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QI: Fachverband Quanteninformation

QI 9: Quantum Machine Learning and Classical Simulability

QI 9.4: Vortrag

Dienstag, 19. März 2024, 10:30–10:45, HFT-FT 101

Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms — •Alexander Nietner — FU-Berlin

Kearns SQ oracle lends a unifying perspective for most classical machine learning algorithms. This no longer holds in case of quantum learning and with respect to the SQ or QSQ oracle. In this work we explore the problem of learning from an evaluation oracle, which provides an estimate of function values. We introduce an intuitive framework that yields unconditional lower bounds for learning from evaluation queries and characterizes the query complexity for learning linear function classes. The framework is directly applicable to the QSQ setting and virtually all algorithms based on loss function optimization.

We first apply this formalism to the QSQ setting studying the learnability of unitary and Clifford quantum circuit states at different depth regimes and prove exponential separations of learning stabilizer states from QSQs versus from quantum copy access.

Our second application is to analyze popular QML settings and to develop an intuitive picture that goes beyond that of barren plateaus. This enables us to show how the implications of a barren plateau depend on the particular setting, which gives new and valuable insights into variational algorithms.

Keywords: QSQ; Quantum Learning; Barren Plateau; Unconditional Lower Bounds