Realizing Quantum Computers

No quantum computer has so far been built. However, there are several proposals for how to actually realize quantum computers. Among them are realizations on arrays of quantum dots [28], on polymers [27,29], on optical systems with Mach-Zehnder interferometers [53] and on arrays of laser-cooled ions trapped in electromagnetic fields [31]. 

we will review some of the ideas given by Lloyd in [27] since they have very general applicability. They may be applied to quantum computers realized on polymers, on arrays of cold trapped ions, and on arrays of quantum dots. The example of computation on a heteropolymer will be discussed. The generalization to computation on the other systems is self-evident. 

In [27] a one-dimensional periodic array of molecules ABC ABC... is considered. The molecules are quantum-mechanical two-level systems that can be in a ground state (0) or exited state (1). If there are no interactions between the molecules, a transition from one state to the other can be induced by a photon with the resonant frequency uja-, b-, or ujc- It is important that A, B, and C have different resonant frequencies so that one can selectively switch a state for one kind of molecule. 

In general the resonant frequencies for the possible transitions are all different. This enables one to drive transitions selectively. If a pulse of the correct length (tt-pulse) cj Q is applied to the polymer, all the molecules B with their neighbor A in an excited state and C in a ground state will switch. All others will be unaffected. 

The main ideas from [27] for performing computation on such polymers will now be described. They are sufficient to compute any function that can be computed on a Turing machine. This implies that it is possible to simulate any other computer on the polymer computer [51]. Whether the polymer computer is universal in a strict sense is not known yet. To be called universal, a computer must be able to simulate any other computer in polynomial time. The ability to simulate other computers regardless of the time is not sufficient. Nonethless, the term universal is sometimes inaccurately used in this looser sense without regard to computation time. 

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

S. Lloyd, A potentially realizable quantum computer, Science 261, 1569 (1993) J.l. Cirac,... 

The time evolution of such a system is described by a 2 °x2 °matrix This demonstrates the complexity of quantum mechanical time evolution. At the same time it becomes clear that quantum systems have - due to the fact that they describe the evolution of all possible states simultaneously - a sort of inner parallelism . Therefore, they will be an ideal medium for real parallel computations as soon as the dynamical behaviour of the quantum states can be controlled in isolation from the rest of the world (with which an interaction is only needed if one wants to read out the result). New experimental possibilities for realizing quantum computers, ranging from neutral atoms interacting with microwaves over optical cavities and nuclear spins to trapped ions, offer most promising perspectives [15]. The chapters by Tino Gramss and Thomas Pellizzari on the Theory of Quantum Computation and First Steps Towards a Realization of Quantum Computers, respectively, will introduce the reader to recent developments in this exciting field. 

Sect. 5.9 reviews and discusses the prospects of actually realizing quantum computers. This subject is outlined more rigorously in this book by Thomas Pellizzari. In Sect. 5.10 an important generalization of Feynman s and Margolus idea is described It is possible to construct quantum Turing machines with time-independent and local Hamiltonians. This has very general consequences for the decidability of certain questions about the time evolution of a quantum system. 

Lanthanide Complexes as Realizations of Qubits and Qugates for Quantum Computing... 

The basic element of a quantum computer is the quantum bit or qubit. It is the QC counterpart of the Boolean bit, a classical physical system with two well-defined states. A material realization of a qubit is a quantum two-level system, with energy eigenstates, 0) and 1), and an energy gap AE, which can be in any arbitrary superposition cp) = cos(d/2) 0) + exp(i0)sin(0/2) l).These pure superposition states can be visualized by using a Bloch sphere representation (see Figure 7.1). 

Within its orbit, which has some of the characteristics of a molecular orbital because it is shared with electrons on the surrounding atoms, the electron has two possible spin multiplicity states. These have different energies, and because of the spin-multiplicity rule, when an (N-V) center emits a photon, the transition is allowed from one of these and forbidden from the other. Moreover, the electron can be flipped from one state to another by using low-energy radio-frequency irradiation. Irradiation with an appropriate laser wavelength will excite the electron and as it returns to the ground state will emit fluorescent radiation. The intensity of the emitted photon beam will depend upon the spin state, which can be changed at will by radio-frequency input. These color centers are under active exploration for use as components for the realization of quantum computers. 

This chapter has emphasized the special and central role that feedback plays in virtually all aspects of control over molecular quantum phenomena. In terms of applications, the manipulation of chemical reactions still stands as a prime historical objective. However, other rich applications abound. For example, the growing interest in the field of quantum computing is a potentially exciting area [14], and any practical realization of quantum computers will surely entail control over quantum phenomena. Other unforeseen applications may also lie ahead. 

Finally, with the aim of industrial applications, assembling the magnetic molecules onto various substrates is another important field, but one that has been less studied. The application potential of magnetic molecular materials in the manufacture of molecular based memory devices, quantum computing, and spintronics devices, requires an understanding of the interactions between the material and substrate in order to manipulate the spin and electronic states of the target system to realize the desired specific properties [137]. 

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