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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
If you need an exponential number of coupled oscillators to construct a general purpose computer, then you don't have the exponential speedup.
Earlier quoted context omitted.
My lay understanding of the problem with classical algorithms is basically that a lack of resolution means you need to monte carlo the thing millions of times... which is why it's slow. If you could model it as a set of quantum states of similar inaccuracy, wouldn't that by definition be just as (in)accurate but faster? [edit] this reminds me of something I read about how NASA doesn't predict solar eclipses by trying…
People were predicting solar eclipses thousands of years ago with no calculators or even a modern understanding of math. Can't be that hard.
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
The quantum algorithm couldn't simulate these things.
> Further, we use this mapping to prove that any problem efficiently solvable by a quantum algorithm can be recast as a problem involving a network of coupled oscillators, albeit exponentially many of them. Is this a new result, giving that quantum field theory is described in terms of quantum harmonic oscillators?
The thing that stands out to me is the described proof of BQP-completeness where they say they prove any quantum system can be similarities as balls and springs, but later they say you may need an exponential number of springs for a classical simulation. That sounds like the BQP reduction would be exponential, guess I'll have to read the paper to see what I'm missing.
I'll read it when I'm home. But I want to say that the fact that this is from google "quantum AI" makes me doubt the legitimacy. They are really ruining their reputation with all the absurd quantum stuff they have been publishing, e.g: their wormhole stuff and a lot of quantum neural networks bs.
The "wormhole" thing was scientifically interesting as a quantum simulation of a non-trivial gravitational thing. A lot of the media stuff was garbage, but the actual science they did was quite cool.
One of the most important insights you take away from a physics undergrad is that you can model much of physical phenomena as a harmonic oscillator. The reason for this is quite simple 1. Every closed system has a fixed total energy, so many systems just settle into an oscillating state, where kinetic energy converts into potential and back. 2. Most real world systems are approximately closed, so they leak energy til…
This is overly complicated. The reason harmonic oscillators pop up everywhere is even simpler and more general than that. It models first order perturbations over a stable equilibrium. For sufficiently small perturbations around a stable equilibrium everything is an harmonic oscillator. It's basically taking the first order perturbation of a Taylor expansion around a local minima.
That's the same reason, why we linearize nonlinear systems around the equilibria to apply linear control theory, right?
While in control, this makes sense to me, since the goal is often to stabilize the system, how does this help with modeling the whole system in general (far away from any equilibrium point)?
A very cool result!
It'd be interesting to see how many other systems can be approximated by the system they've solved for (without incurring an exponential penalty in the translation).
One of the most important insights you take away from a physics undergrad is that you can model much of physical phenomena as a harmonic oscillator. The reason for this is quite simple 1. Every closed system has a fixed total energy, so many systems just settle into an oscillating state, where kinetic energy converts into potential and back. 2. Most real world systems are approximately closed, so they leak energy til…
Would a 3-or-more body gravitational problem be one of these that could use a speed up?