Zhou You

Measuring global quantum properties—such as the fidelity to complex multipartite states—is an essential yet experimentally challenging task. Classical shadow estimation offers favorable sample complexity but typically relies on deep circuits difficult to realize on current platforms. We propose the robust phase shadow (RPS), a framework based on random circuits with controlled-𝑍 as the unique entangling gate type, tailored to architectures like trapped ions and neutral atoms. everaging tensor diagrammatic reasoning, we show that RPS matches the performance of Clifford-based methods. Importantly, our approach supports a noise-robust extension via classical post-processing, enabling reliable estimation under arbitrary gate-dependent Pauli noise where existing techniques fail. Additionally, we design an efficient post-processing algorithm resolving computational bottlenecks. Our results provide a scalable route for estimating global properties in noisy quantum systems.