Variational Neural Annealing

Abstract

Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for groundstate solutions of a target Hamiltonian. While powerful, simulated annealing is known to have prohibitively slow sampling dynamics when the optimization landscape is rough or glassy. Here we show that by generalizing the target distribution with a parameterized model, an analogous annealing framework based on the variational principle can be used to search for groundstate solutions. Modern autoregressive models such as recurrent neural networks provide ideal parameterizations since they can be exactly sampled without slow dynamics even when the model encodes a rough landscape. We implement this procedure in the classical and quantum settings on several prototypical spin glass Hamiltonians, and find that it significantly outperforms traditional simulated annealing in the asymptotic limit, illustrating the potential power of this yet unexplored route to optimization.

19 pages, 9 figures, 1 table

References in corpus (7)

• A class of quantum many-body states that can be efficiently simulated
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Dilated Recurrent Neural Networks
• Optimal Control of Majorana Zero Modes
• Cooling dynamics of pure and random Ising chains
• Classical Quantum Optimization with Neural Network Quantum States
• The deep learning and statistical physics applications to the problems of combinatorial optimization

Cited by in corpus (11)

• Combinatorial Optimization with Physics-Inspired Graph Neural Networks
• Classical variational simulation of the Quantum Approximate Optimization Algorithm
• From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
• Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems
• A Bayesian generative neural network framework for epidemic inference problems
• Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization
• Supplementing Recurrent Neural Networks with Annealing to Solve Combinatorial Optimization Problems
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
• Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning
• Exploring explicit coarse-grained structure in artificial neural networks
• Adiabatic quantum computing with parameterized quantum circuits