1. Quantum Fundamentals

Qubit Mathematics — Quiz

Test your understanding of qubit mathematics with 5 practice questions.

Practice Questions

Question 1

In the Bloch representation $\rho=\tfrac{1}{2}(I+\mathbf{r}\cdot\boldsymbol{\sigma})$, what is the purity $\mathrm{Tr}(\rho^2)$ in terms of the Bloch vector length $r=|\mathbf{r}|$?

Question 2

For the qubit density matrix $\rho=\tfrac{1}{2}(I+\mathbf{r}\cdot\boldsymbol{\sigma})$, what are its eigenvalues?

Question 3

What is the commutator $[\sigma_y,\sigma_z]=\sigma_y\sigma_z-\sigma_z\sigma_y$ for Pauli matrices?

Question 4

For the states $|+\rangle=\tfrac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$ and $|R\rangle=\tfrac{1}{\sqrt{2}}(|0\rangle+i|1\rangle)$, what is the state fidelity $F=|\langle+|R\rangle|^2$?

Question 5

Which of the following is the correct matrix representation of the rotation $R_y(\theta)=\exp(-i\theta\sigma_y/2)$?