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THU: Thursday Contributed Sessions

THU 2: Quantum Information: Concepts and Methods I

THU 2.6: Vortrag

Donnerstag, 11. September 2025, 15:30–15:45, ZHG002

Optimal randomized measurements for a family of non-linear quantum properties — Zhenyu Du¹, •Yifan Tang², Andreas Elben³, Ingo Roth⁴, Jens Eisert², and Zhenhuan Liu¹ — ¹Tsinghua University, Beijing, China — ²Freie Universität Berlin, Berlin, Germany — ³Paul Scherrer Institute, Villigen, Switzerland — ⁴Technology Innovation Institute, Abu Dhabi, United Arab Emirates

Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal sample complexity for specific tasks, 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(Oρ²) for an arbitrary observable O—an essential quantity in quantum computing and many-body physics. 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 circuit complexities in practical applications. Numerical experiments validate that ORM requires substantially fewer state samples to achieve the same precision compared to classical shadows.

Keywords: Quantum learning; Quantum error mitigation; Randomized measurement protocols; Quantum non-linear properties; Unitary designs