Practical limits of DMRG/MPS bond dimension for simulating random-geometry circuits

Ascertain the practical upper limits of matrix-product-state bond dimension achievable by DMRG implementations for simulating N = 56 random-geometry circuits at depths 10–20 with error-per-gate ε ≈ 3.2 × 10^−3, and quantify the classical resources required to reach these fidelities.

Background

The authors evaluate approximate tensor-network simulation using DMRG/MPS for random-geometry circuits and find that the required bond dimensions grow rapidly, with extrapolations indicating that near-maximal bond dimensions may be needed by depth 20 to match experimental fidelities. They discuss current state-of-the-art bond dimensions and associated computational costs.

They explicitly note uncertainty about how far bond dimensions can be pushed in practice for these circuits, motivating a concrete question about achievable limits and resources.