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Complexity Phase Diagram for Interacting and Long-Range Bosonic Hamiltonians
Nishad Maskara1,2, Abhinav Deshpande2,3,4, Adam Ehrenberg2,3
1Department of Physics, California Institute of Technology, Pasadena, California 91125, USA.
Physical Review Letters
|October 21, 2022
Summary
This study reveals that bosonic lattice models transition from easily simulated to computationally hard as they evolve. This complexity shift is linked to quantum correlations and depends on interactions and hopping, defining distinct simulation phases.
Area of Science:
- Quantum Many-Body Physics
- Computational Complexity Theory
- Condensed Matter Physics
Background:
- Classically simulating quantum many-body systems is a major challenge.
- Understanding the computational complexity of quantum systems is crucial for theoretical and experimental advancements.
- Previous studies focused on specific types of interactions and hopping in bosonic models.
Purpose of the Study:
- To classify phases of a bosonic lattice model based on computational complexity.
- To investigate how time evolution affects the simulability of these systems.
- To extend existing complexity phase diagrams to include number-conserving on-site interactions and long-range hopping.
Main Methods:
- Constructing a complexity phase diagram distinguishing classically simulable ('easy') and hard-to-simulate ('hard') phases.
- Deriving analytic bounds for the phase boundary based on evolution time and interaction locality.
- Analyzing the impact of on-site interactions and long-range hopping on computational complexity.
Main Results:
- The system transitions from classically simulable to classically hard as it evolves in time.
- The phase transition location is related to bounds on quantum correlation spread and information transfer protocols.
- On-site interactions do not alter the transition point's location but change its nature, leading to sharp (interacting) and coarse (noninteracting) transitions.
Conclusions:
- Computational complexity provides a framework for classifying phases in bosonic lattice models.
- The interplay between quantum correlations, information transfer, and system evolution dictates the transition to computational hardness.
- This work establishes a foundation for exploring complexity-driven phenomena in many-body quantum systems.
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