Quantum logic operations

Extraction of information from the register—in a sense, cashing in your chips — would be associated with collapse of the wavefunction to one of its components (), with a probability a,p. A quantum logic operation pcriormod on the input... 

F.A. Bonk, E.R. de Azevedo, R.S. Sarthour, J.D. Bulnes, J.C.C. Freitas, A.P. Guimard, I.S. Ohveira, T.J. Bonagamba, Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography, J. Magn. Reson. 175 (2005) 226. 

Magnetic Resonance Force Microscopy (MRFM) appeared in the last few years as an important technique to implement quantum logical operations and readout of qubits states in a... 

Figure 7.3 Schematic representation of the operations of some quantum logic gates acting on two qubits. In quantum computation, single qubit rotations (Figure 7.2) and CNOT (controlled-NOT) or INSWAP quantum gates are universal.

Gershenfeld and Chuang s two-qubit system [101] uses an NMR machine and the protons in 25. They demonstrated a nonlinear interaction between spins, a prerequisite for quantum logic gates. This was realized through the controlled-NOT operation (CNOT) which conditionally flips one spin based on the value of another [102], This gate can be considered as a quantum XOR gate. 

Thus far, studies of coherent optical processes in a PBG have assumed fixed (static) values of the atomic transition frequency [Quang 1997], However, in order to operate quantum logic gates, based on pairwise entanglement of atoms by field-induced dipole-dipole interactions [Brennen 1999 Petrosyan 2002 Opatrny 2003], one should be able to switch the interaction on- and off-, most conveniently by AC Stark-shifts of the transition frequency of one atom relative to the other, thereby changing its detuning from the PBG edge. 

The key to making a quantum logic gate is to provide conditional dynamics that is, we desire to perform on one physical subsystem a unitary transformation which is conditioned upon the quantum state of another subsystem [46]. In the context of cavity QED, the required conditional dynamics at the quantum level has recently been demonstrated [50,51]. For trapped ions, conditional dynamics at the quantum level has been demonstrated in verifications of zero-point laser cooling where absorption on the red sideband depended on the motional quantum state of the ion [11,12]. Recently, we have demonstrated a CN logic gate in this experiment, we also had the ability to prepare arbitrary input states to the gate (the keyboard operation of step (2a) below). 

The state represented by Eq. (15) is of the same form as that ofEq. (10). Both involve entangled superpositions and both are subject to the destructive effects of decoherence. Creation of SchrOdinger cats like Eq. (10) is particularly relevant to the ion-based quantum computer because the primary source of decoherence will probably be due to decoherence of the n=0,l) motional states during the logic operations. 

We conclude by discussing a possible application of quantum logic in the realm of atomic physics. This application has the advantage of being useful with a relatively small number of ions and logic operations. 

Ordered arrays of nanocrystals can be thought of as arrays of SETs, where the electrostatic interaction between neighboring SETs acts as wireless communication means. It has been suggested by Korotkov [64] and Lent [961] that simple logical operations can be performed on a circuitry consisting of arrays of SETs in the form of chains or cells with suitable insulating spacers. An electric field applied in one direction polarizes the strings into either the 0 or the 1 state. Lent s scheme, named quantum cellular automata, instead... 

Bell, A. T. The impact of nanoscience on heterogeneous catalysis. Science 299,1688-1691 (2003). Lee, T. H. Dickson, R. M. Discrete two-terminal sin e nanoduster quantum optoelectronic logic operations at room temperature. Prcc. Natl Acad. Sci. USA 100, 3043-3046 (2003). 

Figure 3.1 Quantum logic gates symbols for one and two-qubit operations. Adapted with permission from [1].

In classical computation, any logical operation can be done from combinations of the logic gate nand (NOT-AND). The similar is true in quantum computing any quantum operation can be implemented using a set of universal logic gates. Such a set is composed of the Hadamard (H), controlled NOT (CNOT), phase (S) and jr/8 (T). 

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