Zhian Jia | 贾治安

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My primary research focus is in mathematical physics and theoretical physics. I am particularly interested in topological field theory, topological order, generalized symmetry for quantum field theory and lattice model, topological quantum computation, quantum information theory, quantum computation theory, quantum algebras (especially tensor category, Hopf algebras and related topics), and the operator algebraic approach to QFT. For more details, please see my Research page.
$$ \operatorname{Hopf}: \mu\circ (\operatorname{id}\otimes S) \circ \Delta = \eta\circ \varepsilon = \mu \circ (S\otimes \operatorname{id}) \circ \Delta$$ $$\operatorname{Bulk-Boundary}: \mathsf{Bulk} \simeq Z(\mathsf{Boundary}) $$ $$\operatorname{TQFT}: \mathsf{Cob}_{d+1} \to \mathsf{Hilb} $$ $$\operatorname{QECC}: \mathsf{R}\circ \mathsf{E}(\varrho) \propto \varrho $$ $$\text{index}(D) = \int_{{T^*}M} \text{Ch} (\psi(\sigma_H(D))) \wedge \text{Td}(M)$$ In addition to my work in mathematics and physics, I enjoy reading books—two of my favorites are "One Hundred Years of Solitude" and "On the Road"—as well as traveling and writing. Check this link for my 2024 reading list. I am also active on several platforms where I engage in popular science communication. I enjoy discussing interesting topics with people, so feel free to reach out to me via email.

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Valuable Resources

  • TQFT : This page will collect some useful information about TQFT, topological order, topological quantum computation, etc.
  • TQFT ArXiv Daily : 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.
  • Quantum Information Arxiv Daily : details coming soon.

  • Work with me

  • For quantum information: My primary focus is on theoretical quantum information and quantum computation. If you have a solid background in quantum information theory, please feel free to email me. Some keywords of my recent interests are: temporal quantum process, quantum stochastic process, quantum chaos, quantum error-correction, topological code, Floquet code, quantum machine learning, neural network state, Bell nonlocality and Kochen-Specker non-contextuality, etc.
  • For mathematical physics or TQFT, topological order and non-invertible symmetry: A strong foundation in mathematics and quantum field theory is essential, ideally including familiarity with tensor categories and Hopf algebras. If you have a keen interest in mathematics, feel free to reach out to me.

  • Latest news

  • 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.
  • 2024/09/14 | Our paper, titled "Shedding Light on the Future: Exploring Quantum Neural Networks through Optics," has been accepted for publication 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.
  • 2024/09/06 | 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.
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  • 2024/07/29 | Our paper titled "Antilinear superoperator, quantum geometric invariance, and antilinear symmetry for higher-dimensional quantum systems" is now published on Quantum Information Processing, collaborative work with Lu Wei, Dagomir Kaszlikowski and Sheng Tan, [arXiv: 2202.10989].
  • 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.
  • 2024/07/23 | The paper "Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model " is now published on Journal of High Energy Physics, collaborative work with Dagomir Kaszlikowski and Sheng Tan, [arXiv: 2403.04446].
  • 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].
  • 2024/06/10 | The paper titled "Electric-magnetic duality and Z2 symmetry enriched Abelian lattice gauge theory" is now published on Journal of Physics A: Mathematical and Theoretical, collaborative work with Dagomir Kaszlikowski and Sheng Tan, [arXiv:2201.12361].
  • 2024/05/25 | The preprint titled "Electric-magnetic duality and Z2 symmetry enriched Abelian lattice gauge theory" is now accepted for publication on Journal of Physics A: Mathematical and Theoretical, collaborative work with Dagomir Kaszlikowski and Sheng Tan, [arXiv:2201.12361].
  • 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, 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.
  • 2023/12/21 | The paper titled "Quantum space-time marginal problem: global causal structure from local causal information " is now published on New Journal of physics, collaborative work with Minjeong Song, and Dagomir Kaszlikowski.
  • 2023/12/08 | The preprint titled "Quantum space-time marginal problem: global causal structure from local causal information " is now accepted for publication on New Journal of physics, collaborative work with Minjeong Song, and Dagomir Kaszlikowski.
  • 2023/10/30 | My friends and I are currently organizing a reading seminar focused on mathematical physics. The seminar will delve into three key topics: (i) Spin Systems on Infinite Lattices; (ii) Aspects of Quantum Field Theory; and (iii) Atiyah-Singer Index Theorem.
  • 2023/07/21 | The paper titled "Boundary and domain wall theories of 2d generalized quantum double model" is now published online: JHEP07(2023)160, collaborative work with Dagomir Kaszlikowski, and Sheng Tan.
  • 2023/07/19 | The paper titled "On weak Hopf symmetry and weak Hopf quantum double model" is now published online: Commun. Math. Phys. 402, 3045–3107 (2023), collaborative work with Sheng Tan, Dagomir Kaszlikowski and Liang Chang.
  • 2023/06/12 | The preprint titled "Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states" is now accessible online: [arXiv:2306.05958], a collaborative work with Xiangjing Liu, Yixian Qiu, Fei Li, Oscar Dahlsten.
  • 2023/05/26 | The preprint titled "The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes " is now accessible online: [arXiv:2305.15649], a collaborative work with Dagomir Kaszlikowski.
  • 2023/03/27 | The TQFT ArXiv Daily and Quantum Information Arxiv Daily are created.
  • 2023/03/24 | The preprint "Quantum space-time marginal problem: global causal structure from local causal information " is now available online: [arXiv:2303.12819], collaborative work with Minjeong Song, and Dagomir Kaszlikowski.
  • 2023/02/16 | The preprint "On weak Hopf symmetry and weak Hopf quantum double model" is now available online: [arXiv:2302.08131], collaborative work with Sheng Tan, Dagomir Kaszlikowski and Liang Chang.
  • 2022/12/20 | I am now serving as a guest editor of special issue Quantum Computation & Simulation of the journal "INTELLIGENT COMPUTING".
  • 2022/08/16 | "Quantum simulation of indefinite causal order induced quantum refrigeration" is now published online: Phys. Rev. Research 4, L032029(2022), collaborative work with Huan Cao et al.
  • 2022/07/11 | "Boundary and domain wall theories of 2d generalized quantum double model" is now available on arxiv: [arXiv:2207.03970]
  • 2022/06/06 | The reading seminar on measurement-based quantum computation is now lauched: Reading seminar: Measurement-based quantum computation.
  • 2022/02/22 | “Antilinear superoperator and quantum geometric invariance for higher-dimensional quantum systems” is now available on arXiv: [arXiv:2202.10989].
  • 2022/01/28 | “Electric-magnetic duality of Z2 symmetry enriched cyclic Abelian lattice gauge theory” is now available on arXiv: [arXiv:2201.12361].
  • I have moved to CQT, NUS, Singapore.
  • Time isn't the main thing, it's the only thing.