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Our approach outperforms and offers several advantages over comparable algorithms, such as an improved scaling of the computational cost with respect to the bond dimension for periodic systems. We showcase the versatility of our approach by studying the phase diagrams and correlation functions of the dissipative quantum Ising model with collective dephasing and long-ranged power law interactions for spin chains of up to N<\/mml:mi>=<\/mml:mo>100<\/mml:mn><\/mml:math> spins.<\/jats:p>","DOI":"10.22331\/q-2024-09-17-1475","type":"journal-article","created":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T08:40:19Z","timestamp":1727080819000},"page":"1475","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems"],"prefix":"10.22331","volume":"8","author":[{"given":"Dawid A.","family":"Hryniuk","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom"},{"name":"London Centre for Nanotechnology, University College London, Gordon Street, London WC1H 0AH, United Kingdom"}]},{"given":"Marzena H.","family":"Szyma\u0144ska","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom"}]}],"member":"9598","published-online":{"date-parts":[[2024,9,17]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. 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