Is quantum physics (easily?) computable?

by Solvent1 min read18th Oct 201134 comments


Personal Blog

So I've been trying to read the Quantum Physics sequence. I think I've understood about half of it- I've been rushed, and haven't really sat down and worked through the math. And so I apologize in advance for any mistakes I make here.

It seems like classical mechanics with quantized time is really easy to simulate with a computer: every step, you just calculate force, figure out where velocity is going, then add the change in position to the new position.

Then when you change to relativity, it seems like it's suddenly a lot harder to implement. Whereas classical mechanics are easy on a computer, it seems to me that you would have to set up a system where the outcomes of relativity are explicitly stated, while the classical outcomes are implicit.

The same thing seems to occur, except more, with quantum physics. Continuous wave functions seems to be far harder than discrete particles. Similarly, the whole thing about "no individual particle identity" seems more difficult, although as I think of it now, I suppose this could be because the whole concept of particles is naive.

It doesn't seem like the computation rules simply get harder as we learn more physics. After all, trying to do thermal physics got a lot easier when we started using the ideal gas model.

Also, it's not just that ever improving theories must be ever more difficult to implement on a computer. Imagine that we lived inside Conway's Game of Life. We would figure out all kinds of high level physics, which would be probably way more complex than the eventual B3/S23 which they would discover.

It feels like the actual implemented physics shouldn't much affect how computation works. After all, we live in a quantum universe and classical physics is still simpler to compute.

Is there any value to this speculation?