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The effect of noise is to give us outputs that are not quite correct. The effect of noise that occurs throughout a computation will be quite complex in general, as one would have to consider how each gate transforms the effect of each error. There is a very good article that shows Noise and its effect in practical using Qiskit https://qiskit.org/textbook/ch-...

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You are analysing the case where you know a unitary has definitely been applied on the first qubit. In that case, it should not be surprising that there's no change in entanglement. You can take a couple of perspectives: single qubit unitaries do not change entanglement. To change entanglement with a unitary requires a two-qubit unitary. If you know what ...

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I would like to add to keisuke.akira answer. The Noise Model in which only a Single Qubit Flips is correct. However we can assume a more general Noise Model which may be more realistic and still see the use of Bit Flip Code. Since Quantum Circuits are analog, hence it is rare that a qubit flips completely. It is more likely that there is a small coherent ...

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We're trying to build a code to protect against single bit flips. That is, we are assuming the noise model. By assumption, it has the form $\sigma_x \otimes \mathbb{I} \otimes \mathbb{I}$, therefore, it only flips one of them. Of course, in general, the noise does whatever it wants, and therefore, we need to build codes that can protect against more general ...

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The filters help in reducing the out-of-band radiations in the system, but quantum measurements are not only susceptible to thermal radiation or external noises. For fast computation using transmon qubits, a DRAG or Derivative Removal by Adiabatic Gate in which a fine-tuned of out of phase pulse is applied, proportional to the derivative of the original ...

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You do not need to use the density matrix approach. However, as the most general representation of a quantum state, doing so has several advantages. You can simulate noise using just statevectors using probabilistic approaches, eg wavefunction monte-carlo, that converge to the density matrix results in the limit of many repetitions. Along this same thread of ...

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Noise effects introduce classical uncertainty in what the underlying state is. A mixed state is a statistical ensemble of several quantum states $|\psi_i\rangle$ (not necessarily orthogonal), with respective probabilities $p_i$. With the state vector you can represent pure states, not mixed ones. Instead, with the density operator you can represent both pure ...

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