As a physicist, I would expect a "128 bit quantum computer" to be a device which contains 128 qubits coupled in something which is called a "coherent quantum state", and which allows "coherent operations" on these qubits. Such a device would be a general purpose processor which can execute any kind of quantum algorithm. However, this is
not what D-Wave is selling. Their device apparently does make use of quantum effects, but it is based on completely different principles, called "quantum annealing". It contains a quantum system built up from superconducting circuits whose energy can be influenced by the applied voltages. Quantum effects can drive such a system into the global minimum of its total energy. Carefully adjusting the applied voltages so that the energy landscape of this device matches some mathematical function thus allows finding the global minimum of this function, a problem which is known as "optimization". This is the only problem that can be solved with this type of "quantum computer".
Building a true general purpose quantum computer is much harder. Coherently coupling even a few qubits is very difficult since the state of "quantum coherence" can be destroyed by very tiny external disturbances. The quantum system must be highly isolated from anything "incoherent" outside, such as thermal noise. Performing operations on such an isolated system is even more difficult since one has to change the state of the quantum system without losing its coherence. Finally, reading out the result of a quantum computation is equivalent to performing a measurement on the quantum state, which will destroy its coherence.
Recently the
Center for Optical Quantum Technologies has been inaugurated at my university. One of their research projects includes putting atoms in a lattice, so that each atom is influenced by the state of its neighbors, which means that the atoms are coupled. This lattice is constructed by very stable laser beams in a very clean vacuum so that the system is isolated from the environment. Further laser beams can be used to "switch" the state of the atoms and to perform operations on their quantum state. I don't know exactly how many atoms they have coupled so far (maybe 3 - 5), because I work at a different institute, but it takes very sophisticated technology to do anything like this, and we are very far from even 8 bit quantum computer chips...