It's nothing fundamental, as far as I am aware. Depends on what you mean by "fundamental".
There is no known way to simulate a quantum computer, using a classical computer, in polynomial time. A quantum computer is just a kind of quantum system, so we know that some quantum systems cannot be efficiently modeled (barring revolutionary advances in simulation algorithms).
When your simulations take superpolynomial time, it tends to be easy to find problems which you simply do not have the computational resources to solve, and you may not be able to solve interesting versions of the problem. There are lots of examples of problems like this. However, I don't consider this to be a fundamental difference.
For example, satellite navigation systems are just fine calculating directions for driving all the way across the continental US, even though that's a very "large" instance of the problem that they are solving. But if you try to find the fastest route for a delivery driver to make a hundred deliveries within one city, good luck. This is just an analogy, and I'd like to emphasize that "no KNOWN algorithm" efficiently solves these problems, and that we haven't proven whether such an algorithm exists.
Thanks! By "fundamental," I was curious about the nature of the problem's difficulty, moreso than the progress on solutions. And computational intractability due to system properties makes sense!
There is no known way to simulate a quantum computer, using a classical computer, in polynomial time. A quantum computer is just a kind of quantum system, so we know that some quantum systems cannot be efficiently modeled (barring revolutionary advances in simulation algorithms).
When your simulations take superpolynomial time, it tends to be easy to find problems which you simply do not have the computational resources to solve, and you may not be able to solve interesting versions of the problem. There are lots of examples of problems like this. However, I don't consider this to be a fundamental difference.
For example, satellite navigation systems are just fine calculating directions for driving all the way across the continental US, even though that's a very "large" instance of the problem that they are solving. But if you try to find the fastest route for a delivery driver to make a hundred deliveries within one city, good luck. This is just an analogy, and I'd like to emphasize that "no KNOWN algorithm" efficiently solves these problems, and that we haven't proven whether such an algorithm exists.