Dayue Qin

Quantum error mitigation is a critical technology for extracting reliable computations from noisy quantum processors, proving itself essential not only in the near term but also as a valuable supplement to fully fault-tolerant systems in the future. However, its practical implementation is hampered by two major challenges: the expansive cost of sampling from quantum circuits and the reliance on unrealistic assumptions, such as gate-independent noise. Here, we introduce Classical Noise Inversion (CNI), a framework that fundamentally bypasses these crucial limitations and is well-suited for various quantum applications. CNI effectively inverts the accumulated noise entirely during classical post-processing, thereby eliminating the need for costly quantum circuit sampling and remaining effective under the realistic condition of gate-dependent noise. Apart from CNI, we introduce noise compression, which groups noise components with equivalent effects on measurement outcomes, achieving the optimal overhead for error mitigation. We integrate CNI with the framework of shadow estimation to create a robust protocol for learning quantum properties under general noise. Our analysis and numerical simulations demonstrate that this approach substantially reduces statistical variance while providing unbiased estimates in practical situations where previous methods fail. By transforming a key quantum overhead into a manageable classical cost, CNI opens a promising pathway towards scalable and practical quantum applications.

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.