Accelerating two-dimensional tensor network optimization by preconditioning

TL;DR

This paper introduces a preconditioning method to accelerate gradient-based optimization of tensor networks, significantly reducing computational costs and improving convergence in quantum many-body simulations.

Contribution

We develop an efficient preconditioner for iPEPS optimization that enhances convergence speed and computational efficiency across various models and contraction schemes.

Findings

Substantial reduction in optimization steps needed

Improved efficiency in Heisenberg and Kitaev models

Broad applicability to different tensor network setups

Abstract

We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of evaluating energies and gradients, and an ill-conditioned optimization landscape that slows convergence. To reduce the number of optimization steps, we introduce an efficient preconditioner derived from the leading term of the metric tensor. We benchmark our method against standard optimization techniques on the Heisenberg and Kitaev models, demonstrating substantial improvements in overall computational efficiency. Our approach is broadly applicable across various contraction schemes, unit cell sizes, and Hamiltonians, highlighting the potential of preconditioned optimization to advance tensor network algorithms for strongly correlated systems.