KrMM Recurrences: HPC-Enhanced Estimators for Nonlinear Classical Shadows
Abstract
While quantum technologies are rapidly evolving, near-term applications heavily rely on hybrid quantum-classical paradigms. Among these, the classical shadows framework has gained a lot of traction, not only for quantum information science, but also for the development and verification of quantum hardware. It allows to efficiently classically estimate many properties of quantum states from randomized measurements alone, a task that is otherwise intractable due to the destructive nature of measurements in quantum systems. There are, however, many properties of interest that are, due to their very problem formulation, not efficiently estimable. In this work, we identify a computational kernel occurring in estimators of polynomial functions, a class of problems that are in general computationally difficult to solve. We show that this structure allows a row-wise partition that, together with a custom SIMD vectorization, enables massive parallelization and can reduce the computational cost significantly. We show applicability and scalability of the approach on different tasks, and our results showcase that the approach allows high sequential throughput and close-to-ideal parallel scaling. The work thus provides a new way of identifying and exploiting structure in classical shadow estimators, resulting in practical advantages on inherently difficult problems.
Related
BibTeX
@misc{gruber2026krmm,
title = {{KrMM Recurrences: HPC-Enhanced Estimators for Nonlinear Classical Shadows}},
author = {Matthias Gruber and Sabrina Herbst and Ivona Brandic and Vincenzo De Maio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26472},
eprint = {2610.26472},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26472},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - KrMM Recurrences: HPC-Enhanced Estimators for Nonlinear Classical Shadows
AU - Matthias Gruber
AU - Sabrina Herbst
AU - Ivona Brandic
AU - Vincenzo De Maio
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26472
UR - https://arxiv.org/abs/2610.26472
AB - While quantum technologies are rapidly evolving, near-term applications heavily rely on hybrid quantum-classical paradigms. Among these, the classical shadows framework has gained a lot of traction, not only for quantum information science, but also for the development and verification of quantum hardware. It allows to efficiently classically estimate many properties of quantum states from randomized measurements alone, a task that is otherwise intractable due to the destructive nature of measurements in quantum systems. There are, however, many properties of interest that are, due to their very problem formulation, not efficiently estimable. In this work, we identify a computational kernel occurring in estimators of polynomial functions, a class of problems that are in general computationally difficult to solve. We show that this structure allows a row-wise partition that, together with a custom SIMD vectorization, enables massive parallelization and can reduce the computational cost significantly. We show applicability and scalability of the approach on different tasks, and our results showcase that the approach allows high sequential throughput and close-to-ideal parallel scaling. The work thus provides a new way of identifying and exploiting structure in classical shadow estimators, resulting in practical advantages on inherently difficult problems.
ER -