I work in quantum information, and I need support for complex semidefinite programs.

I use MATLAB/Octave, with the SeDuMi solver (to share open source code) or MOSEK (amazing, with free academic licenses).

For the modeling, I use either YALMIP (amazing breadth of functionality, though additional features tend to not compose well), and CVX (restricted use cases, but I find it amazingly robust).

I haven't made the jump to Python (CVXPY support for complex variables seems missing/shaky), or Julia (I tend to write OOP-lite code and haven't been able to wrap my head around Julia's abstractions).

I've also been exploring exploiting symmetries in convex programs, see https://replab.github.io/web