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.
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.
I used to think that a major difference is that analog computing is in principle based on the simulation of continuous laws, involving reals, while digital computing operates exclusively on countable sets. But, in the light of current knowledge in computing theory, this distinction is probably naive because I suspect that physics could be formalized as well using only computable reals, of which there is only a countable number.
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.
In general, a quantum computation is thought of as a digital computation, however there is a variant of quantum computer called a "continuous variable quantum computer" or CVQC, that can be considered an analog computer. I believe they are primarily used in quantum simulation, but they are not something I have studied, so I don't know much more about them than the acronym.
With that said, there are things about "digital" quantum computers that seem very analog. For example, say you start with a quantum register in the ground state, and then you evolve the state unitarily, and finally measure the state.
In some sense, you started with a zeroed out array of classical bits, and ended with an array of classical bits which were the result of the computation, but the unitary evolutions in-between seem very analog. They must be modeled with complex matrices, and the states resulting from the unitary transformations have real amplitudes, etc. But because the output is clearly digital, we consider it a digital computation.
If we could "measure" electron spin wrt an axis (for instance) and get an arbitrary real value, then quantum computing would be analog... But then we would be living in some other universe, with even weirder physics :P
While most schemes for making quantum computers involve digital techniques, there are indeed some analog devices called adiabatic quantum computers (AQC). See Going digital may make analog quantum computer scaleable | Ars Technica for more details.
I believe I understand the basis of your question: The information encoded in one bit in an ordinary modern computer can be described by two (binary) values, commonly written as 0 or 1 or (better for the point at issue) as +1 or -1. However, if you wish, this can be depicted graphically as something being at the north pole or the south pole of an Earth-like sphere. This would be a needlessly elaborate way of depicting how a bit holds information, but it is legitimate. Would navigators bother to use an analog globe if they existed only on the two poles?
The information encoded in a quantum computer cannot be written as either a +1 or -1, fundamentally because the information encoded in a qubit (the quantum-computer equivalent of a bit) can have any value between +1 and -1. One way of depicting this is on a sphere that, like a globe, has analog latitude and longitude markings.
Such a sphere can be the Bloch sphere, a unit sphere borrowed from solid spherical geometry and trigonometry. We can give such a sphere lines of latitude and longitude. The bad new is that encoding a point between the poles now entails less familiar trig and complex numbers. The good news is that any such point can be clearly evaluated, including for describing the information encoded in a qubit. Yes, in effect this Bloch sphere resembles an obviously analog globe! In this sense I agree; quantum computers can be envisioned as relying on analog mathematical tools.