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arXiv · 2607.15493

The Complexity of Dynamical Correlators: Operator Shadows and Exponential Learning Separations

Shao-Hen Chiew·Armando Angrisani·Zoe Holmes
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Abstract

Quantum platforms can realize many-body dynamics beyond classical simulation yet complete readout remains intractable: the cost of extracting accessible information scales exponentially with system size. Classical shadows and Bell sampling offer scalable, multi-observable estimation from randomized or entanglement-assisted measurements. Here we aim to push these ideas beyond static snapshots to dynamical correlators, including out-of-time-ordered correlators (OTOCs) and two-point functions. In particular, we introduce the notion of the shadow of an operator, defined as the classical shadow of the vectorized time-evolved operator. Pauli operator-shadows enable simultaneous estimation of all local OTOCs, while Clifford operator-shadows enable efficient simultaneous estimation of all two-point correlators. Alternatively, Bell sampling allows one to simultaneously compute all diagonal OTOCs. We also prove information-theoretic lower bounds for learning OTOCs, fully characterizing their query complexities in many cases, and yielding exponential separations that formalize when the vectorized approach provides measurement-efficiency advantages.

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Shao-Hen Chiew, Armando Angrisani, Zoe Holmes. 2026-07-16. The Complexity of Dynamical Correlators: Operator Shadows and Exponential Learning Separations. https://arxiv.org/abs/2607.15493

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