A classical computer composed of '0' or '1' transistors stores $2^n$ states.
Is it true that a quantum computer composed of '0' or '1' or '0 & 1' qubits stores $3^n$ states?
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2$\begingroup$ Colin's answer is right. If you have a classical computer with 4 bits, it has 16 possible states, but can only hold 1 of those states at a time. If it were a quantum computer, it could hold all 16 states at the same time, and each state has a complex amplitude reflecting its probability of being observed. That's the superposition. $\endgroup$– Mike DunlaveyCommented Dec 20, 2012 at 2:24
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$\begingroup$ A key difference between classical and quantum computers is speed: we can use some much faster algorithms on quantum computers. "the search for the factors of very large integers... with a quantum computer... we can perform the test on all numbers simultaneously and thus only a single test is needed to find the right answer." quoted from scientificamerican.com/… $\endgroup$– raindropCommented Jan 14, 2013 at 21:00
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$\begingroup$ What is the maximum number of bits of information that a qubit can store? $\endgroup$– SeekerCommented Dec 27, 2016 at 19:19
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No, it is not true. A quantum computer stores the same $2^n$ states that the classical computer stores. The difference is that the quantum computer stores a linear superposition of those states, where the classical computer can only store one of those states at a time. What you refer to as '0 & 1' qubits are actually linear superpositions of the two basis qubits 0 and 1.
answered Dec 20, 2012 at 1:17
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2$\begingroup$ A classical computer can also store a superposition of all $2^n$ states if you are thinking in terms of probability distributions. So the difference between quantum and classical is more subtle, and is a matter of ongoing debate and research. $\endgroup$ Commented Dec 20, 2012 at 13:19
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$\begingroup$ this thread is a bit old, but your point is really interesting. Please, could you elaborate it further? $\endgroup$– neilsonCommented Jun 20, 2022 at 10:45