We used to have analog computers several decades ago Modern

We used to have analog computers several decades ago. Modern days computers are Digital. What about Quantum computers? Is it analog or digital? I am asking this since qubit can be many things at the same time.

Solution

No, quantum computers are not the same as analog computers (at least in principle).

Analog computers simulate the (mathematical) problem to be solved by building a physical system that obeys the same constraints/laws as the mathematical problem. The answers are obtained by observing and measuring the behavior of the physical simulation. Its accuracy is that of the simulation (there may be parasitic effects), the accuracy of the initial conditions, the setting of problem parameters in particular, and the measurement on the result.

Accuracy may also be limited by the scale range of applicability of the phenomena used for the simulation. For example, if the answer is given by a level of water in some container, you may be limited by capillarity effects (which can be accounted for to some extent) and by the fact that measuring water level with more accurcy that the diameter of a molecule may not be very meaningful.

But despite these shortcomings, the principle of analog computing is that the world is supposed to obey continuous laws and operates with values from the real numbers (which may not be true).

Digital computing, on the other hand, operates exclusively with integers (or countable sets), even if we take an ideal (but implementable) computation model allowing integers and adresses of any size. It is in the countable realm, while real values are not.

Quantum computing will mainly allow you to do several digital computations in parallel (to state it simply). It is always a finite cross product of several computations, and hence stays in the countable realm. You may think of it as the cross-product construction of an automaton that simulates two or more computations of simpler automata (though it is even less general than that from what I understand of it). These finite cross product constructions never leave the countable realm.