Hello, I work in quantum information.

Recently, SCS added native support for the complex semidefinite cone. This should improve performance for SDPs with complex variables, since it avoids the standard trick of mapping the problem to a real cone by doubling the matrix dimension.

As far as I can tell, the only high-level interface that currently exposes this cone is JuMP.jl in Julia. The whole story is described in this blog post by araujoms, who both added complex-cone support to SCS and wrote the JuMP interface. In a reply to a comment of mine on the post, Mateus argues that this approach is state of the art for large-scale problems.

I’ve been using cvxpy for several years, and I occasionally need to push matrix dimensions as far as possible. Having access to this feature in cvxpy would be extremely useful, but I don’t currently have the expertise to implement the interface myself.