Target qubits

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]. 

Figure 4.16 Inset - scheme of coupling between noisy source qubit 1 and quiet target qubit...

To experimentally demonstrate that the gate works, we first verify that we obtain the desired CNOT (appropriately conditioned) for the input qubits in states HH, HV, VH and VV. In Fig. 4 we compare the count rates of all 16 possible combinations. Then, it was proven that the gate also works for a superposition of states. The special case where the control input is a 45° polarized photon and the target qubit is a H photon is very interesting we expect that the state H + V)ai H)a2 evolves into the maximally entangled state ( HH)b11,2 + VV)b1 b2)- We input the state I ) first we measure the count rates of the 4 combinations of the output polarization (HH,..., VV) and then after going to the +), —) linear polarization basis a Ou-Hong-Mandel interference measurement is possible this is shown in Fig. 5. 

Figure 3.4 Various controlled operations applied to a target qubit. Adapted with permission from [1].

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 ... 

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 penalty parameter is important for appropriate laser pulse optimization and chosen based upon numerical adjustments. The integer z corresponds to the number of multiple target qubit states that are being optimized to represent the quantum logic gate. For 1-qubit operations, z = 2 and for 2-qubit operations, z = 4. 

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