Learning quantum symmetries

arXiv:2609.38085 · quant-ph · Submitted 2026-09-29 · Read on arXiv

quant-ph

Submitted: 2026-09-29

Updated: 2026-09-30

Terminology

• Core — 31× in this paper · explained in 2 episodes
• Hidden Subgroup Problem — 27× in this paper
• Sample Complexity — 5× in this paper · explained in 15 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Quantum Physics — 3× in this paper · explained in 11 episodes
• Entanglement — 2× in this paper · explained in 4 episodes
• Query Complexity — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Algorithmic Primitives — 1× in this paper · explained in 1 episode
• Fidelity — 1× in this paper · explained in 2 episodes
• Stabilizer States — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Quantum state isomorphism problems for groups
• Solution to the Hidden Subgroup Problem for a Class of Noncommutative Groups
• Pseudoentanglement Ain't Cheap
• The abelian state hidden subgroup problem: Learning stabilizer groups and beyond
• The hidden subgroup problem for infinite groups
• Learning T-conjugated stabilizers: The multiple-squares dihedral StateHSP
• Learning stabilizer states by Bell sampling
• Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of non-abelian Groups
• Solving approximate hidden subgroup problems: quantum heuristics to detect weak entanglement

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• 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