Improved Quantum Algorithms for Black-Box Abelian Group Decomposition

arXiv:2609.36480 · quant-ph · Submitted 2026-09-29 · Read on arXiv

quant-ph

Submitted: 2026-09-29

Updated: 2026-10-04

Terminology

• Quantum Circuits — 7× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Query Complexity — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes

Sources

• An efficient quantum algorithm for computing $S$-units and its applications
• The computational power of normalizer circuits over black-box groups
• Hidden Subgroup States are Almost Orthogonal
• Creating superpositions that correspond to efficiently integrable probability distributions
• A Subexponential Time Algorithm for the Dihedral Hidden Subgroup Problem with Polynomial Space

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity