Name：贾治安 in simplified Chinese; given name: Zhian 治安, surname: Jia 贾; Zhian Jia or Zhi-An Jia in Mandarin Chinese; name used before: Zhih-Ahn Jia. [pronunciation of my name: ]
Curriculum Vitae : CV, Web version of cv (updated intermittently)
Welcome to my homepage!
I am a researcher in mathematical and theoretical physics, focusing on the mathematical structures of quantum theory—ranging from quantum field theory and quantum phases of matter to quantum information and computation.
My recent work centers on topological field theories and their lattice realizations (topological orders), as well as generalized symmetries in both field-theoretic and lattice frameworks. I am also deeply engaged in axiomatic quantum field theory, especially geometric and operator-algebraic approaches.
These directions connect naturally to my broader interests in quantum algebra and topology, including tensor categories, (quasi, weak) Hopf algebras, TQFTs, cobordism, low-dimensional topology, and knot and braid theory.
I began my research career in quantum information and computation theory, which continues to inspire and complement my work in mathematical physics.
$$ \operatorname{Hopf}: \mu\circ (\operatorname{id}\otimes S) \circ \Delta = \eta\circ \varepsilon = \mu \circ (S\otimes \operatorname{id}) \circ \Delta$$
$$\operatorname{Bulk-Boundary}: \mathsf{Bulk} \simeq Z(\mathsf{Boundary}) $$
$$\operatorname{TQFT}: \mathsf{Cob}_{d+1} \to \mathsf{Hilb} $$
$$\operatorname{QECC}: \mathsf{R}\circ \mathsf{E}(\varrho) \propto \varrho $$
$$\text{index}(D) = \int_{{T^*}M} \text{Ch} (\psi(\sigma_H(D))) \wedge \text{Td}(M)$$
$$\operatorname{Anyon condensation}: \mathbf{C} \to \mathsf{Mod}_L(\mathbf{C})= \mathbf{C}_L$$
$$\operatorname{SymTFT}: \mathbf{B}_{sym} + Z(\mathbf{B}_{sym}) + \mathbf{B}_{phys} $$
For more details of my research, please refer to my
research page and publication/preprint page.
If you are interested in these topics, feel free to contact me via email.
“On some shelf in some hexagon, it was argued, there must exist a book that is the cipher and perfect compendium of all other books, and some librarian must have examined that book; this librarian is analogous to a god. In the language of this zone there are still vestiges of the sect that worshiped that distant librarian. Many have gone in search of Him. For a hundred years, men beat every possible path and every path in vain. How was one to locate the idolized secret hexagon that sheltered Him? Someone proposed searching by regression: To locate book A, first consult book B, which tells where book A can be found; to lo cate book B, first consult book C, and so on, to infinity....It is in ventures such as these that I have squandered and spent my years. I cannot think it unlikely that there is such a total book on some shelf in the universe. I pray to the unknown gods that some man-even a single man, tens of centuries ago-has perused and read that book. If the honor and wisdom and joy of such a reading are not to be my own, then let them be for others. Let heaven exist, though my own place be in hell. Let me be tortured and battered and annihilated, but let there be one instant, one creature, wherein thy enormous Library may find its justification.”
I am also actively engaged in academic communication through conferences, seminars, and collaborative community activities, aiming to contribute to and learn from the broader scientific community.
See this page for details about my academic activities, including the conferences and workshops I have participated in or plan to attend, as well as my editorial and reviewing work.
I also actively engage in popular science communication and digital content creation in mathematics and theoretical physics across multiple platforms.
I enjoy discussing interesting topics with others, so feel free to reach out via email.
Beyond my work in mathematics and physics,
I enjoy reading books—some of my favorites are "One Hundred Years of Solitude", "Don Quixote", "Moby-Dick", "The Brothers Karamazov", "On the Road", "Pale Blue Dot"—as well as traveling and writing.
Check this link (in Chinese) for my 2025 reading list.
GIF is based on a video by ScienceClic
Some Resources
: This page will be updated automatically every eight hours using arXiv API and Github Actions (modified from This Project). I'm trying to list different topics about TQFT separately, a list of keywords will be given later. I also strongly recommend that you check out Delcamp's ArXiv Digest for TQFT, which is another great resource for staying up-to-date with the latest research in this field.
: Automatically collecting arXiv papers in quantum information theory.
Latest news
2025/09/19 | Our paper "Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory" is now published on Journal of High Energy Physics. This is a collaborative work with Qiang Jia.
2025/08/11 | I will be a teaching assistant for "PC5228: Quantum Information and Computation" this semester. The instructor is Dagomir Kaszlikowski. Some useful (but non-official) materials will be posted on this link.
2025/08/06 | Our paper titled "Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems" is now published on Physical Review B. This is a collaborative work with Lu Wei, Yufeng Wang, Dagomir Kaszlikowski, Haibin Ling.
2025/08/04 | My paper titled "Quantum Cluster State Spin Chain with Ising Fusion Category Symmetry: A Perspective from Weak Hopf SymTFT" is now available on arXiv: [arXiv:2508.02424].
2025/07/02 | Our paper titled "Weak Hopf tube algebra for domain walls between 2d gapped phases of Turaev-Viro TQFTs" is now available on arXiv: [arXiv:2507.01515]. This is a collaborative work with Sheng Tan.
2025/06/13 | Our old preprint （2018） is now made published on Entropy： "An efficient algorithmic way to construct Boltzmann machine representations for arbitrary stabilizer code". This is a collaborative work with Yuan-Hang Zhang, Yu-Chun Wu and Guang-Can Guo.
2025/05/28 | Our paper titled "Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory" is now available on arXiv: [arXiv:2505.22261]. This is a collaborative work with Qiang Jia.
2025/02/28 | Our paper titled "Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems" is now available on arXiv: [arXiv:2502.20723]. This is a collaborative work with Lu Wei, Yufeng Wang, Dagomir Kaszlikowski, Haibin Ling.
2024/12/27 | My paper titled "Quantum Cluster State Model with Haagerup Fusion Category Symmetry" is now available on arXiv: [arXiv:2412.19657].
2024/12/19 | My paper titled "Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory" is now available on arXiv: [arXiv:2412.15336].
...
2024/09/27 | Our paper, titled "Shedding Light on the Future: Exploring Quantum Neural Networks through Optics," is now published on Advanced Quantum Technologies. [arXiv: 2409.02533] This is a collaborative work with Shang Yu, Aonan Zhang, Ewan Mer, Zhenghao Li, Valerio Crescimanna, Kuan-Cheng Chen, Raj B. Patel, Ian A. Walmsley, and Dagomir Kaszlikowski.
2024/09/20 | The paper titled "Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation" is now published on Journal of High Energy Physics, here is the link.
2024/09/06 | The paper titled "Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation" is now accepted for publication in Journal of High Energy Physics.
2024/09/04 | Our paper titled "Shedding Light on the Future: Exploring Quantum Neural Networks through Optics" is now available on arXiv [arXiv: 2409.02533], collaborative work with Shang Yu, Aonan Zhang, Ewan Mer, Zhenghao Li, Valerio Crescimanna, Kuan-Cheng Chen, Raj B. Patel, Ian A. Walmsley, and Dagomir Kaszlikowski.
2024/08/04 | Our paper titled "The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes" is now published on Advanced Quantum Technologies, collaborative work with Dagomir Kaszlikowski
2024/08/01 | I will be a teaching assistant for "PC5228: Quantum Information and Computation" this semester. The instructor is Dagomir Kaszlikowski. Some useful materials will be posted on this link.
2024/07/25 | The preprint titled "The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes" is now accepted for publication on Advanced Quantum Technologies, [arXiv:2305.15649], a collaborative work with Dagomir Kaszlikowski.
2024/07/17 | Our paper titled "Antilinear superoperator, quantum geometric invariance, and antilinear symmetry for higher-dimensional quantum systems" is now accepted for publication on Quantum Information Processing,
collaborative work with Lu Wei, Dagomir Kaszlikowski and Sheng Tan, [arXiv: 2202.10989].
2024/06/18 | The paper titled "Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model" is now accepted for publication on Journal of High Energy Physics,
collaborative work with Dagomir Kaszlikowski and Sheng Tan, [arXiv: 2403.04446].
2024/05/16 | The paper titled "Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation" is now is now available on arXiv [arXiv:2405.09277].
2024/03/13 | The paper titled "Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states" is now published on New journal of physics,a collaborative work with Xiangjing Liu, Yixian Qiu, Fei Li, and Oscar Dahlsten.
2024/03/08 | The paper titled "Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model" is now available on arxiv, collaborative work with Sheng Tan,
Dagomir Kaszlikowski.
Orcid: 0000-0001-8588-173X
Inspire HEP: Zhian Jia
Arxiv: link
Physics Stack Exchange: link
Twitter X: Zhian Jia
