4. Quantum Error Correction

Noise Models — Quiz

Test your understanding of noise models with 5 practice questions.

Practice Questions

Question 1

Which noise model causes an isotropic contraction of the Bloch sphere by a factor $(1-p)$?

Question 2

Under the single-qubit bit-flip channel with error probability $p$, how does the Bloch vector $\mathbf{r}=(r_x,r_y,r_z)$ transform?

Question 3

In a single-qubit depolarizing channel defined by $\mathcal{D}_p(\rho)=(1-p)\rho+\tfrac{p}{3}(X\rho X+Y\rho Y+Z\rho Z),$ what is the probability of applying the operator $Y$ to the state?

Question 4

A qubit prepared in the excited state $|1\rangle$ undergoes amplitude-damping noise with damping parameter $\gamma=0.3$. What is the population $\langle1|\rho'|1\rangle$ of the excited state after the noise?

Question 5

For a single-qubit phase-flip channel with error probability $p$, the density matrix off-diagonal element $\rho_{01}$ transforms as $\rho_{01}\to k\,\rho_{01}$. What is $k$?