The quantum query complexity of the semigroup product problem

arXiv:2609.39974 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 95 pages, 1 figure

Code: https://github.com/troyjlee/monoid-product

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Core — 27× in this paper · explained in 2 episodes
• Query Complexity — 26× in this paper · explained in 2 episodes
• APEX — 13× in this paper · explained in 1 episode
• Verification — 3× in this paper · explained in 2 episodes
• Adjacency Matrix — 2× in this paper · explained in 1 episode
• Generalization — 2× in this paper · explained in 13 episodes
• Block Encoding — 1× in this paper · explained in 4 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes

Sources

• Quantum Lower and Upper Bounds for 2D-Grid and Dyck Language
• A Quantum Query Complexity Trichotomy for Regular Languages
• On the quantum time complexity of divide and conquer
• Representation Theory of Finite Semigroups, Semigroup Radicals and Formal Language Theory
• Quantum Amplitude Amplification and Estimation
• Note on Sunflowers
• Quantum Speedup Based on Classical Decision Trees
• Quantum Walks and Electric Networks
• Quantum Algorithm for k-distinctness with Prior Knowledge on the Input
• Improved Quantum Query Upper Bounds Based on Classical Decision Trees
• Quantum query complexity of some graph problems
• Negative weights make adversaries stronger
• Quantum Subroutine Composition
• Quantum query complexity of state conversion
• Reflections for quantum query algorithms
• Davenport constant for semigroups II

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