# Brute force gate decomposition of (specific) 4 qubit unitary matrix

I have a specific 4-qubit 16x16 unitary matrix $$U$$ with $$9$$ parameters. My goal is to find a gate decomposition in terms of e.g. {Rx, Ry, Rz, CNOT}. I feel like there must be a brute force way to find that, but the parametrization is making it non-trivial. Would appreciate any pointers, input or help regarding that :-)

Thank you in advance! Kind regards, Korbinian

• Why are you not using qiskit or similar libraries to do this? quantumcomputing.stackexchange.com/questions/28424/… Commented Jun 2, 2023 at 18:12
• Its a numeric 16x16 matrix right? Symbolic unitary synthesis is a harder problem. Wasnt entirely sure what you meant when you said 9 parameters. Commented Jun 2, 2023 at 21:03
• Can you give your concrete matrix? Commented Jun 4, 2023 at 1:41
• I'm looking for a brute - force algorithm to find a decomposition for a specific 4-qubit unitary matrix. The matrix is parameterized, which makes the problem a bit harder, that is why I mentioned it. Commented Jun 5, 2023 at 12:42
• So can you write your unitary out? Such as $\left( \begin{matrix} \cos \theta& -\sin \theta\\ \sin \theta& \cos \theta\\ \end{matrix} \right)$? Commented Jun 6, 2023 at 5:13