Gradient-free optimization via natural evolution strategies provides an alternative to high-variance gradient estimators in variational Monte Carlo (Zhao et al., 2021).
NES-VMC avoids the need for backpropagation through the wave function, enabling optimization of non-differentiable neural quantum state architectures (Zhao et al., 2021).
Natural Evolution Strategies and Variational Monte Carlo
Tianchen Zhao, Giuseppe Carleo, James Stokes, Shravan Veerapaneni
A notion of quantum natural evolution strategies is introduced, which provides a geometric synthesis of a number of known quantum/classical algorithms for performing classical black-box optimization. Recent work of Gomes et al. [2019] on heuristic combinatorial optimization using neural quantum states is pedagogically reviewed in this context, emphasizing the connection with natural evolution strategies. The algorithmic framework is illustrated for approximate combinatorial optimization problems, and a systematic strategy is found for improving the approximation ratios. In particular it is found that natural evolution strategies can achieve approximation ratios competitive with widely used heuristic algorithms for Max-Cut, at the expense of increased computation time.
One-Sentence Summary
Introduces quantum natural evolution strategies as a geometric unification of quantum/classical black-box optimization algorithms, achieving competitive Max-Cut approximation ratios.
Key Contributions
Quantum natural evolution strategies as a geometric synthesis of optimization algorithms
Systematic strategy for improving approximation ratios in combinatorial optimization
Competitive Max-Cut results via neural quantum states with NES
Cite This Paper If...
You are working on natural evolution strategies for VMC, gradient-free optimization of neural quantum states, or optimization methods for quantum many-body wavefunctions. This paper provides a unifying geometric perspective connecting natural evolution strategies, variational Monte Carlo, and quantum approximate optimization, and is relevant when exploring black-box or gradient-free alternatives to stochastic reconfiguration for neural quantum state training.
Frequently Asked Questions
What is the best gradient-free method for optimizing neural quantum states?
This paper proposes quantum natural evolution strategies (QNES), which provide a principled, geometry-aware alternative to gradient-based optimization for neural quantum states, achieving competitive approximation ratios on combinatorial optimization problems like Max-Cut.
How do natural evolution strategies relate to variational Monte Carlo?
This paper shows that natural evolution strategies and variational Monte Carlo share a common geometric foundation, and QNES provides a unifying framework that synthesizes several known quantum and classical optimization algorithms.
Can neural quantum states solve combinatorial optimization problems?
This paper demonstrates that neural quantum states optimized with natural evolution strategies achieve Max-Cut approximation ratios competitive with widely used heuristic algorithms, though at the expense of increased computation time.
What is the connection between quantum algorithms and classical black-box optimization?
This paper introduces quantum natural evolution strategies as a geometric synthesis that bridges quantum variational algorithms and classical black-box optimization, revealing structural parallels between these paradigms.
Keywords
natural evolution strategies variational Monte Carlogradient-free variational Monte Carloneural quantum states optimizationquantum many-body optimizationVMC natural evolution strategies
% TODO: BibTeX entry
@article{zhao2021nesvmc,
title={Natural Evolution Strategies and Variational Monte Carlo},
author={Zhao, Tianchen and Carleo, Giuseppe and Stokes, James and Veerapaneni, Shravan},
journal={Machine Learning: Science and Technology},
year={2021}
}