Who can sample forever? Shot noise effects in quantum linear regression

arXiv:2610.12015 · quant-ph · Submitted 2026-10-08 · Read on arXiv

quant-ph

Submitted: 2026-10-08

Updated: 2026-10-08

Code: https://github.com/salvatore-lorenzo/MTR

Terminology

• Hilbert Space — 8× in this paper · explained in 2 episodes
• Regularization — 6× in this paper · explained in 3 episodes
• Fidelity — 4× in this paper · explained in 2 episodes
• Systematic Bias — 4× in this paper · explained in 3 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Homogeneity — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Calibration — 2× in this paper · explained in 7 episodes
• Error Decomposition — 2× in this paper · explained in 3 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Hybrid Models — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Shadow Tomography — 1× in this paper · explained in 4 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Challenges and Opportunities in Quantum Machine Learning
• A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance
• Variational Quantum Algorithms
• Barren plateaus in quantum neural network training landscapes
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Does provable absence of barren plateaus imply classical simulability?
• Barren Plateaus in Variational Quantum Computing
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms
• Expressibility and trainability of parameterized analog quantum systems for machine learning applications
• Limitations of optimization algorithms on noisy quantum devices
• Concentration of Data Encoding in Parameterized Quantum Circuits
• Supervised quantum machine learning models are kernel methods
• Quantum machine learning beyond kernel methods
• Potential and limitations of quantum extreme learning machines
• Harnessing disordered quantum dynamics for machine learning
• On fundamental aspects of quantum extreme learning machines
• State estimation with quantum extreme learning machines beyond the scrambling time
• Quantum Extreme Learning of molecular potential energy surfaces and force fields
• Experimental property-reconstruction in a photonic quantum extreme learning machine

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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