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arXiv · 2606.12035

Shadow Engineering of Quantum Processes

Tian-Ci Tian·De-Tao Jiang·Wei-Ming Zhu·Wei-You Liao·Hong-Wei Li·He-Liang Huang
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Abstract

Characterizing quantum processes is essential for hardware benchmarking, error diagnosis, and algorithm verification. While recent work [PRX QUANTUM \textbf{4}, 040337 (2023)] extended classical shadows from quantum state to quantum process, enabling efficient single-channel $\mathcal{E}$ property prediction, its applicability to composite processes $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$ remains unexplored. We introduce shadow engineering, a framework encoding the classical shadows of processes into sparse transfer matrices to predict $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$ properties with proven polynomial sample complexity, matching single-channel efficiency while exponentially lower than quantum process tomography. Crucially, this approach repurposes existing $\mathcal{E}_m$-shadow data without physical execution of $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$, enabling flexible quantum process characterization with minimal hardware overhead. We demonstrate the framework's effectiveness and practicality on a superconducting quantum processor for typical applications such as error mitigation and Hamiltonian dynamical simulation. This framework unlocks new capabilities for predicting complex quantum behaviors without physical re-execution, with immediate applications in near-term device calibration and quantum simulation.

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Tian-Ci Tian, De-Tao Jiang, Wei-Ming Zhu, Wei-You Liao, Hong-Wei Li, He-Liang Huang. 2026-06-10. Shadow Engineering of Quantum Processes. https://arxiv.org/abs/2606.12035

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