You could, but it is a bit pointless. The idea is that mathematically a superposition of analog waves looks the same as the superposition of quantum states, so you can get exactly the same behaviour using the natural laws of physics. A digital system that modelled the waves would require an absurd amount of resolution since the interference effects need to be modelled accurately. In essence you are throwing away most of your information capacity by switching to digital on/off signals from superimposed waves even though you are using the same wires. The reason quantum computing is interesting in the first place is to use all that wasted information to produce a Massive gain in computing power in a much smaller system.

Probably because an analog signal will provide a continuous high-resolution sweep of values, without any aliasing.

You can resolve continuous ranges of values with very high precision, albeit at the expense of exacting and repeatable accuracy.

Digital circuits work fine for simulating, and emulating, quantum computers. They probably chose analog circuits because that's what they like to work with, or because the more-direct encoding allows for efficiencies.

Not quite true. The analog version is inherently parallel, the digital version is not (cf the MATLAB simulation discussed in the paper). The parallelism of the analog system increases exponentially with it's size, the digital system only linearly. So an analog computer built in the way they indicate might be able to create a useful and powerful practical system to test quantum algorithms on long before quantum computing becomes a reality, whereas the digital model cannot be more powerful than the computer it is running on and will struggle to model even moderately complicated quantum systems.

Probably has something to do with the determinism of digital systems.

Analog systems are equally deterministic. In fact, a digital circuit is just an analog circuit where the interpretation of the voltages is quantized.

An analog radio tuned to read nothing but static is not deterministic.

Just because you can't determine what it will do doesn't mean that it's nondeterministic. You just don't have enough information about the hundreds of billions of radio sources scattered all throughout the galaxy. You probably don't have any better information about what the radio station a few kilohertz away will broadcast next, either.