Unified Uncertainty Quantification Framework Bridging Noisy Quantum Backends Across Variational Quantum Algorithms and Quantum Signal Processing

How can researchers reliably compare the performance of noisy quantum backends across fundamentally different types of quantum algorithms? Current metrics like quantum volume or gate fidelity often fail to predict how a specific device will perform on a complex, application-level scientific task. This paper addresses this gap by creating a unified statistical framework that treats both variational quantum algorithms (VQAs) and non-variational quantum signal processing (QSVT) as probes of hardware reliability.

The authors propose a backend-aware uncertainty quantification (UQ) pipeline that treats every execution as a data tuple consisting of input parameters and noisy task outputs. This pipeline applies to ten distinct VQA families—including VQE, QAOA, and VQLS—as well as the reconstruction of Green's functions via QSVT. The workflow employs Bayesian optimization guided by Gaussian process surrogates to explore the parameter space, followed by posterior refinement, global sensitivity analysis, and density estimation. This allows the framework to move beyond reporting a single 'best' result, instead characterizing the stability and robustness of the backend's performance across the entire parameter landscape.

The study demonstrates that a single statistical interface can effectively benchmark both variational and non-variational workloads. By applying this framework to four IBM quantum backends, the authors show that backend performance is highly workload-dependent; a device that excels at one task may fail at another due to specific noise correlations or calibration issues. The framework produces 'sensitivity fingerprints' that identify which control parameters are most critical for success on a given backend, and it provides a resource-cost analysis that distinguishes between workloads dominated by single heavy circuits versus those requiring many smaller characterization circuits. This unified approach reveals patterns of agreement and disagreement that highlight the limitations of using any single benchmark as a universal proxy for quantum hardware quality.