How to explain in layman’s terms the significance of the difference of qubits of the D-Wave and IBM QX?

Question

So, @AndrewO mentioned recently that he has had 'encounters' with people wondering why D-Wave has a lot more qubits than IBM. Of course, this comparison is faulty, since the IBM and D-Wave's machine may both exploit quantum effects to a certain degree, IBM's machine matches the thing the TCS people call a 'Quantum computer' a bit more than D-Waves's alleged quantum annealer.

How do you explain to a novice why IBM is still reaching important milesstones, even though the D-Wave has a lot more 'qubits'. I understand that an easy answer is, 'well, you're comparing apples and pears', but that is merely relying on your possible authority and simply doesn't explain anything!

How can you explain that those devices are different, how can you dispell the myth that the number of qubits is not the only metric to judge quantum devices? (preferably to a layman, but assuming basic (undergrad?) physics knowledge is ok, if needed)

Answer 1

In the classical case, there is a pretty big difference between digital computers and analogue ones. The methodology and hardware is very much distinct (in all cases I know of, at least).

The divide is still there in the quantum case, but it doesn't run quite as deep. The hardware can be similar, but requirements on how it behaves and how to manipulate it are different. This means that both circuit model quantum computers and quantum annealers can both measure device size using the same metric, the number of qubits, but it is measuring very different and completely non-equivalent things.

Basically, it is like comparing the length of a slide rule to that of a smartphone, and using that to make statements about their computational power.

Answer 2

Easiest thing talk about the algorithms for each architecture and the difference between physical and logical qubits. As far as I know we do not know yet how to perform quantum error correction efficiently on an adiabatic machine. Most computations on these devices are just repeated lots and lots of times without much error correction. For the gate model error correcting codes exist - leading to a smaller number of logical qubits. On the other hand the gate model is universal so you can run algorithms on it which are proved to be faster than any known classical counterpart (notably Grover and Shor). Thus the gate model is much more powerful and still worth investigating.