2. Quantum Gates Circuits

Gate Decomposition — Quiz

Test your understanding of gate decomposition with 5 practice questions.

Practice Questions

Question 1

What is the number of real parameters required to specify an $n$-qubit unitary in SU($2^n$) ignoring global phase?

Question 2

What is the maximum number of CNOT gates required to decompose an arbitrary two-qubit unitary up to single-qubit gates?

Question 3

Which gate sequence implements a controlled-$R_z(\theta)$ using two CNOT gates and single-qubit rotations?

Question 4

What are the Euler angles $(\alpha,\beta,\gamma)$ in $U=R_z(\alpha)R_y(\beta)R_z(\gamma)$ implementing the Pauli-$Y$ gate (ignoring global phase)?

Question 5

How does the number of two-level unitaries required to decompose an $n$-qubit unitary scale asymptotically?