Spin-glass droplets learning and approximate optimization with tensor networks
Year: 2018
Type: preprint
Abstract: We devise a deterministic heuristic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent Gibbs distribution of all possible configurations. Employing approximate tensor-network contractions we are able to efficiently map the low-energy spectrum of some quasi-two-dimensional Hamiltonians. We exploit the local nature of the problems to compute spin-glass droplets geometries, which provides a new form of compression of the low-energy spectrum. It naturally encompasses sampling, which otherwise, for exact contraction, is $\#P$ hard in general. In particular, for the hardest known problems devised on Chimera graphs known as Deceptive Cluster Loops and for up to $2048$ spins, we find of the order of $10^{10}$ degenerate ground states in a single run of our algorithm, computing better solutions than have been reported on some of the hard instances. Our gradient-free approach could provide new insight into the structure of disordered spin-glass complexes, with ramifications both for machine learning and noisy intermediate-scale quantum devices.
Source: arXiv (Cornell University)
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3034513873