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ACM SIGACT News

SIGACT News Complexity Theory Column 127 and 128

Ben Lee Volk

Published Mar 31, 2026• 0 citations
Publisher

Abstract

Dear Readers, After a short hiatus, the complexity theory column is back with a double feature! In this issue, we present a column by Mitali Bafna on Size-Efficient PCPs from High-Dimensional Expanders, and a column by Fernando Granha Jeronimo, Itai Leigh and Pei Wu on the landscape of complexity classes surrounding QMA(2). Both columns are excellent, and I am sure you will find them both enjoyable and enlightening. Many thanks to the authors for their hard work! What's coming up next in the pipeline? If all goes according to plan, we will feature guest columns by Geoffroy Couteau; Jesse Goodman (on seedless extractors); Davi Castro-Silva, Arkopal Dutt, and Tom Gur (on connections between additive combinatorics and quantum complexity theory); Debarati Das; and Jeroen Zuiddam (on matrix multiplication, moment polytopes and asymptotic spectra). Stay tuned for upcoming issues of SIGACT News!

DOI
10.1145/3802807.3802812

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When it comes to NP, its natural definition, its wide applicability across scientific disciplines, and its timeless relevance, the writing is on the wall: There can be only one. Quantum NP, on the other hand, is clearly the apple that fell far from the tree of NP. Two decades since the first definitions of quantum NP started rolling in, quantum complexity theorists face a stark reality: There's QMA, QCMA, QMA1, QMA(2), StoqMA, and NQP. In this article aimed at a general theoretical computer science audience, I survey these various definitions of quantum NP, their strengths and weaknesses, and why most of them, for better or worse, actually appear to fit naturally into the complexity zoo.
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