If they care about performance, why not design custom ASICs?
You should not write a C++ interpreter. You especially shouldn't write an interpreter of a language that looks almost just like C++, but is different from it in unpredictable ways, some of which contribute to bad coding habits and/or make normal C++ more difficult to learn.
Strictly sequential files are a bad model for data if most of your time is spent constructing more-and-more elaborate subsets of that data. When we want to examine a subset, we practically have to make a complete copy of all the data falling into that subset. You want to make a small tweak to your selection? Make a new copy all over again.
There are two big wins that modern big data has developed that we could benefit greatly from if the switchover costs weren't too high. The first is distributing data over many disks on many nodes and bringing the code to the data instead of bringing the data to the code. The more disks your data is on, the less you have to wait on seek times. The second is storing the data in a way that is not strictly sequential in a single set of files, so that if you want to look at a subset of the data, you can effectively do that without having to make a copy of that subset.
subatomic particles simply don't have precise position/momentums.
This is exactly correct. Exact position and exact momentum are not properties that a particle may possess simultaneously, no matter how well or poorly you might try to measure them.
Ok, here is some mathematical object called a state. What can I do with a state? Well, I can apply linear operators to a state. Given the properties of linear operators, there are some states that are unaffected (up to an overall scalar multiplication) by each operator. Call those "eigenstates". Call one of the operators the "position" operator. Find the eigenstates of the position operator. Now, I can compute, for any given state, how much overlap with each position eigenstate there is as a function of the corresponding eigenvalue. That overlap is a complex scalar function of position, which we can call a wave function, if we like.
It's actually much cleaner to start from this sort of abstraction and define the more concrete "wave function" from it than the other way around, partly because it allows you to more easily consider state spaces that, for example, don't have any operators with continuous eigenvalue spaces, like the spins of the ions in a ferromagnetic lattice, or the excitations of atoms/molecules in laser cavity.
Check chapter 9, (pages 237 and following), of the second edition of Principles of Quantum Mechanics by Ramamurti Shankar. Or, section 1.6 (page 18-20) and section 3.5 (page 110-118), of the second edition of Introduction to Quantum Mechanics by David J. Griffiths.
I'm sorry that I can't hyperlink to a physical book. But maybe you could go to your local public library and find a copy of one of them.
A successful [software] tool is one that was used to do something undreamed of by its author. -- S. C. Johnson