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We prove that the computation of the Kronecker coefficients of the symmetric group is contained in the complexity class #BQP.
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Adam Krawczyk · 1999
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“Positivity Problems and Conjectures in Algebraic”
Richard Stanley · 2000
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“Thomason’s algorithm for finding a second Hamiltonian circuit through a given edge in a cubic graph is exponential on Krawczyk’s graphs”
Kathie Cameron · 2001
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“Geometric complexity theory I: An approach to the P vs. NP and related problems”
Ketan Mulmuley and Milind Sohoni · 2001
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“Quantum Merlin-Arthur proof systems: Are multiple Merlins more helpful to Arthur?”
Hirotada Kobayashi, Keiji Matsumoto and Tomoyuki Yamakami · 2003
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“A combinatorial interpretation for the coefficients in the Kronecker product s ( n − p , p ) ∗ s λ s_{(n-p,p)}\ast s_{\lambda} ”
Cristina Ballantine and Rosa Orellana · 2006
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“Generic Quantum Fourier Transforms”
Cristopher Moore, Daniel Rockmore and Alexander Russell · 2006
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“On Perfect Completeness for QMA”, 2008
Scott Aaronson · 2008
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“Geometric complexity theory II: towards explicit obstructions for embeddings among class varieties”
Ketan Mulmuley and Milind Sohoni · 2008
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“Symmetry, representations, and invariants”
Roe Goodman and Nolan Wallach · 2009
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“Note on quantum counting classes” http://www.cse.cuhk.edu.hk/~syzhang/papers/SharpBQP.pdf
Yaoyun Shi and Shengyu Zhang · 2009
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“Representation theory of the symmetric groups: the Okounkov-Vershik approach, character formulas, and partition algebras”
Tullio Ceccherini-Silberstein, Fabio Scarabotti and Filippo Tolli · 2010
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“Quantum Computation and Quantum Information”
Michael. Nielsen and Isaac. Chuang · 2010
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“Computational difficulty of computing the density of states”
Brielin Brown, Steven Flammia and Norbert Schuch · 2011
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“Geometric complexity theory and tensor rank”
Peter Bürgisser and Christian Ikenmeyer · 2011
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Peter Bürgisser, Joseph Landsberg, Laurent Manivel and Jerzy Weyman · 2011
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“Computing multiplicities of Lie group representations”
“A simplified Kronecker rule for one hook shape”
Ricky Liu · 2017
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“Introduction to geometric complexity theory” https://www.dcs.warwick.ac.uk/~u2270030/teaching_sb/summer17/introtogct/gct.pdf , 2018
Markus Bläser and Christian Ikenmeyer · 2018
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“Kronecker coefficients and noncommutative super Schur functions”
Jonah Blasiak and Ricky Liu · 2018
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“No occurrence obstructions in geometric complexity theory”
Peter Bürgisser, Christian Ikenmeyer and Greta Panova · 2019
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“Generalized Foulkes modules and maximal and minimal constituents of plethysms of Schur functions”
Rowena Paget and Mark Wildon · 2019
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“On geometric complexity theory: Multiplicity obstructions are stronger than occurrence obstructions”
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Matthias Christandl, Brent Doran and Michael Walter · 2012
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“Geometric complexity theory, tensor rank, and Littlewood-Richardson coefficients”, 2012
Christian Ikenmeyer · 2012
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“Achieving Perfect Completeness in Classical-Witness Quantum Merlin-Arthur Proof Systems”
Stephen. Jordan, Hirotada Kobayashi, Daniel Nagaj and Harumichi Nishimura · 2012
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“Explicit lower bounds via geometric complexity theory”
Peter Bürgisser and Christian Ikenmeyer · 2013
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“Geometric Complexity Theory IV: nonstandard quantum group for the Kronecker problem”
Jonah Blasiak, Ketan Mulmuley and Milind Sohoni · 2015
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“A study of the representations supported by the orbit closure of the determinant”
Shrawan Kumar · 2015
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“Kronecker coefficients for some near-rectangular partitions”
Vasu Tewari · 2015
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Julian Dörfler, Christian Ikenmeyer and Greta Panova · 2020
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“The computational complexity of plethysm coefficients”
Nick Fischer and Christian Ikenmeyer · 2020
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“Implementing geometric complexity theory: On the separation of orbit closures via symmetries”
Christian Ikenmeyer and Umangathan Kandasamy · 2020
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“Plethysms of symmetric functions and highest weight representations”
Melanie de Boeck, Rowena Paget and Mark Wildon · 2021
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“What is in #P and what is not?”
Christian Ikenmeyer and Igor Pak · 2022
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“What is a combinatorial interpretation?” arXiv:2209.06142, 2022
Igor Pak · 2022
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“The Beauty of Braids” Plenary talk at the ICM 2022, http://www.math.uni-bonn.de/ag/stroppel/TheBeautyofBraids_ICMVortragStroppel.pdf , 2022
Catharina Stroppel · 2022
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“Quantum complexity of the Kronecker coefficients”, 2023
Sergey Bravyi, Anirban Chowdhury, David Gosset, Vojtech Havlicek and Guanyu Zhu · 2023
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“Positivity of the symmetric group characters is as hard as the polynomial time hierarchy”
Christian Ikenmeyer, Igor Pak and Greta Panova · 2023
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“A randomized classical oracle separating QMA and QCMA” To appear in the Proceedings of the Computational Complexity Conference (CCC 2023), 2023
Anand Natarajan and Chinmay Nirkhe · 2023
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“Complexity and asymptotics of structure constants” arXiv:2305.02553, 2023
Greta Panova · 2023
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