So this isn't quantum computing (in the qubit sense), but instead a different computer architecture (demonstrated on an FPGA) that's based on Fowler–Nordheim (FN) quantum tunneling (a real physical effect, used in flash memory, but simulated here).
From the paper:
> The FN-dynamics may be realized either by a physical FN-tunneling device or via a digital emulation of the FN-tunneling dynamical systems. In this work, we employ the digital emulation to achieve the precision required for simulated annealing in the low-temperature regime.
With a "real" (read: analog) FN device, you potentially get large speed ups and even larger cost/energy savings, because the physics is essentially working for "free" -- that's the quantum part.
What's unclear is how scalable the autoencoder architecture would be with analog FN devices today.