Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
Thomas Barthel, Qiang Miao · Physical review. B./Physical review. B · 2025
Strongly correlated quantum matter, such as the insufficiently understood high- temperature superconductors, are difficult to simulate numerically. The multiscale entanglement renormalization ansatz (MERA) is a hierarchical class of tensor networks that efficiently captures the typical ground-state entanglement structures. Motivated by recent advances to employ MERA in quantum-classical algorithms, the authors take a fresh look here, analyzing new variations of the approach including tensor Trotterization and importance sampling. Optimal contraction sequences and algorithmic phase diagrams show that these quantum-inspired methods can substantially reduce computational costs.