Controlled-NOT gate

The quantum-controlled NOT gate with the trapped ions can be implemented by exciting the collective quantized motion of the ions with lasers. The coupling of the motion of the ions is provided by the coulombic repulsion which is the dominant interaction for small ion-ion separations of the order of a wavelength. The final read-out of the quantum register (state measurement of the individual qubits) at the end of the computation can be accomplished using quantum jumps with unit efficiency [107, 108]. 

Figure 3.5 Controlled-NOT gate subject to the control qubit to be in the state 0). Adapted with permission from [1],...

In the NIST experiment the four classical basis states were prepared and the the controlled-NOT gate was applied. Afterwards the state of the system was measured with the quantum jump technique (see Sect. 6.4.4). The 2-bit quantum gate yielded the expected result with a reliability of 90%. The sources of errors that are responsible for this probability of failure will be discussed in Sect. 6.8.4. 

When used together, the three gates NOT, CONTROLLED NOT and CONTROLLED CONTROLLED NOT constitute a universal reversible set, and can thus be used to construct an arbitrary logical circuit. 

Figure 2.11 Sample fragment of a quantum circuit illustrating the effect of some typical quantum gates a SWAP operation between the upper and centre qubits is effected through three consecutive controlled-NOT ...

Research on multi-qubit molecules starts with the synthesis and characterization of systems that seem to embody more than one qubit, for example, systems with weakly coupled electron spins. Indeed, many molecular structures include several weakly coupled magnetic ions [76-78]. On a smaller scale, the capability of implementing a Controlled-NOT quantum logic gate using molecular clusters... 

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. 

Figure 4 This graph shows that the scheme indeed works for the linear polarizations H, V. Four-fold coincidences for all the 16 possible combinations of inputs and outputs are shown. When the control qubit has the logical value 0 (HH or HV), the gate works as the identity gate. In contrast, when the control qubit has the logical value 1 (VH or VV), the gate works as a NOT gate, flipping the second input bit. Noise is due to the non ideal nature of the PBSs.

Finally, it should be kept in mind that we have treated diffusion-controlled reactions within a particular simple model. More complex situations arise when the diffusion itself is more complex, for example when it proceeds on restricted pathways or when it is controlled by gating. Also, the assumption that reaction occurs at one fixed distance does not always hold, as is the case when the species B are excited molecules that disappear by fluorescence quenching. 

This finding inunediately suggested that one chain can be used to deliver chemical protons for oxygen chanistry in BNC, and another to translocate pumped protons. The majority of currently discussed models of CcO are based on this idea. However, it is not clear yet how the enzyme controls the gating of protons at Glu242 site to be delivered for chemistry and for pumping. 

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