Complexity Phase Diagram for Interacting and Long-Range Bosonic Hamiltonians

Nishad Maskara, Abhinav Deshpande, Adam Ehrenberg, Minh C. Tran, Bill Fefferman, and Alexey V. Gorshkov

Phys. Rev. Lett. 129, 150604 – Published 7 October 2022

Abstract

We classify phases of a bosonic lattice model based on the computational complexity of classically simulating the system. We show that the system transitions from being classically simulable to classically hard to simulate as it evolves in time, extending previous results to include on-site number-conserving interactions and long-range hopping. Specifically, we construct a complexity phase diagram with easy and hard “phases” and derive analytic bounds on the location of the phase boundary with respect to the evolution time and the degree of locality. We find that the location of the phase transition is intimately related to upper bounds on the spread of quantum correlations and protocols to transfer quantum information. Remarkably, although the location of the transition point is unchanged by on-site interactions, the nature of the transition point does change. Specifically, we find that there are two kinds of transitions, sharp and coarse, broadly corresponding to interacting and noninteracting bosons, respectively. Our Letter motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.

Received 15 June 2019
Revised 18 May 2022
Accepted 12 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.150604

Physics Subject Headings (PhySH)

Boson sampling Cold gases in optical lattices Computational complexity Quantum algorithms Quantum protocols Quantum simulation

Bose-Hubbard model Many-body techniques

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Nishad Maskara^1,2,*, Abhinav Deshpande ^2,3,4,*, Adam Ehrenberg^2,3, Minh C. Tran^2,3,5, Bill Fefferman^2,6,7, and Alexey V. Gorshkov^2,3

¹Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
²Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
³Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
⁴Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
⁵Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
⁶Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA
⁷Department of Computer Science, University of Chicago, Chicago, Illinois 60637, USA