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Global optimization of spin Hamiltonians with gain-dissipative systems
Kirill P Kalinin1, Natalia G Berloff2,3
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, United Kingdom.
Scientific Reports
|December 14, 2018
Summary
Researchers developed new gain-dissipative algorithms for solving complex optimization problems, inspired by quantum and classical spin simulators. These algorithms show potential for outperforming classical computers in specific large-scale computations.
Area of Science:
- Quantum Physics and Computation
- Computational Complexity and Optimization
- Condensed Matter Physics
Background:
- Analog simulators based on gain-dissipative systems have shown promise for finding global minima of spin Hamiltonians (e.g., Ising and XY models).
- Dynamical adjustment of gain and coupling strengths is a critical feedback mechanism in these analog simulators.
- These systems offer a platform for studying spin system properties and benchmarking physical simulator performance.
Purpose of the Study:
- To develop a novel class of gain-dissipative algorithms for global optimization of NP-hard problems.
- To compare the performance of these new algorithms against classical global optimization techniques.
- To explore the potential of analog simulators for accelerating computations relevant to spin systems and optimization.
Main Methods:
- Development of gain-dissipative algorithms inspired by the operational principles of analog spin simulators.
- Theoretical analysis and numerical estimations of the proposed algorithms' performance.
- Comparative performance evaluation against established classical global optimization algorithms.
Main Results:
- The novel gain-dissipative algorithms demonstrate a viable approach for global optimization of complex problems.
- Theoretical and numerical results indicate potential for significant speedups over classical methods for large problem instances.
- Analog simulators, when realized, are projected to outperform classical computations by several orders of magnitude under specific operational assumptions.
Conclusions:
- Gain-dissipative algorithms offer a promising new avenue for tackling NP-hard optimization problems.
- Analog simulators based on these principles could provide substantial computational advantages for specific scientific and computational challenges.
- The developed algorithms and theoretical framework serve as a benchmark for future physical implementations of gain-dissipative simulators.
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