Complexity phase diagram for interacting and long-range bosonic Hamiltonians
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.
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.Attached Files
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Additional details
- Eprint ID
- 100490
- Resolver ID
- CaltechAUTHORS:20200103-095429282
- NSF
- PHY-1748958
- Department of Energy (DOE)
- Army Research Office (ARO)
- W911NF-12-1-0541
- Army Research Laboratory
- Air Force Office of Scientific Research (AFOSR)
- FA9550-18-1-0148
- Heising-Simons Foundation
- Caltech Summer Undergraduate Research Fellowship (SURF)
- Department of Defense
- Army Research Office (ARO)
- W911NF-17-1-0025
- NSF
- CCF-1410022
- Created
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2020-01-05Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field