The Ion Trap QC

The central part of this chapter is devoted to a detailed explanation of the ion trap QC proposed by Cirac and Zoller (Sect. 6.4). Here I will explain how quantum communication between single ions can be established by using a mode of collective motion (phonon). This is done by storing the particles in a linear trap. A group at the National Institiute of Standards and Technology in Boulder/Colorado has already successfully demonstrated the main aspects of the proposal experimentally (Monroe et al. 1995). I will briefly discuss their experiment. 

In Sect. 6.6 a proposal to implementing a QC based on optical cavity quantum electrodynamics is described (Pellizzari et al. 1995). The scheme is similar to the ion trap QC in the sense that the atomic quantum bits are resting in a trap. However, quantum communication is provided by photons instead of phonons. 

Correction scheme for errors which take place during quantum computations seem to be even more important. A possible approaches is discussed in Sect. 6.8.6. The scheme is designed for the ion trap QC and corrects for errors during the ions communicate with each other (Cirac et al. 1996b). 

The ion trap QC (Cirac and Zoller 1995) is based on qubits stored in internal levels of ions as described in Sect. 6.2.2. A string of ions is stored in a linear ion trap as schematically depicted in Fig. 6.3. A few details on this technology are given... 

In the ion trap QC the quantum gate (6.18) is performed in three steps. Let us first outline these steps before we discuss them in more detail. Fig. 6.6 shows the necessary operations on the three quantum systems involved in the gate ion i, ion j, and the CM phonon mode. Step (i) the qubit stored in the ith atom is transferred to the CM phonon mode by an laser pulse with an appropriate frequency and duration. That is, if ion i is in the excited state e)i a vibration in the string of ions is induced. On the other hand, if ion i is in the ground state p)i the ions remain in place. This is done in order to make the qubit accessible to all the other ions. Since all ions participate in the CM motion they all can see the quantum... 

A simplified version of a 2-bit quantum gate based on the ion trap QC proposal has already been demonstrated experimentally at NIST in Boulder (Monroe et al. 1995). In their experiment a single Be+-ion was stored in an ion trap. The motion of the ion was cooled by laser cooling techniques to the motional ground state 0)cm (for trapping and cooling technology see Sect. 6.4.5). 

In Sect. 6.31 have listed three basic requirements that any system used for quantum computing must fulfill. At present the ion trap QC seems to be closer to meet these requirements than any other proposal. I will discuss these requirements point by point ... 

Computational errors. The second kind of errors takes place only while quantum gates are performed. Computational errors may have a variety of reasons. One type of error occurs when the transformations needed to perform quantum gates are not accurate. For example, in the ion trap QC the duration of the pulses may not be... 

In this section I will discuss a recently proposed error correction scheme designed particularly for the ion trap QC (Cirac et al. 1996). The scheme corrects for an important source of errors during the execution of 2-bit quantum gates. Because the scheme is not intended to correct for the most general error it can be implemented efficiently with regard to time and memory overhead. It is likely that this scheme can be tested as soon as a prototype ion trap QC is available. 

Fig. 6.16 Conditional sign-change gate with error correction in the ion trap QC. First the two qubits ionvolved in the gate are doubled. The gate is performed on the code word as a sequence of four subgates. After each subgate a measurement is performed to determine if an error has taken place. If an error is detected the state before the erroneous subgate can be recovered and the particular subgate can be tried again.

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