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I am trying to see which features we know are necessary for mixed-state quantum computing to avoid the algorithms being efficiently simulated on classical computers.

In the case of pure-state quantum computing for instance we know that the entanglement must grow with the size of the problem we wish to simulate. We also know it is not sufficient because of the Gottesman Knill theorem.

I know that in the case of mixed-state quantum computing the situation is "more complicated". I am trying to find a relatively recent review that summarizes all that we know about the resources required in mixed-state quantum computing, especially the role of entanglement. This is the purpose of my question.

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Perhaps a bit old to come under the "recent" category, but the following PhD thesis is worth a look: https://arxiv.org/abs/0807.4490 Also, not a review, but I got intrigued by entanglement in the DQC1 model at some point and wrote a little about it: https://arxiv.org/abs/1508.06474

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  • $\begingroup$ Thank you very much. The thesis is indeed not super recent but this is a starting point of a good summary, I will take a look! Thanks for your paper as well (I already read it a bit actually ;) ). I wait for other potential answers that could provide more recent reviews. $\endgroup$
    – Marco Fellous-Asiani
    Commented Apr 1, 2022 at 11:59

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