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Complexity phase diagram for interacting and long-range bosonic Hamiltonians

Maskara, Nishad and Deshpande, Abhinav and Tran, Minh C. and Ehrenberg, Adam and Fefferman, Bill and Gorshkov, Alexey V. (2019) Complexity phase diagram for interacting and long-range bosonic Hamiltonians. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200103-095429282

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Abstract

Recent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity theory aims to classify computational problems based on how the time required to solve the problem scales as the problem size becomes large. In this work, we use insights from complexity theory to classify phases in interacting many-body systems. Specifically, we demonstrate a "complexity phase diagram" for the Bose-Hubbard model with long-range hopping. This shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality. We find that classification of complexity phases is closely related to upper bounds on the spread of quantum correlations, and protocols to transfer quantum information in a controlled manner. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1906.04178arXivDiscussion Paper
Additional Information:We thank Michael Foss-Feig, James Garrison, and Rex Lundgren for helpful discussions and to the authors of Ref. [26] for sharing their results with us. N. M., A. D., M. C. T., A. E., and A. V. G. acknowledge funding from the NSF Ideas Lab on Quantum Computing, DoE BES Materials and Chemical Sciences Research for Quantum Information Science program, DoE ASCR Quantum Testbed Pathfinder program, NSF PFC at JQI, ARO MURI, ARL CDQI, and AFOSR. M. C. T. also acknowledges support under the NSF Grant No. PHY-1748958 and from the Heising-Simons Foundation. N. M. also acknowledges funding from the Caltech SURF program. A. E. also acknowledges funding from the DoD. B. F. is funded in part by AFOSR YIP No. FA9550-18-1-0148 as well as ARO Grants No. W911NF-12-1-0541 and No. W911NF-17-1-0025, and NSF Grant No. CCF-1410022.
Funders:
Funding AgencyGrant Number
NSFPHY-1748958
Department of Energy (DOE)UNSPECIFIED
Army Research Office (ARO)W911NF-12-1-0541
Army Research LaboratoryUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0148
Heising-Simons FoundationUNSPECIFIED
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Department of DefenseUNSPECIFIED
Army Research Office (ARO)W911NF-17-1-0025
NSFCCF-1410022
Record Number:CaltechAUTHORS:20200103-095429282
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200103-095429282
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100490
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Jan 2020 03:52
Last Modified:05 Jan 2020 03:52

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