof-of-principle systems have been proposed, synthesized and studied in the field of molecular spin qubits. In fact, due to the fast development of the field, several chemical quantum computation reviews using magnetic molecules as spin qubits have been published over the past decade, covering both experimental and theoretical results [67-69]. Only in a minority of experiments implementing non-trivial one- or two-qubit gates has been carried out, so in this aspect this family is clearly not yet competitive with other hardware candidates.1 Of course, the main interest of the molecular approach that makes it qualitatively different is that molecules can be chemically engineered to tailor their properties and acquire new functionalities. 

Here we will focus on electron spin qubits and thus we will not be discussing NMR quantum computing, where molecules played a key role in the early successes of quantum information processing. 

Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Quantum Information, Cambridge University, Cambridge. 

DiVincenzo, D.P. (1995) Topics in quantum computers, in Mesoscopic Electron Transport, NATO ASI Series E (eds L. Kowenhoven, G. Schoen, and L. Sohn), Kluwer Academic Publisher, Dordrecht, arXiv cond-mat/9612126 [cond-mat.mes-hall]. 

Lloyd, S. (1993) A potencially realizable quantum computer. Science, 261, 1569-1571. 

Kielpinski, D., Monroe, C. and Wineland, D.J. (2002) Architecture for a large-scale ion-trap quantum computer. Nature,... 

R., Schuster, D. and M0lmer, K. (2009) Quantum computing with an electron spin ensemble. Phys. Rev. Lett.,... 

Stamp, P.C.E. and Gaita-Arino, A. (2009) Spin-based quantum computers made by chemistry hows and whys. /. Mater. Chem., 19, 1718. 

F. and Roubeau, O. (2012) Design of magnetic coordination complexes for quantum computing. Chem. Soc. Rev.,... 

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