Quantum computing and Nanoscale "CAD"

[BWV]

Reading a book on Nanotechnology and venture capitalist Steve Jurvetson makes the statement that traditional computer aided design, like one might use to test an airplane wing design, is not powerful enough to work at the quantum level in designing nanoscale systems. He writes:

"Although scientists have known for 100 years how to write down the equations an engineer needs to solve in order to understand any quantum system, no computer has ever been built powerful enough to solve them. Today's supercomputers choke on any system larger than a water molecule"

he goes on to say, without much elaboration that quantum computing can easily handle these sorts of problems resulting in "an exact prediction of how a system will behave in nature - something that is literally impossible for a traditional computer, no matter how powerful"

Question is what is he specifically referring to that is so computationally intensive and what is it about quantum computing that solves the problem so neatly?

[Yuchi]

"an exact prediction of how a system will behave in nature - something that is literally impossible for a traditional computer, no matter how powerful"

Isn't this impossible regardless, according to Heisenberg's Uncertainty?

[peter0302]

Isn't this impossible regardless, according to Heisenberg's Uncertainty?

Well, he means an accurate prediction of how a system will behave, to within the levels of statistical deviation mandated by the HUP.


Question is what is he specifically referring to that is so computationally intensive and what is it about quantum computing that solves the problem so neatly?

The wave functions becomes ginormously complex when you get beyond the hydrogen atom. You need to solve the Schrodinger equation for the system, and that requires advanced differential equations, which computers are not good at solving.

I'm not sure why the computers can't simulate the systems using brute-force though, i.e., dividing time into very small slices and then noting how it behaves over time.

[BWV]

Well, he means an accurate prediction of how a system will behave, to within the levels of statistical deviation mandated by the HUP.


The wave functions becomes ginormously complex when you get beyond the hydrogen atom. You need to solve the Schrodinger equation for the system, and that requires advanced differential equations, which computers are not good at solving.

I'm not sure why the computers can't simulate the systems using brute-force though, i.e., dividing time into very small slices and then noting how it behaves over time.


So is it like Navier Stokes equations in fluid dynamics - where there are not closed form solutions and the numerical solutions are computationally intensive?

[peter0302]

Precisely.

Or even calculating the evolution of the solar system (which, at least as of 2000 when I was getting my CS degree) was a big problem for computers.

[Alex Monras]

Well, the reason classical computers cannot deal with quantum systems is because, in order to simulate a given number of particles, you end up with exponentially large hilbert spaces (exponential in the number of particles).
This prevents anything realistic beyond very simple things to be simulated.

Which leads to the original Feynman idea. 10 atoms may be very hard to simulate, but nature actually known what to do with them, right? So nature is extremely powerful in computational power, otherwise it couldn't tell all these atoms how to interact, or their wave functions how to evolve.
Basically, the simplest idea is the quantum simulator original by Feynman and refined some years ago by Cirac, which basically amounts to engineer interactions among quantum systems such that the hamiltonian just looks like the system you want to simulate. That is today called "analog" quantum computer, and probably the first quantum computer that will be able to solve relevant problems.

Cheers,

Alex