# Are there works on “quantum parametrized complexity”?

I am a research scholar who works in Algorithms and Complexity theory, I use parameterized complexity to some extent. I don't know if researchers in quantum complexity have started using parameterized complexity or not, so I will not comment on that. I tried to search on google but did not find able to find anything.

Question : Are there works on "quantum parametrized complexity"?

• Van den Nest and Briegel [https://arxiv.org/pdf/quant-ph/0610040.pdf] show that measurement-based quantum computing, which is performed on a family of graph states G, can be classically efficiently simulated if G has a decidable C$_2$MS logic theory (based on a result of Courcelle and Oum implying bounded rank-width of such graphs).