Intrinsic Mixed-State Topological Order by Zijian Wang, Zhengzhi Wu, Zhong Wang

“…Decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. …”
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Noisy Approach to Intrinsically Mixed-State Topological Order by Ramanjit Sohal, Abhinav Prem

“…We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed state can display intrinsically mixed-state topological order (imTO)—topological order that is not expected to occur in the ground state of 2D local gapped Hamiltonians. …”
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Topological ordering during flexible to rigid transitions in disordered networks by Micoulaut, Matthieu

“…Results not only reveal that densified silicates display topological ordering on lengthscales of about 25 Å, but also display obvious threshold behaviors close to the isostatic condition when the network undergoes a flexible to rigid transition. …”
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Compactness on Soft Topological Ordered Spaces and Its Application on the Information System by T. M. Al-shami

“…Furthermore, we investigate the conditions under which these concepts are preserved between the soft topological ordered space and its parametric topological ordered spaces. …”
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The Existence and Stability of Solutions for Vector Quasiequilibrium Problems in Topological Order Spaces by Qi-Qing Song

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Toward a Classification of Mixed-State Topological Orders in Two Dimensions by Tyler D. Ellison, Meng Cheng

“…However, decoherence due to interactions with the environment is inevitable—thus motivating the investigation of topological orders in the context of mixed states. Here, we take a step toward classifying mixed-state topological orders in two spatial dimensions by considering their (emergent) generalized symmetries. …”
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Coalescence of multiple topological orders in quasi-one-dimensional bismuth halide chains by Jingyuan Zhong, Ming Yang, Wenxuan Zhao, Kaiyi Zhai, Xuan Zhen, Lifu Zhang, Dan Mu, Yundan Liu, Zhijian Shi, Ningyan Cheng, Wei Zhou, Jianfeng Wang, Weichang Hao, Zhenpeng Hu, Jincheng Zhuang, Jinhu Lü, Yi Du

“…Abstract Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications for future quantum devices, can be driven by topological phase transition through modulating intrinsic or extrinsic ordering parameters. …”
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The Nachbin compactification via convergence ordered spaces by D. C. Kent, Dongmei Liu

Subjects: “…topological ordered space…”
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Entanglement in BF theory. Part I. Essential topological entanglement by Jackson R. Fliss, Stathis Vitouladitis

“…Abstract We study the entanglement structure of Abelian topological order described by p-form BF theory in arbitrary dimensions. …”
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Quantum Spin Ice in Three-Dimensional Rydberg Atom Arrays by Jeet Shah, Gautam Nambiar, Alexey V. Gorshkov, Victor Galitski

“…With recent theory proposals and an experiment showing preliminary signs of Z_{2} topological order [G. Semeghini et al., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. …”
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(SPT-)LSM theorems from projective non-invertible symmetries by Salvatore D. Pace, Ho Tat Lam, and Ömer M. Aksoy

“…We complement our analysis with the SymTFT, where the projectivity causes it to be a topological order non-trivially enriched by translations. …”
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Multi-FPGA Partitioning Method Based on Topological Levelization by Nabil Kerkiz, Amr Elchouemi, Don Bouldin

“…This paper presents a partitioning method based on topological ordering and levelization. The proposed method, termed RPL, performs multi-FPGA partitioning by taking into account six different partitioning constraints. …”
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Porous Biodegradable Metals for Hard Tissue Scaffolds: A Review by A. H. Yusop, A. A. Bakir, N. A. Shaharom, M. R. Abdul Kadir, H. Hermawan

“…With further optimization in topologically ordered porosity design exploiting material property and fabrication technique, porous biodegradable metals could be the potential materials for making hard tissue scaffolds.…”
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Perturbative Stability and Error-Correction Thresholds of Quantum Codes by Yaodong Li, Nicholas O’Dea, Vedika Khemani

“…Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. …”
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Short and long-range magnetic ordering and emergent topological transition in (Mn1−xNix)2P2S6 by Nasaru Khan, Deepu Kumar, Shantanu Semwal, Yuliia Shemerliuk, Bernd Büchner, Koushik Pal, Saicharan Aswartham, Pradeep Kumar

“…Though, there are some exceptions to Mermin-Wagner theorem in particular low dimensional magnetic systems with topologically ordered phase transitions. Here, we present an in-depth temperature dependent analysis for the bulk single crystals of two-dimensional (Mn1−xNix)2P2S6 with x = 1, 0.7, 0.3, 0 using the Raman spectroscopy supported by first-principles calculations of the phonon frequencies. …”
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