Statea of quantum computer are not unstable or unpredictable. For now, put aside a noise and assume ideal quantum computer. Any state can be desribed by a vector in space $C^{2^n}$, where $n$ is number of qubits. Any operation (with exception to reset and measurement) is a unitrary matrix from space $C^{2^n,2^n}$. So far everything is perfectly predictable. Of course, when you measure a state, you get a random results but this is determined by the vector describing the state (or in other words by probability distribution or wave function). This all mean that a quantum computer behaves in predictable way even though its nature is probabilistic.

Now on noise, yes it is true that the noise is unpredictable. However, to eliminate the noise is a matter of engineering and development. There is a so-called threshold theorem which states that with sufficiently large number of qubits you are able to reduce noise under certain level $\epsilon.$

Morever, there is a lot of probabilistic algorithms used on classical computers. They are employed in optimization, determining if some number is prime and machine learning etc. But this does not render classical computer unpredictable.

2In essence, qubits (your so-called "quantum registers") have radically different properties than bits (which holds the discrete set of values 0 and 1) enabling them to be used to construct otherworldly mathematical objects that works fundamentally different from your so-called "predictable math", which are effecient at solving certain class of problems that may be difficult for bit-based computers to solve. – DannyNiu – 2021-02-10T06:04:14.177

I was under the impression that qubits were translated into a separate stateful registry after their state was mathematically predicted. – Daniel Jerome – 2021-02-10T15:49:40.077