Provably Efficient Learning Algorithms for Noisy Quantum State and Process Tomography

Chenyang Li, Shengxin Zhuang, YuKun Zhang, Jingbo Wang, Yusen Wu, Xiao Yuan, Chuan Wang

Keywords: quantum machine learning, quantum state tomography, quantum process tomography

Abstract: Characterizing noisy $n$-qubit states and processes is vital yet lacks scalability with conventional methods. Considering the circuit under unital or non-unital independent and identically distributed (i.i.d) single-qubit noise where each local gate follows the local 2-design assumption, we propose a structure-free learning algorithm that reconstructs any noisy process or state from measurement data. The proposed algorithm yields ${\rm poly}(n,1/\epsilon)$ sample complexity and classical post-processing running time for target accuracy $\epsilon$ in the *average case* scenario over the random circuit ensemble. We numerically benchmark the algorithm on both unital and non-unital i.i.d single-qubit noise channels, and our results indicate that the algorithm remains highly effective and accurate even for specific quantum circuits, such as noisy Hamiltonian dynamics, suggesting its broader practical utility. This work offers a new approach to practical quantum-process learning, and suggests a potential path for scalable process characterization in near-term quantum devices.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 9252