Quantum computers are going to have enormous number of operations per second (in some situations exponentially more than classic computers).
Does it also hold for memory size? Are QC going to have exponentially increased memory?
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No, quantum computers are not going to have an enormous number of operations per second, in fact they are probably going to be much slower in the foreseeable future. The situation with memory seems even bleaker – so far only a handful of bits.
The big advantage of quantum computers is that they can run quantum algorithms, which work rather differently from classical algorithms. Very informally, they provide a way of going through many possibilities at the same time. This gives an exponential speed up for some tasks, and a polynomial speedup for others – in terms of the number of operations. Even though each individual operation is going to be slower, since you need to run drastically fewer, the overall algorithm would run much faster.