2019 Fiscal Year Annual Research Report
Entanglement Detection and Characterization of Topological States
| Project/Area Number |
19F19326
|
|---|
| Research Institution | Institute of Physical and Chemical Research |
|---|
Principal Investigator |
NORI FRANCO 国立研究開発法人理化学研究所, 開拓研究本部, 主任研究員 (50415262)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ZHANG YU-RAN 国立研究開発法人理化学研究所, 開拓研究本部, 外国人特別研究員
|
|---|
| Project Period (FY) |
2019-11-08 – 2022-03-31
|
| Keywords | Multipartite / entanglement / quantum Fisher / non-Markovianity / non-Hermitian / topological phases / quantum walks / dynamical phase transitions |
|---|
| Outline of Annual Research Achievements |
Theoretical studies: We demonstrate that multipartite entanglement, witnessed by quantum Fisher information, can characterize the quantum topological phase transition in the spin-1/2 toric code model on a square lattice with external fields. We investigated second-order topological (SOT) phases in non-Hermitian systems and show that a 2D non-Hermitian SOT insulators can host zero-energy modes at its corners. We also investigate two classes of non-Hermitian systems: one from a Lorentz-symmetry violation and the other from a complex mass with Lorentz invariance. We proposed a measure of non-Markovianity for open quantum processes via skew information under incoherent completely positive and trace-preserving maps. Experimental collaborations: We experimentally studied quantum walks of one and two strongly correlated microwave photons in a 1D array of 12 superconducting (SC) qubits with short-range interactions and demonstrate the dynamics of single- and double-excitation states on a Bose-Hubbard ladder with 20 qubits on a 24-qubit SC processor. We experimentally investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field using 16 all-to-all connected SC qubits. We experimentally demonstrate the engineering of multiple dissipative channels by controlling the adjacent nuclear spins of a nitrogen-vacancy center in diamond and observe the quantum Fisher information flowing to and from the environment through different channels.
|
| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
We have completed early topics in our proposal and are preparing the manuscripts. Some of our works have been successfully published. Meanwhile, our collaborations with experimental groups are very smooth and several manuscripts have been posted online and submitted to scientific journals.
|
| Strategy for Future Research Activity |
We plan to use the density matrix renormalization group and matrix product states to study the multipartite entanglement of topological ordered phases in interacting many-body systems. We will numerically study the multipartite entanglement of SPT phases in the interacting Kitaev chain. We also plan to numerically investigate the multipartite entanglement of Abelian and non-Abelian fractional quantum Hall states in 2D lattices, whose ground-state degeneracy increases with the number of defects. In addition, when searching for the appropriate generators for quantum Fisher information (QFI) is a complicated task, we will try to introduce the machine learning and neural network methods to solve the problem. We plan to investigate the nature of anomalous non-Hermitian topological phenomena using multipartite entanglement. We will firstly consider the 1D tight-binding non-Hermitian SSH model with a chiral symmetry, and then study the non-Hermitian super lattice SSH model using advanced numerical methods. In addition to the first order case, we also plan to use multipartite entanglement for the investigation of the non-Hermicity of second-topological insulators. We plan to investigate the multipartite entanglement of topological states in quenched and localized systems. The topological order or SPT order would collapse when the system quenches with an external field and would stay localized with disorders, which could be well described by the multipartite entanglement witnessed by QFI.
|
Research Products
(1 results)
