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This is because if control qubit is in arbitrary state then how can it be made to control the CNOT gate? What is the interface between Control Qubit and CNOT Gate?

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    $\begingroup$ Hi Ashish! Welcome to QCSE! Do you know, in general, how a $\mathsf{CNOT}$ gate works on qubits? One qubit, say the top qubit, "controls" the negation another qubit, say the bottom qubit. If the top qubit is $|0\rangle$ then the bottom qubit does not get negated; otherwise if the top qubit is $|1\rangle$ then the bottom qubit gets negated. The top qubit is the control qubit here. The entire operation is called the $\mathsf{CNOT}$ operation. Both qubits can be in a superposition! But this is what the gate does... $\endgroup$ – Mark S Jul 26 at 17:27
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    $\begingroup$ Are you asking about the hardware? Like what pulses are used? $\endgroup$ – AHusain Jul 26 at 18:31
  • $\begingroup$ Thanks Mark, I have some experience with Quantum Algorithms so I understand the working of CNOT gates theoretically, however when it comes to implementation, I am unable to follow as i find that there are two kinds of gates one are like Hadamard or Rotation gates which essential act upon qubits and does not need input from another Qubit. The other kind of gates are Controlled gates like CNOT which need input from at least one Qubit to act on other Qubit(s). I will continue... $\endgroup$ – Ashish Jul 28 at 14:14
  • $\begingroup$ continued part... The moment a gate needs a Qubit's state to decide what operation to perform, it becomes difficult to understand implementation through resonators as given in papers because somehow they are not including explicit steps which I am used to reading in Algorithm literature... If you can point to a literature for layman then it would be great... The implementation of first type of gates like Hardamard makes sense but not Second type of CNOT gates... Pl. help. $\endgroup$ – Ashish Jul 28 at 14:21
  • $\begingroup$ Hi AHusain, I want to have a logical understanding of physical implementation of CNOT gate. Pl. refer to my comments on Mark's comment. $\endgroup$ – Ashish Jul 28 at 14:23
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First of all let me welcome you to QCSE! I'm new myself.

IBM operates superconducting qubits based on josephson junctions. The basic architecture of the chip can be visualized as a graph with qubits at the vertices and superconducting, microwave resonators as the edges. Their native two-qubit operation is something called a cross-resonance gate. Basically, the control qubit is driven at the transition frequency of the target qubit. This induces a coupling between the two that depends on the amplitude of the drive signal. By tuning this amplitude, you can obtain an effective hamiltonian that corresponds to the generator of the clifford group $[ZX]^{1/2}$. This, combined with single-qubit rotations, can give you a CNOT gate. For more details I'd recommend this paper.

Hope this helps.

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  • $\begingroup$ Thanks, I will read and try to understand the attached paper and request you to go through my comments in response to Mark's comment. $\endgroup$ – Ashish Jul 28 at 14:35
  • $\begingroup$ Further, "control qubit is driven at the transition frequency of the target qubit", say if Control Qubit is in arbitrary state then what will be the effect of driving Control Qubit on its state? It would be great if you could point to a literature for layman where a logical understanding i.e. step by step procedure of physical implementation of CNOT is explained with examples on its behavior when Control Qubit is in arbitrary state & controlling multiple CNOTs. $\endgroup$ – Ashish Jul 28 at 14:49

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