Is there any systematic way to decompose a two-level unitary matrix into single-qubit and CNOT operations?

Question

I would like to make a quantum circuit from the following matrix. matrix to be transformed into qubit operations How can I decompose this matrix into qubit operations such as Rotation Y, Control-NOT and so on ?

FYI, I read a book named "Quantum Computation and Quantum Information" written by Nielsen & Chuang, in particular Section 4.5.

Answer 1

A universal method to decompose 2-qubit unitaries into primitive gates is sometimes referred to as "Krauss-Cirac decomposition". Here are several sources:

• Optimal Quantum Circuits for General Two-Qubit Gates by Vatan and Williams,
• Optimal Creation of Entanglement Using a Two–Qubit Gate by Kraus and Cirac.
• “Explorations in Quantum Computing” by Williams, chapter 2.

As a side note, such questions are usually better received at Quantum Computing StackExchange.