Theoretical Physics

Zhian Jia | 贾治安

Research

I am currently a Research Fellow at Centre for Quantum Technologies, National University of Singapore.

My researh focused on the mathematical physics and theoretical physics, including TQFT and topological order, generalized symmetry, quantum information theory, quantum computation theory, quantum machine learning, etc.

Main Research Topics

A list of my current research directions.

Topological Order, TQFT and Related Mathematical Physics

Generalized symmetry, Quantum double model, Levin-Wen string-net model, Chern-Simons theory, Quantum Hall effect, SPT and SET phases, etc.

Coming soon...
Open System Topological Phase

Open system dynamics (with non-Hermitian Hamiltonians as a special case), symmetry of Lindbladians, mixed-state long-range entanglement, mixed-state TQFT, etc.

Coming soon...
Spatial and Temporol Quantum Correlations

Bell-Kochen-Specker theorem, entanglement, quantum steering, Leggett-Garg inequality, pseudo-density operator, quantum process matrix, quantum causality, uncertainty relation, etc.

Coming soon...
Tensor Network & Neural Network

Efficient methods for simulating complex many-body quantum systems, quantum neural network states, neural network density operator, etc.

Coming soon...
Quantum Machine Learning

Various quantum neural networks, the no free lunch theorem, trainability, etc.

Coming soon...

Keywords of Research

Physics and Mathematics

The following are some keyworkds of my research in physics and mathematics:

Research Interests

My research focuses on quantum information and quantum computation, topological order and TQFT, quantum topology and algebra, etc.

TQFT, CFT, tensor categories, Hopf algebras, weak Hopf algebras, quasi-Hopf algebras, Frobenius algebras.

Topological order, SPT, SET, mixed-state topological phases.

Generalized symmetry, non-invertible symmetry, higher-form symmetry, subsystem symmetry.

Topological quantum error-correcting codes, homological codes, topological quantum computation.

Space-time states, pseudo-density operators, superdensity operators, doubled density operators.

Quantum causality, process matrices, quantum Bayesian inference, quantum retrodiction.

Quantum correlations: quantum discord, quantum entanglement, quantum steering, Bell nonlocality, quantum contextuality.

Research Interests

Mathematical Physics
Topological Order & TQFT
Quantum Field Theory
Quantum Topology & Algebra
Tensor Categories & Hopf Algebras
Quantum Information Theory
Quantum Foundations
Quantum Computation Theory
Quantum Phases of Matter
Tensor Networks & Neural Network States
Quantum Machine Learning

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Theoretical Physics

Research

Main Research Topics

Topological Order, TQFT and Related Mathematical Physics

Open System Topological Phase

Spatial and Temporol Quantum Correlations

Tensor Network & Neural Network

Quantum Machine Learning

Keywords of Research

Research Interests

Research Interests

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.