Reduced scaling variational tensor network algorithm inspired by quantum information tools

Classical shadow techniques have been widely applied in quantum information science as efficient post-processing protocols for extracting observables from measurement outcomes on quantum hardware. In this work, we transfer their power to classical computation by interpreting a classical tensor-network ansatz as a quantum state that can be "measured'' through Monte Carlo sampling. This perspective enables a classical-shadow-enhanced variational tensor-network algorithm, which achieves asymptotically lower computational scaling with respect to system size compared to conventional variational Monte Carlo tensor-network methods for the same statistical accuracy. We benchmark our approach on two-dimensional long-range Heisenberg models and observe a crossover point where the new algorithm outperforms standard approaches when the lattice size is beyond 8×8. Our work not only paves the way for large-scale tensor-network simulations, but also demonstrates that quantum-information techniques can serve as powerful tools to advance classical many-body computation.