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

<ul>
<li><a href="https://arxiv.org/pdf/quant-ph/0308006.pdf" rel="noreferrer">Optimal Quantum Circuits for General Two-Qubit Gates</a> by Vatan and Williams,</li>
<li><a href="https://arxiv.org/pdf/quant-ph/0011050.pdf" rel="noreferrer">Optimal Creation of Entanglement Using a Two–Qubit Gate</a> by Kraus and Cirac.</li>
<li>“Explorations in Quantum Computing” by Williams, chapter 2.</li>
</ul>

<p>As a side note, such questions are usually better received at <a href="https://quantumcomputing.stackexchange.com/">Quantum Computing StackExchange</a>.</p>
Is there any systematic way to decompose a two-level unitary matrix into single-qubit and CNOT operations?
<p>I would like to make a quantum circuit from the following matrix.
<a href="https://i.stack.imgur.com/ongkh.gif" rel="nofollow noreferrer">matrix to be transformed into qubit operations</a>
How can I decompose this matrix into qubit operations such as <code>Rotation Y</code>, <code>Control-NOT</code> and so on ?</p>

<p>FYI, I read a book named "Quantum Computation and Quantum Information" written by Nielsen &amp; Chuang, in particular Section 4.5.</p>