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Please clarify: Let's say we have 3 bits of memory for classical computation (CC), we can represent any number between 0 and 7. On the other hand, with 3 qubits of memory for quantum computation (QC), we can represent any number between 0 and 7 along with additional superposition states. Does that mean CC requires less memory storage compared to QC?

Would appreciate to share references. Thanks

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    $\begingroup$ 3 qubits of memory do not "oppose" to 8 bits of memory. A qubit and a bit are different in logic and it's not straightforward to compare them. Try to reformulate the question by considering, e.g., 8 bits vs. 8 qubits. $\endgroup$ Apr 2, 2023 at 12:11
  • $\begingroup$ The amount of classical memory (bits) grows as log(N). The same happens with quantum memory (qubits). Still, the comparison is not straightforward and is more related to what you can do with one and the other. E.g. superposing. $\endgroup$ Apr 3, 2023 at 11:09
  • $\begingroup$ Please keep on refining this question, rather than creating new ones. $\endgroup$ Apr 3, 2023 at 11:59
  • $\begingroup$ Let's make it simple: 3 qubits takes more memory storage (space) or 3 bits? If same, where amplitude/complex numbers of qubit resides? And what is(are) advantage(s) of QC in terms of memory storage? $\endgroup$
    – MAK
    Apr 4, 2023 at 17:46

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Bits and qubits are logical concepts. The comparison comes in the logic. Specifically, a Hilbert space is more general than a Boolean space.

To answer your question, one need to, first, consider a problem; then show the amount of storage (qubits) necessary to solve it with a quantum computer and comparing it with the amount of storage (bits) to solve it with a classical computer.

Since the Hilbert space is more general, any problem and, more specifically, any classical solver using $\mathcal{O}(f(n))$ bits, can be simulated with no more than $\mathcal{O}(f(n))$ qubits.

The above is merely theoretical. Now, considering the physical implementations, classical computers are much more advanced than quantum computers. Meaning that, let's say, a bit is much cheaper and reliable than a qubit.

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