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Consider a classical computer, one making, say, a calculation involving a large amount of data. Would quantum memory allow it to store that information (in the short term) more efficiently, or better handle that quantity of data?

My thought would be it isn't possible, due to the advantage of quantum information storage being in the superpositions, and the data from a classical computer being very much not in a superposition, but I'd like to see if this is correct.

Either way, citations for further reading would be much appreciated.

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    $\begingroup$ Related: quantumcomputing.stackexchange.com/questions/115/… and quantumcomputing.stackexchange.com/questions/1195/… $\endgroup$
    – Sanchayan Dutta
    Commented Mar 25, 2018 at 17:48
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    $\begingroup$ Also related: quantumcomputing.stackexchange.com/questions/1244/… (as a mix between quantum and classical might be need for 'big' data) $\endgroup$
    – Discrete lizard
    Commented Mar 25, 2018 at 18:09
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    $\begingroup$ you cannot use a quantum memory to store (in a recoverable way) more information that you would with classical memories. What do you mean by "handle" though? If you are "handling" data in the sense of processing it, aren't you basically talking of a quantum processor/computer? The question then becomes whether one can use a QC to help processing classical data... is this what you are asking? $\endgroup$
    – glS ♦
    Commented Mar 25, 2018 at 18:09
  • $\begingroup$ @glS I don't mean handling in the sense of processing. This question is wondering whether quantum memory can help augment classical memory. It seems like my suspicions that it cannot are confirmed. $\endgroup$
    – auden
    Commented Mar 25, 2018 at 18:11
  • $\begingroup$ @heather does this answer your question then? physics.stackexchange.com/q/358628/58382 $\endgroup$
    – glS ♦
    Commented Mar 25, 2018 at 18:13

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In summary, no.

If you think about it, this makes sense. When measuring a quantum system with $n$ qubits, you get $n$ bits of information. the $2^n$ figure exists only when the system is in superposition, which a classical computer cannot access.

The specific theorem in question here is Holevo's theorem. To quote Wikipedia:

In essence, the Holevo bound proves that given $n$ qubits, although they can "carry" a larger amount of (classical) information (thanks to quantum superposition), the amount of classical information that can be retrieved, i.e. accessed, can be only up to $n$ classical (non-quantum encoded) bits.

See this physics question and answer(s) as well. (Thanks to glS for linking to this in the comments.)

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    $\begingroup$ Note that while quantum mechanics doesn't give you any increase in storage capacity, it can in some circumstances give you a doubling of the transmission capacity via superdense coding. $\endgroup$
    – tparker
    Commented Mar 27, 2018 at 22:20

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