New findings reveal that computing Kronecker coefficients fits within the #BQP class, highlighting advances in quantum algorithms and representation theory.
We prove that the computation of the Kronecker coefficients of the symmetric group is contained in the complexity class #BQP . This improves a recent result of Bravyi, Chowdhury, Gosset, Havlicek, and Zhu. We use the same quantum algorithmic tools that are used in their paper, combined with additional classical representation theoretic insights. We also prove the analogous result for the plethysm coefficients and the row sums of the symmetric group character table.
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Ikenmeyer et al. (2025) studied this question.
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