Tomography-assisted noisy quantum circuit simulator using matrix product density operators

In recent years, efficient quantum circuit simulations incorporating ideal noise assumptions have relied on tensor network simulators, particularly leveraging the matrix product density operator (MPDO) framework. However, experiments on real noisy intermediate-scale quantum (NISQ) devices often involve complex noise profiles, encompassing uncontrollable elements and instrument-specific effects such as crosstalk. To address these challenges, we employ quantum process tomography (QPT) techniques to directly capture the operational characteristics of the experimental setup and integrate them into numerical simulations using MPDOs. Our QPT-assisted MPDO simulator is then applied to explore a variational approach for generating noisy entangled states, comparing the results with standard noise numerical simulations and demonstrations conducted on the Quafu cloud quantum computation platform. Additionally, we investigate noisy MaxCut problems, as well as the effects of crosstalk and noise truncation. Our results provide valuable insights into the impact of noise on NISQ devices and lay the foundation for enhanced design and assessment of quantum algorithms in complex noise environments.