GALIC: Hybrid Multi-Qubitwise Pauli Grouping for Quantum Computing Measurement

Observable estimation is a core primitive in NISQ-era algorithms. Two primary grouping schemes for simultaneous Pauli measurements have been proposed: fully commutativity (FC) and qubit-wise commutativity (QWC), with no compelling means of interpolation. In this work, we propose a generalized framework for designing and analyzing context-aware hybrid FC/QWC commutativity relations. We use our framework to propose a noise-and-connectivity-aware grouping strategy: Generalized backend-Aware pauLI Commutation (GALIC). We demonstrate how GALIC interpolates between FC and QWC, maintaining estimator accuracy in Hamiltonian estimation while lowering variance by an average of 20% compared to QWC. We also explore the design space of near-term quantum devices using the GALIC framework, specifically comparing device noise levels and connectivity. We find that error suppression has a more than 13x larger impact on device-aware estimator variance than qubit connectivity with even larger correlation differences in estimator biases.