[zaroth]

I appreciated the rudimentary presentation of the capabilities and limitations of the machine and calling out the connectivity of the qubits versus a universal quantum machine which would have full connectivity between all the bits.

I’d be curious is there a simple formula for calculating the “effective universal qubits” of the D-Wave?

2,048 indeed sounds like a lot of qubits based on my extremely limited knowledge of quantum, but with only ~6k connections versus fully connected which would be n(n-1)/2 = ~2mil is it just a marketing gimmick?

Why is it useful to push the bit count so high if the connectivity is so limited?

[tbabej]

It's important to note here that the current gate-based quantum processors also suffer from the connectivity problems. It's not just annealers suffering.

In those architectures, the limited connectivity enforces usage of SWAP gates, which increases the circuit depth.

Circuit depth, with imperfect qubits and gates, is currently the limiting factor - we don't have practical error-correction for the chips of today's size. Hence one can only perform a certain number of operations before his computation decoheres and becomes useless.

[klyrs]

I don't know of a good way to compare their real-valued gates to complex gates; it's probably a scaling factor due to encoding those gates as gadgets.

As for full connectivity; this is a benefit over gate-model: they can simulate fully-connected logical qubits; on the order of 2sqrt(Q/2), or 64, in their existing hardware.

As for the high bit count: sparse, structured problems can make very good use of the existing connectivity. Simulations of a cubic lattice are nearly competitive with modern classical hardware, for example. IIRC they can factor 16-bit numbers, too --these problems are "quasiplanar" and have relatively low connectivity requirements.

Full connectivity actually brings some huge engineering challenges; DWave's strategy is more about "this is what's actually possible today" and not "we're going to make universal quantum computers, don't ask us about error correction or crosstalks or calibration of large-scale microwave circuits"