Efficient Learning Algorithms for Noisy Quantum State and Process Tomography

• URL: http://arxiv.org/abs/2603.01521v1
• Date: Mon, 02 Mar 2026 06:50:59 GMT
• Title: Efficient Learning Algorithms for Noisy Quantum State and Process Tomography
• Authors: Chenyang Li, Shengxin Zhuang, Yukun Zhang, Jingbo B. Wang, Xiao Yuan, Yusen Wu, Chuan Wang,
• Abstract summary: We introduce a provably efficient and structure-agnostic learning framework for noisy $n$-qubit quantum circuits.<n>Results provide a scalable and practically relevant route toward characterizing large-scale noisy quantum devices.
• Score: 17.414887413731385
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system size. Here, we introduce a provably efficient and structure-agnostic learning framework for noisy $n$-qubit quantum circuits under generic noise with arbitrary noise strength. We first develop a sample-efficient learning algorithm for unital noisy quantum states. Building on this result, we extend the framework to quantum process tomography, obtaining a unified protocol applicable to both unital and non-unital channels. The resulting approach is input-agnostic and does not rely on assumptions about specific input distributions. Our theoretical analysis shows that both state and process learning require only polynomially many samples and polynomial classical post-processing in the number of qubits, while achieving near-unit success probability over ensembles generated by local random circuits. Numerical simulations of two-dimensional Hamiltonian dynamics further demonstrate the accuracy and robustness of the approach, including for structured circuits beyond the random-circuit setting assumed in the theoretical analysis. These results provide a scalable and practically relevant route toward characterizing large-scale noisy quantum devices, addressing a key bottleneck in the development of quantum technologies.

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