Efficient Learning of Clifford-Scrambled Product States

arXiv:2609.27128 · quant-ph · Submitted 2026-09-22 · Read on arXiv

quant-ph

Submitted: 2026-09-22

Updated: 2026-09-22

Comments: 7 + 25 pages

Code: https://github.com/txhaug/ProductLearner

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

Terminology

• Entanglement — 17× in this paper · explained in 3 episodes
• Trace — 16× in this paper · explained in 2 episodes
• Accuracy — 8× in this paper · explained in 1 episode
• Trace Distance — 8× in this paper · explained in 3 episodes
• Stabilizer States — 5× in this paper · explained in 2 episodes
• Anticoncentration — 3× in this paper · explained in 1 episode
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Entanglement Entropy — 2× in this paper · explained in 2 episodes
• Adaptive Decoding — 1× in this paper · explained in 1 episode
• Agnostic Learning — 1× in this paper · explained in 1 episode
• Alternation — 1× in this paper · explained in 1 episode
• Fidelity — 1× in this paper · explained in 2 episodes
• Local Optimization — 1× in this paper · explained in 2 episodes
• Process tomography — 1× in this paper · explained in 2 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Sample Efficiency — 1× in this paper · explained in 4 episodes
• Shadow Tomography — 1× in this paper · explained in 4 episodes
• Supplementary Material — 1× in this paper

Sources

• Learning stabilizer states by Bell sampling
• Tomography of quantum states with bounded extent
• Efficient certification of intractable quantum states with few Pauli measurements
• Learning Clifford-structured quantum unitaries and Hamiltonians
• Magic-protected entanglement and Clifford-irreducible structure in magic state space

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