Tackling Sampling Noise in Physical Systems for Machine Learning Applications: Fundamental Limits and Eigentasks

Abstract

The expressive capacity of physical systems employed for learning is limited\nby the unavoidable presence of noise in their extracted outputs. Though present\nin physical systems across both the classical and quantum regimes, the precise\nimpact of noise on learning remains poorly understood. Focusing on supervised\nlearning, we present a mathematical framework for evaluating the resolvable\nexpressive capacity (REC) of general physical systems under finite sampling\nnoise, and provide a methodology for extracting its extrema, the eigentasks.\nEigentasks are a native set of functions that a given physical system can\napproximate with minimal error. We show that the REC of a quantum system is\nlimited by the fundamental theory of quantum measurement, and obtain a tight\nupper bound for the REC of any finitely-sampled physical system. We then\nprovide empirical evidence that extracting low-noise eigentasks can lead to\nimproved performance for machine learning tasks such as classification,\ndisplaying robustness to overfitting. We present analyses suggesting that\ncorrelations in the measured quantum system enhance learning capacity by\nreducing noise in eigentasks. The applicability of these results in practice is\ndemonstrated with experiments on superconducting quantum processors. Our\nfindings have broad implications for quantum machine learning and sensing\napplications.\n