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When we are talking about the quantum computation and classical computation, we are saying that quantum computation is exponential faster than the classical one. And that's because the Kronecker product of quantum states and quantum entanglement. Such as [1,0] state and [0,1] state will create a system state [0,1,0,0]. For a larger system, N quantum bits can store 2^N double precision numbers. And here the question raises, is quantum computation just an advanced data compression algorithm?

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  • $\begingroup$ If you don't get an answer here in a few days, you may want to try again at Computer Science $\endgroup$ – Kyle Kanos Nov 29 '18 at 11:14
  • $\begingroup$ When we are talking about the quantum computation and classical computation, we are saying that quantum computation is exponential faster than the classical one. Do you have a reference for this? This sounds wrong. There are certain problems, such as factoring large integers, that are more tractable for a quantum computer than for a classical one. That doesn't mean that quantum computing has some advantage in general over classical computing. $\endgroup$ – Ben Crowell Dec 3 '18 at 2:15
  • $\begingroup$ @BenCrowell that statement is certainly not always true. There are some known instances of problems for which quantum algorithms provide an exponential advantage over the best known classical algorithms, but it seems that some specific (to my knowledge not well characterised) structure of the problem is required for this to be the case. Quantum computation is not expected to be useful for many/most problems (or at least not expected to provide exponential advantages) $\endgroup$ – glS Dec 3 '18 at 13:41
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No, that is not how quantum computation works.

What you are referring to is a common misconception associated with quantum computation. Quantum mechanics cannot be used to store more data than what is classically possible. More precisely, it is not possible to use $N$ qubits to store more than $N$ bits of information in a useful way.

What is true is that, in general, to fully characterise the state of $N$ qubits you need to specify $2^N$ real numbers, and that simulating quantum systems is in general (expected to be) classically hard. This is however very different than saying that quantum mechanics allows for increased storage capability, which is wrong.

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