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In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states.<\/jats:p>","DOI":"10.22331\/q-2025-08-07-1823","type":"journal-article","created":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T07:36:06Z","timestamp":1756280166000},"page":"1823","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Density matrix representation of hybrid tensor networks for noisy quantum devices"],"prefix":"10.22331","volume":"9","author":[{"given":"Hiroyuki","family":"Harada","sequence":"first","affiliation":[{"name":"Department of Applied Physics and Physico-Informatics, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan"}]},{"given":"Yasunari","family":"Suzuki","sequence":"additional","affiliation":[{"name":"NTT Computer and Data Science Laboratories, NTT Corporation, 3-9-11 Midori-cho, Musashino-shi, Tokyo 180-8585, Japan"}]},{"given":"Bo","family":"Yang","sequence":"additional","affiliation":[{"name":"LIP6, Sorbonne Universit\u00e9, 4 Place Jussieu, Paris 75005, France"},{"name":"Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"}]},{"given":"Yuuki","family":"Tokunaga","sequence":"additional","affiliation":[{"name":"NTT Computer and Data Science Laboratories, NTT Corporation, 3-9-11 Midori-cho, Musashino-shi, Tokyo 180-8585, Japan"}]},{"given":"Suguru","family":"Endo","sequence":"additional","affiliation":[{"name":"NTT Computer and Data Science Laboratories, NTT Corporation, 3-9-11 Midori-cho, Musashino-shi, Tokyo 180-8585, Japan"},{"name":"JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan"}]}],"member":"9598","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al. 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