Shadow tomography for classical tensor network simulations

• URL: http://arxiv.org/abs/2606.29133v1
• Date: Sun, 28 Jun 2026 00:43:06 GMT
• Title: Shadow tomography for classical tensor network simulations
• Abstract summary: We show that shadow-tomography-inspired ideas can offer similarly improved sample scaling for estimating observables on tensor network states on classical computers.<n>We develop strategies for both spin (bosonic) and fermionic systems, tailored to the contraction requirements of tensor networks.<n>We demonstrate practical advantage by simulating systems with long-range interactions, including the 2D long-range Heisenberg model and an ab-initio quantum chemistry Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Shadow tomography has appeared as a powerful tool for estimating observables on quantum computers from a small number of samples. We show that shadow-tomography-inspired ideas can offer similarly improved sample scaling for estimating observables on tensor network states on classical computers after proper adaptation. We develop strategies for both spin (bosonic) and fermionic systems, tailored to the contraction requirements of tensor networks, and generate scaling improvements of factors of $O(N)$ to $O(N^{3})$ (where $N$ is system size), depending on the specific task and system type. For the important and difficult task of evaluating the expectation value of long-range interacting Hamiltonians, we achieve the optimal $O(1)$ overall scaling (up to logarithmic factors) for an arbitrarily fixed relative Monte Carlo error in both spin and fermionic systems. Additionally, we show that shadow estimators offer more stable gradients of observables in variational optimization tasks than standard Monte Carlo estimators. We demonstrate practical advantage by simulating systems with long-range interactions, including the 2D long-range Heisenberg model and an ab-initio quantum chemistry Hamiltonian.

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