In short, quantum mechanics has a major issue at its core: quantum states evolve by purely deterministic, fully time reversible, evolutions of the wave function. But, once a classical apparatus measures a quantum system, the wave function collapses to a single point corresponding to the measurement result. This collapse is non-deterministic, and not time reversible.

It is also completely undefined in the theory: the theory doesn't say anything at all about what interaction constitutes "a quantum interaction", that keeps you in the deterministic time evolution regime; and what interactions constitute "a measurement" and collapse the wave function.

So, this is a major gap in the core of quantum mechanics. Quantum computers are all about keeping the qubits in the deterministic evolution state while running the program, and performing a measurement only at the end to get a classical result out of it (and then repeating that measurement a bunch of times, because this is a statistical computation). So, the hope is that they might shed some light on how to presicsely separate quantum interactions from measurements.