Accelerating two-dimensional tensor network optimization by preconditioning
arXiv:2511.09546 · doi:10.1103/h396-yc28
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.
9 pages,4 figures
References in corpus (26)
- Time-dependent variational principle for quantum lattices
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Accurate determination of tensor network state of quantum lattice models in two dimensions
- Quantum Natural Gradient
- Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
- Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
- Variational optimization algorithms for uniform matrix product states
- Differentiable Programming Tensor Networks
- Variational optimization with infinite projected entangled-pair states
- The iPEPS algorithm, improved: fast full update and gauge fixing
- Gradient methods for variational optimization of projected entangled-pair states
- Tangent-space methods for uniform matrix product states
- Faster Methods for Contracting Infinite 2D Tensor Networks
- Excitations and the tangent space of projected entangled-pair states
- Simulating excitation spectra with projected entangled-pair states
- Riemannian optimization of isometric tensor networks
- Excitations with projected entangled pair states using the corner transfer matrix method
- Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
- Automatic differentiation applied to excitations with Projected Entangled Pair States
- Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
- An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
- Stable and efficient differentiation of tensor network algorithms
- Differentiable programming tensor networks for Kitaev magnets
- Matrix product state fixed points of non-Hermitian transfer matrices
- Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
- Kac-Moody symmetries in one-dimensional bosonic systems