A remark on the quantum complexity of the Kronecker coefficients

TL;DR

This paper shows that calculating Kronecker coefficients, important in representation theory, can be efficiently handled within the quantum complexity class #BQP, extending previous results with new insights.

Contribution

It improves the understanding of the quantum complexity of Kronecker and plethysm coefficients using quantum and classical methods.

Findings

Kronecker coefficients are in #BQP complexity class

Extended results to plethysm coefficients

Utilized quantum tools and classical representation theory

Abstract

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 only the quantum computing tools that are used in their paper and additional classical representation theoretic insights. We also prove the analogous result for the plethysm coefficients.