Searches have returned absolutely no results on this question. With that in mind, I assume the answer is either painfully obvious ('of course quantum computers get no advantage when it comes to storing data') or the question has just not been studied. Intuitively it makes sense the quantum algorithms would gain no advantage related to storage, but memory hard functions seem to be a rather budding new technology and I wonder to what degree of certainty that intuition can be verified, if at all.

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    $\begingroup$ If we are talking about functions like Argon2, the answer is yes. Since the only attack is the optimal Grover's algorithm (and Brassard et al.'s that requires much more qbits to achieve cube-root instead of the square root of Grover's algorithm see the table) $\endgroup$
    – kelalaka
    May 27, 2022 at 3:57
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    $\begingroup$ cryptobook.nakov.com/quantum-safe-cryptography $\endgroup$
    – kelalaka
    May 27, 2022 at 4:03


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