TERRA: Tensor-network Error-mitigated Robust Randomized Algorithm

We introduce TERRA (Tensor-network Error-mitigated Robust Randomized Algorithm), a practical and versatile algorithmic framework that unifies tensor-network error mitigation with robust shallow shadows to enable scalable and noise-resilient quantum algorithm development on current quantum devices. We demonstrate TERRA within the recently proposed multi-observable dynamic mode decomposition (MODMD) approach on simulators and IBM superconducting processors. We show efficient spectrum learning for the 1D Fermi–Hubbard models at large scale, achieving improved accuracy relative to standalone MODMD and other available methods. We anticipate that TERRA will serve as a widely applicable algorithmic building block for utility-scale algorithm design, providing a practical pathway toward scalable, noise-resilient computation on near-term devices.