Maybe in the distant future. There are really three steps: writing, storage, reading. Writing: There are dreams of using biology to write DNA (currently we us

Maybe in the distant future. There are really three steps: writing, storage, reading. Writing: There are dreams of using biology to write DNA (currently we use chemical synthesis). See the San Diego startup Molecular Assemblies. That could miniaturize a big part of it and not require your body to host bottles of nasty chemicals. Maybe you could find clever ways of siphoning the chemical building blocks and ATP energy from the host. Storage and retrieval: maybe just have bioinert containers implanted. You’d like to be able to reuse them so ideally there would be a robust flushing mechanism. Reading: the Minion reader from Oxford Nanopore that this paper uses is about the size of a usb stick. The technology inside is a hybrid of electronics and protein. This technology will undoubtedly get better and smaller as sequencing has a a lot of R and D money going into it.