2020 Fiscal Year Annual Research Report
Entanglement Detection and Characterization of Topological States
| Project/Area Number |
19F19326
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| Research Institution | Institute of Physical and Chemical Research |
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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)
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| 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
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| Project Period (FY) |
2019-11-08 – 2022-03-31
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| Keywords | quantum simulator / superconducting / phase transition / non-Markovian / multichannels in diamond / information backflow |
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| Outline of Annual Research Achievements |
In our recent theoretical manuscript in preparation, we investigated multipartite entanglement (ME) of the topologically ordered state in the toric code (TCM). ME can characterize the topological phases (TPs) in the 2D TCM with external fields. With spin operators by the dual transformation, the quantum Fisher information (QFI) density of the ground state is written in terms of the reduced Wilson loops, whose scaling behavior signals the TPs. We observed thermalization and localization of ME of the topological state. In arXiv:2102.03046, we showed that dynamical localization makes the time evolution local, keeping topological order robust after a quantum quench. Our results will be helpful for further investigations on the robust TPs against external disturbance and topological-protected quantum computation. We also collaborated with experimental groups, working on different platforms. In Sci. Adv. (2020), we used ME to detect dynamical phase transitions in the system, consisting of 16 superconducting (SC) qubits. In PRL (2020), we demonstrated the engineering of multiple dissipative channels by controlling the adjacent nuclear spins of a NV center. With controllable non-Markovian dynamics of the open system, we observed that the QFI flows to and from the environment using multiple noisy channels. In arXiv:2103.11434, using a 19-qubit SC processor, we reported the characterization of multiparticle entangled states generated during its nonlinear dynamics.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
In our theoretical manuscript, we investigated on the topic of the first aim of our proposal. We studied topological phase transitions in the toric code model and demonstrated that topological order can be characterized by multipartite entanglement (ME) defined in the dual space. Our results also conformed to other approaches, when predicting that the topological order is very fragile to a quenched transverse field. We studied ME of the quenched states to demonstrate the dynamical localization of topological order. A series of our works applying ME, instead of bipartite entanglement, to study topological states, as a successful signature of topological states and topological phase transitions, will be of great help for understanding topology in condensed matter physics. In addition, ME can be much easier to realize with current experimental parameters, compared to bipartite entanglement requiring for state tomography. Recently, we have successfully collaborated with several experimental groups with different platforms. In diamond, we observed the non-Markovian dynamics of open systems via the backflow of quantum Fisher information (FI). Using superconducting qubits, we observed the dynamical phase transitions via ME witnessed by spin squeezing. We also measured the nonlinear squeezing parameter and achieved a large metrological gain via extracting the FI. With these results taken into consideration, we thus conclude that our research progresses as planned.
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| Strategy for Future Research Activity |
After completing the theoretical manuscript, we will work on the second topic (ii). Our former works focus on the exactly solvable models, and there is growing interest in the effects of the interaction in many-body systems. We plan to apply numerical methods to study the multipartite entanglement (ME) of topological phases in the interacting systems. At first, we plan to study the topological phases in the interacting Kitaev chain, which can only be exactly solved at few symmetric points. We also would like to investigate ME of topological states in other systems, e.g., Abelian and non-Abelian fractional quantum Hall states in 2D lattices. Then, we would like to investigate the third topic (iii). In details, we would like to investigate the 1D tight-binding non-Hermitian SSH model, and study the non-Hermitian super lattice SSH model using tensor network based numerical methods. In addition, we would like to apply ME to investigate the topological phase transitions in the non-Hermitian second-order topological insulators and superconductors. In addition, we also would like to investigate other topics, such as quantum information scrambling, many-body localization versus thermalization, and multi-parameter quantum metrology, which all have close relationships with ME. We also have further plans and proposals to collaborate with several experimental group, e.g., multi-parameter quantum phase estimation, Thouless pumping, and quantum thermalization.
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[Journal Article] Probing the dynamical phase transition with a superconducting quantum simulator,2020
Author(s)
Kai Xu, Zheng-Hang Sun, Wuxin Liu, Yu-Ran Zhang, Hekang Li, Hang Dong, Wenhui Ren, Pengfei Zhang, Franco Nori, Dongning Zheng, Heng Fan, and H. Wang
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Journal Title
Science Advances
Volume: Vol. 6, no. 25
Pages: 4935-1～6
DOI
Peer Reviewed / Int'l Joint Research
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