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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

Korbinian
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  • Why are you not using qiskit or similar libraries to do this? https://quantumcomputing.stackexchange.com/questions/28424/qiskit-can-you-get-circuit-from-unitary-matrix?rq=1 – Abdullah Khalid Jun 02 '23 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. – Callum Jun 02 '23 at 21:03
  • Can you give your concrete matrix? – narip Jun 04 '23 at 01:41
  • 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. – Korbinian Jun 05 '23 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) $? – narip Jun 06 '23 at 05:13
  • Yes, there is an explicit form of the 16x16 matrix in terms of cos sin etc. – Korbinian Jun 08 '23 at 12:14
  • So, can you write it in your post? – narip Jun 08 '23 at 12:18
  • This is called unitary synthesis, and the BQSKit package can do this using one of its synthesis algorithms. If you want a tool to do it, try bqskit. If you are curious on how this is done, you can check out ths qsearch, leap, or qfast papers reference on bqskit's website: bqskit.lbl.gov – edyounis Jul 17 '23 at 21:06

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