Shadow Engineering of Quantum Processes

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.