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

2026-07-15

AI Summary

This work addresses the current lack of a unified framework for quantifying the reliability of noisy quantum backends in both variational quantum algorithms (VQAs) and quantum signal processing tasks, such as Green’s function reconstruction via quantum singular value transformation (QSVT). It proposes the first benchmarking framework that integrates variational and non-variational workloads through uncertainty quantification, combining Bayesian optimization, posterior refinement, sensitivity analysis, and robust parameter density estimation. The approach systematically evaluates performance across ten representative VQA and QSVT tasks on multiple quantum backends, enabling identification of robust parameter regions, backend-specific failure modes, and calibration sensitivities. Furthermore, it facilitates cross-platform reliability ranking and resource requirement prediction, establishing a standardized evaluation protocol for deploying practical quantum algorithms.

Abstract

We present an uncertainty quantification (UQ) framework for application level benchmarking and characterization of noisy quantum backends. The framework compares two workload classes under one statistical pipeline: noisy intermediate scale quantum (NISQ) variational quantum algorithms (VQAs) and Quantum Singular Value Transformation (QSVT) based Green's function reconstruction. For the VQA branch, we evaluate ten benchmark families spanning chemistry, optimization, simulation, compiling, linear solving, partial differential equations, metrology, error correction, tomography, and channel fidelity estimation. For the QSVT branch, we reconstruct orbital resolved Green's functions and spectral peaks from a block encoded real time propagator. The workflow combines Bayesian optimization, posterior distribution refinement, sensitivity analysis, robust parameter density estimation, backend ranking, noise correlation, and resource estimation analysis. Instead of reporting only one best parameter vector, the framework identifies robust parameter regions, residual gaps to ideal behavior, backend specific failure modes, and calibration sensitive uncertainty. The result is a common benchmark for variational and non-variational workloads that measures how reliably each backend reaches useful task level behavior.

Problem

• uncertainty quantification
• noisy quantum backends
• variational quantum algorithms
• quantum signal processing
• benchmarking

Innovation

• Uncertainty Quantification
• Variational Quantum Algorithms
• Quantum Signal Processing
• Noisy Quantum Backends
• Bayesian Optimization