Entanglement among a large number of qubits is a crucial resource for many quantum algorithms. Such many-body states have been efficiently generated by entangling a chain of itinerant photonic qubits in the optical or microwave domain. However, it has remained challenging to fully characterize the generated many-body states by experimentally reconstructing their exponentially large density matrices. Here, we develop an efficient tomography method based on the matrix-product-operator formalism and demonstrate it on a cluster state of up to 35 microwave photonic qubits by reconstructing its 235×235 density matrix. The full characterization enables us to detect the performance degradation of our photon source which occurs only when generating a large cluster state. This tomography method is generally applicable to various physical realizations of entangled qubits and provides an efficient benchmarking method for guiding the development of high-fidelity sources of entangled photons.
@article{arxiv.2410.03345,
title = {Efficient tomography of microwave photonic cluster states},
author = {Yoshiki Sunada and Shingo Kono and Jesper Ilves and Takanori Sugiyama and Yasunari Suzuki and Tsuyoshi Okubo and Shuhei Tamate and Yutaka Tabuchi and Yasunobu Nakamura},
journal= {arXiv preprint arXiv:2410.03345},
year = {2026}
}