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It’s interesting to think about, but the complexity classes are actually equal[1]. This sort of makes sense if you think of quantum computers as simulatable by a classical computer. [1] https://arxiv.org/abs/2001.04383
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MIP*=RE
Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, Henry Yuen
2020 · arXiv
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From the abstract
We show that the class MIP* of languages that can be decided by a classical verifier interacting with multiple all-powerful quantum provers sharing entanglement is equal to the class RE of recursively enumerable languages. Our proof builds upon the quantum low-degree test of (Natarajan and Vidick, FOCS 2018) and the classical low-individual degree test of (Ji, et al., 2020) by integrating recent developments from (Natarajan and Wright, FOCS 2019) and combining them with the recursive compression framework of (Fitzsimons et al., STOC 2019). An immediate byproduct of our result is that there is an efficient reduction from the Halting Problem to the problem of deciding whether a two-player nonlocal game has entangled value $1$ or at most $1/2$. Using a known connection, undecidability of the entangled value implies a negative answer to Tsirelson's problem: we show, by providing an explicit example, that the closure $C_{qa}$ of the set of quantum tensor product correlations is strictly included in the set $C_{qc}$ of quantum commuting correlations. Following work of (Fritz, Rev. Math. Phys. 2012) and (Junge et al., J. Math. Phys. 2011) our results provide a refutation of Connes' embedding conjecture from the theory of von Neumann algebras.
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5 selected excerpts · 5 total mentions
Neutral mention · rule
I'm not really up to date, but a couple recent papers that I found interesting were: In theoretical distributed computing, The Space Complexity of Concencus From Swap [0] solves a problem that has been open for a couple decades, and won Best Paper at PODC 2022. In quantum complexity theory, MIP^* = RE [1] was really big deal when it was published in 2020. It got a (relative) ton of press coverage, and there are lots of articles and blog post available that give a high-level of the result and techniques used. I like this one [2] from Quanta Magazine. [0] https://dl.acm.org/doi/abs/10.1145/3519270.3538420 [1] https://arxiv.org/abs/2001.04383 [2] https://www.quantamagazine.org/landmark-computer-science-pro...
Neutral mention · rule
The paper 'MIP* =RE' https://arxiv.org/abs/2001.04383, where the article is referring to, has already been discussed here extensively. It is also being studied by many people, because it is a very important and surprising result. I guess that Connes conjecture is but one of the many things that is affected by the MIP* =RE result.
Neutral mention · rule
The paper[1] claims that MIP* = RE. At first I wasn't sure whether that was true, because the paper is too long and complicated for me to verify. But then I found a series of questions and answers written by this quantum guy Scott Aaronson[2] and by this other quantum guy Kenneth Regan[3], who both know a bunch of quantum stuff. Each one of their blog posts makes me more certain about MIP* = RE, to the point that now I'm 99.9% sure it's true, even though I could never verify it myself. [1] https://arxiv.org/abs/2001.04383 [2] https://www.scottaaronson.com/blog/?p=4512 [3] https://rjlipton.wordpress.com/2020/01/15/halting-is-poly-ti...
Neutral mention · rule
For those interested, the arxiv link: https://arxiv.org/abs/2001.04383 Be warned, this is 160 pages of dense math. To anyone complaining that the quanta article is "unclear" or not descriptive enough, there's no way around that when summarizing a dissertation.
Keep following the thread.
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