Optimal Learning from Label Proportions with General Loss Functions 👥 Lorne Applebaum, Travis Dick, Claudio Gentile et al. #AIResearch #MachineLearning #LabelProportions #Debiasing #SampleComplexity 🔗 trendtoknow.ai

Optimal randomized measurements for a family of non-linear quantum properties scirate.com/arxiv/2505.09206 #Quantumlearning encounters fundamental challenges when estimating #nonlinear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal #samplecomplexity for specific tasks like state purity estimation, generalizing these protocols to estimate broader classes of non-linear properties without sacrificing optimality remains an open problem. In this work, we introduce the observable-driven randomized measurement (ORM) protocol enabling the estimation of Tr(Oρ^2) for an arbitrary observable O - an essential quantity in #quantumcomputing and #manybodyphysics. ORM achieves this by decomposing the observable O into dichotomic observables and extracting the information of each eigenspace through randomized measurements with block-diagonal unitaries. We establish an upper bound for ORM's sample complexity and prove its optimality for all Pauli observables, closing a gap in the literature. Furthermore, we develop simplified variants of ORM for local Pauli observables and introduce a braiding #randomized measurement protocol for fidelity estimation, both of which significantly reduce #circuitcomplexities in practical applications. Numerical experiments validate that ORM requires substantially fewer state samples to achieve the same precision compared to classical shadows. Warm thanks to Zhenyu Du, @YifanTang1999, @AndreasElben, Ingo Roth, and @liu_zhenhu77178 for the productive collaboration.

#poster #aaai23 #bandit #samplecomplexity