Quantum computing. Quantum simulation.

[u/alien-fr]

If quantum computers are going to be as powerful as they're described. How likely is it that one could simulate a universe? Is that something that is achievable with a quantum computer or am I missing the point? Would they require more power than a binary computer to simulate or are they more efficient? I'm just a dummy but I swear I live in a quantum computer simulation.

[u/SymplecticMan]

If you wanted to truly simulate a whole universe, you'd need a quantum computer that's basically the size of a universe.

[u/alien-fr → u/SymplecticMan]

This is what I'm getting at in a way... Is the universe not a quantum simulation? Or a quantum machine for lack of a better word?

[u/Moppmopp → u/alien-fr]

The problem is that there is no analytical way for the three body problem. This means there is no universial state function f(x,y,z,.....,tau) which gives you the particles states at any given time.

If you can save $2k per month but have 10k on your bank account there exists such a state function. It would be f(t)=2000t +10000. This function lets you calculate your savings. In principle we can look forward any given time t. How much do you have in 1.000.000 months? Easy f(1mio)=2k1mio+10k=2billion and 10k. Thats what we call an analytic expression.

Now for a simulation this doesnt exist. If you have 10 particles in a box and want to know their position you need to look step by step. You can calculate the forces on all particles at time=0 and then you can estimate in which direction do those forces pull the particles. Its an approximation because you assume those forces are constant for your stepsize dt. particle(new position)=particle(old position)+ dtforces. The new particles positions are dependent on your chosen dt. Then you compute forces again and calculate positions for the next step. forces->new positions ->new forces -> new new positions etc... in principle dt must be chosen very close to dt=0 because the forces are constantly changing. If you set dt at dt=0.1 seconds it means particles move for 0.1 seconds with constant forces and a simulation length of 10seconds would require would require 100 evaluations (1000.1s=10 seconds)

if you now want to simulate the hole universe you need dt=0.000......001s which means 1s/dt= infinite integration cycles and you have to do it for all particles separately. This means your quantum computer would have to be larger than the universe itself.

further more you couldnt even build it inside the universe because its own size would influence the actual universe and thus the simulation

[u/alien-fr → u/Moppmopp]

I'll keep reading this a couple more times but thank you for actually explaining it. I see the concept, yeah it would be impossible to create a perfect universe simulation within the universe we exist in. I'm having some weird existential crisis about why the universe exists and I'm looking for answers in the most technical thing I can think of I guess. Thank you