Quantum computing can be used to efficiently simulate quantum many-body systems. Solving such a problem is classically hard because its complexity grows exponentially with the problem size (roughly with the degree of freedoms), which is an inherent consequence of the Schroedinger-equation.
My intuitive understanding of this fact is that using quantum computers, we can essentially simulate the quantum many-body system, thus making the theoretical calculation essentially an experiment.
What about the reverse problem?
More specifically, consider the situation in which
- we have a description of a quantum many-body system, i.e. we know a formalized set of requirements whose behavior it should follow,
- and we are trying to find the actual system for this description?
In a practical example, we have the required properties of a chemical compound. The goal is to find a chemical formula which fulfills the requirements.
This looks for me a harder task as to calculate the physical properties of a known compound (which is, in essence, "only" a solution of the Schroedinger-equation).
For example, such a description of a practical problem in human language would be this:
I want a room temperature superconductor.
And the output would be:
The formula is: ...
We have the dynamics, or some type of behavior of the system. In the case of chemical compounds, it could be, for example, excitation spectrum or superconductivity transition temperature. The important thing is that we have here a different direction: not from a given QM system do we want to calculate the behavior (= Schroedinger equation), but we have a wanted behavior (now: superconductivity transition temperature), we have a nearly-infinite set of possible compounds, and we are looking for the compound which fulfills the selection criteria ($T_c \geq 300K$).