Universal Sample Complexity Bounds in Quantum Learning Theory via Fisher Information Matrix

arXiv:2602.21510 · quant-ph · Submitted 2026-02-25 · Read on arXiv

quant-ph

Submitted: 2026-02-25

Updated: 2026-07-30

Terminology

• Sample Complexity — 76× in this paper · explained in 15 episodes
• Fisher Information — 30× in this paper · explained in 3 episodes
• Entanglement — 27× in this paper · explained in 4 episodes
• Accuracy — 10× in this paper · explained in 1 episode
• Score Function — 7× in this paper · explained in 4 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Benchmarking — 3× in this paper · explained in 3 episodes
• Foundations of Computer Science — 3× in this paper
• Query Complexity — 3× in this paper · explained in 2 episodes
• Shadow Tomography — 2× in this paper · explained in 4 episodes
• Heisenberg Scaling — 1× in this paper · explained in 4 episodes
• Ulsan National Institute of Science and Technology — 1× in this paper
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Quantum advantages for syndrome-aware noisy logical observable estimation
• Hamiltonian Dynamics Learning: A Scalable Approach to Quantum Process Characterization
• Exponential advantage in continuous-variable quantum state learning
• Entanglement-enhanced learning of quantum processes at scale
• On the Fundamental Resource for Exponential Advantage in Quantum Channel Learning
• Restoring Heisenberg scaling in time via autonomous quantum error correction
• Criteria for unbiased estimation: applications to noise-agnostic sensing and quantum channel estimation
• Instance-optimal high-precision shadow tomography with few-copy measurements: A metrological approach

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