If we are going to be talking about the possible computers of the future then don't forget the Quantum Computer using not bits but qubits.
Quantum Computers!
The equivalent of performing the same operation on a classical super computer with 10^150 separate processors...
Sounds pretty good to me.
Course that is with a 500 qubit system and Last I did any real checking into these systems they only had around a few dozen qubits processing at best.
Each of the systems sounds good. But each also has obstacles and problems to overcome.
As for "living ships" I think the closest we have now adays would be in this list of prototypes and future designs.
Next Generation Navies?