[IIAOPSW]

I'm skeptical. If you have an exponential speedup for simulations of coupled oscillators, you can rig a system of coupled oscillators into a general purpose computer [0] and therefore have an exponential speedup for any computation. That seems too good to be true.

[0] https://www.zyvex.com/nanotech/mechano.html

[eigenket]

The logic gates described in that link are more complicated than just coupled harmonic oscillators. They have things like ratchets, or they block each other, or there is buckling.

The quantum algorithm couldn't simulate these things.

[jksk61]

If you need an exponential number of coupled oscillators to construct a general purpose computer, then you don't have the exponential speedup.

[deely3]

Can you elaborate please?

[mk67]

In that case the speedup would be linear.

[naasking]

You would need an exponential number of coupled oscillators to achieve that exponential speedup. Doesn't seem too good to be true to me.

[somat]

I am probably misunderstanding something fundamental. But isn't that exactly what a qubit is. A coupled harmonic oscillator.