Quantum Gate Models & Quantum Circuits

5.3   If you don’t do Hadamard gate, a single-qubit system won’t have superposition. (This is what instructor says about Hadamard gate.  Is this true???  I thought a single-qubit quantum would have superposition anyway no matter there is a Hadamard or not. It is the nature of quantum!)

5.4   It is important that not any quantum state vector has a transformation to another state, e.g. (3 45).  Well, the next topic of Hamiltonian will tell you that the capability of quantum computing is not so limited – you can use Hamiltonian to transfer any state to another state, even if it is an NP problem.

5.5   Circuit_drawer may mistakenly draw a cx as a X gate.  Circuit.draw draws cx correctly.

5.6   When drawing a circuit layout, your using one qubit and two or three qubits at the registering initiation time makes the final state different – even though I think it is only simulation, there may be entanglement if multiple qubit?

5.7  Compilation – Circuit depth is the number of time steps required to execute the circuit, assuming that gates acting on distinct qubits can operate in parallel. On current and near-term quantum computers, we want circuits to be shallow, otherwise decoherence or other forms of noise destroy our calculation.  For simulation, a compilation and translation does not increase circuit depth.  For real physical quantum processor, compilation does increase circuit depth.