Quantum-enhanced shadow tomography of (very many) Pauli observables

by Richard Kueng (JKU Linz)

Wednesday 13 Aug 2025, 11:00 → 12:00 Europe/Zurich

WBBC/111

Shadow tomography protocols have recently emerged as powerful tools for efficient quantum state learning, aiming to reconstruct expectation values of observables with considerably fewer resources than traditional quantum state tomography. For the particular case of estimating Pauli observables, entangling two-copy measurement schemes can offer an exponential improvement in sample complexity over any single-copy strategy conceivable [Huang, Kueng, Preskill, PRL (2021)]. A recent refinement of these ideas by King et al.  King, Gosset, Kothari, Babbush, SODA (2025)] does not only achieve polynomial sample complexity, but also maintains reasonable computational demands and utilizes joint measurements on only a small constant number of state copies. This ‘triple efficiency’ is achievable for any subset of n-qubit Pauli observables, whereas single-copy strategies can only be efficient if the Pauli observables in question have advantageous structure. 

In this work, we complement existing theoretical performance guarantees with the empirical evaluation of triply efficient shadow tomography using classical, noise-free simulations. Our findings indicate that the empirical sample complexity aligns closely with theoretical predictions for stabilizer states and, notably, demonstrates slightly improved scaling for random Gibbs states compared to established theoretical bounds. In addition, we improve a central subroutine in the triply-efficient shadow protocol by leveraging insights from a refined quantum and quantum-inspired convex optimization algorithm [Henze et al. arXiv:2502.15426 (2025)].