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.
A new quantum algorithm for classical mechanics with an exponential speedup
21–30 of 67 posts
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#22I'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.
Stop basing your opinions on titles alone. Most of their blog posts on AI and quantum are exceptionally well written and researched, even the one you referenced: "Making a Dual of a Traversable Wormhole with a Quantum Computer" [1] It's like saying quantum teleportation [2] is BS, just because you don't like the SF sounding word "teleportation". https://blog.research.google/2022/11/making-traversable-worm... https://…
Touche
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#23Is this similar to Ed Gerck's "finding" of a QC algorithm that can break RSA-2048?
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#24I'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.
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#25One 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.
> It's basically taking the first order perturbation of a Taylor expansion around a local minima.
I'm not sure that's less complicated, at least for my level understanding.
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#26One 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…
There is a saying that "physics is a subset of reality that can be approximated by coupled harmonic oscillators".
If they are purely linear - it is simple; just write a matrix of their spring coefficients and diagonalize it. If there are non-linear terms, well, then it isn't. This is the case in one of the Quantum Field Theory (and its instance, the Standard Model), the most fundamental theory describing particles. One of the takes on Feynman diagrams is that it is a series approximation of non-linear interactions in the QFT.
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#27I'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.
Stop basing your opinions on titles alone. Most of their blog posts on AI and quantum are exceptionally well written and researched, even the one you referenced: "Making a Dual of a Traversable Wormhole with a Quantum Computer" [1] It's like saying quantum teleportation [2] is BS, just because you don't like the SF sounding word "teleportation". https://blog.research.google/2022/11/making-traversable-worm... https://…
[deleted]
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#28Earlier quoted context omitted.
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.
> It's basically taking the first order perturbation of a Taylor expansion around a local minima. I'm not sure that's less complicated, at least for my level understanding.
Most things jiggle for a while if you poke them a bit?
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#29Earlier quoted context omitted.
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.
> It's basically taking the first order perturbation of a Taylor expansion around a local minima. I'm not sure that's less complicated, at least for my level understanding.
> > It's basically taking the first order perturbation of a Taylor expansion around a local minima.
>
> I'm not sure that's less complicated, at least for my level understanding.
You know Taylor expansions ? So every complicated function of x can be written as soe expansion of infinite powers of x, a0 +a1 ( x )+a2 ( x^2 ) ... And so on Every complicated force can then be written as a function of displacement x like this , now if x is small ignore the sqaure and higher order terms what you get is the linear part , which looks something like F = a1x + a0 , the a0 part only shifts the default position (you can rewrite x as x-c so that a0 goes to zero,) lo and behold you have F=Kx everything is like your familiar hooks law spring as long as x is small enough.
Re: A new quantum algorithm for classical mechanics with an exponential speedup
#30One 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.
seems circular - if you limit the world to small perturbations over a stable equilibrium of course you get simple harmonic motion, push a spring down a bit it pushes back and starts bouncing, the interesting insight is why can you limit the world to that?
i suppose it’s because most interesting forces are conservative, i.e. if motion doesn’t dissipate energy (like friction, unlike electromagnetism) then energy is conserved so perturbations must bounce. OP contains the key insight- dissipating systems dissipate proportional to total energy, so low energies are approximately stable, IIUC.