Control qubits

We thus have the control bit encoded in 0,4 and in 61, the photon in 0,4 will be the control input to the destructive CNOT gate, and will thus be destroyed, while the second photon in bl will be the output control qubit. 

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.

In general, many different kinds of controlled logic operations can be constructed, where the number of control qubits can vary, as well as the number of controlled (or target) qubits, as shown on Figure 3.4. 

The operation illustrated on Figure 3.4 can be described as the application of the operator U on the target qubits, depending on the value of the product of the control qubits. This is mathematically represented by ... 

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

Now, let us return to the implementation of two-qubit gates. In Chapter 3 we saw that the action of the CNOT gate is invert one of the qubits (the target qubit) provided the other (the control qubit) is in the state 11) . In a two-qubit AB) system this is accomplished by following operators ... 

To implement CNOT in Berman and co-workers scheme, the electronic transitions come to help. Suppose one wants to implement the CNOT operation between a nucleus at r and its neighbor at r + a. The nucleus at r is the target qubit and the one at r - - a the control. First the ferromagnetic sample is set at the control qubit position, and an electron n pulse is applied, at a frequency coeo- This pulse will take the electronic spin from the initial t) state to I J,) state only if the control qubit is in 0). If the control qubit is in 1), the electronic moment will not change upon the pulse action. 

The final section deals with known examples of molecular spin qubits based on lanthanide SIMs. Distinction is made between single-qubit molecules and molecules which embody more than one qubit. This section includes some comments about decoherence in these molecular systems and strategies to control it. 

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 ...

Considering any of these paradigms, a minimal goal for toy models would be to manipulate the quantum dynamics of a small number of spin levels , and that requires a known and controlled composition of the wavefunction, sufficient isolation and a method for coherent manipulation. As illustrated in Figure 2.13, the first few magnetic states of the system are labelled and thus assigned qubit values. The rest of the spectrum is outside of the computational basis, so one needs to ensure that these levels are not populated during the coherent manipulation. 

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... 

A quantum algorithm can be seen as the controlled time evolution of a physical system obeying the laws of quantum mechanics. It is therefore of utmost importance that each qubit may be coherently manipulated, between arbitrary superpositions, via the application of external stimuli. Furthermore, all these manipulations must take place well before its quantum wave function, thus the information it encodes, is corrupted by the interaction with external perturbations. The need to properly isolate qubits but, at the same time, to rapidly... 

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.

In this equation, C andT refer to control and target qubits, respectively. The resulting state (output of the qugate) is said to be an entangled state of the two qubits, that is, a state that cannot be written as a product of states for each qubit [30]. The occurrence of such entangled states is another characteristic trait of QC, at the basis of secure quantum communication or cryptography. It also implies that, as opposed to what happens with a classical bit, an arbitrary quantum bit cannot be copied (the COPY classical operation is, in fact, based on the application of a succession of classical CNOT gates) [4]. 

Single (or multiple) electrons or holes can be bound locally to a small semiconductor nanostructure or to a single impurity in a solid. The resulting discrete energy levels can be used to define a spin qubit. Coherent control and read-out... 

Control of the Magnetic Anisotropy of Lanthanide Ions Chemical Design of Spin Qubits 7.3.2.1 Mononuclear Single Molecule Magnets... 

Unlike the case of enhancement of yield of product in a chemical reaction, control of qubit state transfers in a quantum computer is useful only if the control does generate sensibly perfect fidelity of population transfer. Fortunately, a typical qubit has a spectrum of states that is much simpler than that of a polyatomic molecule, so that control protocols that focus attention on the dynamics of population transfer in two- and three-level systems are likely to capture the essential dynamics of population transfer in a real qubit system. A large fraction of the theoretical effort devoted to describing such transfers has been confined to those simple cases. To a certain extent, many of these studies are analogous to... 

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