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arXiv:2607.14392

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

Priyabrata Senapati, Vibin Abraham, Qiang Guan, Bo Peng

cs.ETcs.CEphysics.comp-phquant-phSubmitted Jul 15, 2026• Announced Jul 17, 2026• 0 citations
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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.

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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.
Quantum computing offers speedups, but NISQ processors face hardware-induced errors that degrade fidelity and reproducibility. We introduce an uncertainty-aware benchmarking framework that combines uncertainty quantification with global sensitivity analysis to evaluate not only peak fidelity but also its reliability over time. Using Bayesian Optimization with SGLD refinement under fixed budgets, seeds, bounds, and trust-region rules, and repeating runs across days, we capture calibration drift and quantify efficiency, stability, landscape complexity, and maintenance cost. A noise-aware Gaussian process surrogate provides scalable sensitivity estimates without error mitigation. Applied to VQAMET and VQC on three IBMQ backends, the framework delivers actionable guidance for co-tuning and backend selection, complementing and often outperforming quantum volume style metrics.
Benchmarking noisy quantum computers for variational workloads requires more than a single best energy number: two backends may reach similar energies while differing sharply in convergence speed, stability, and parameter sensitivity. We present a compact uncertainty quantification driven benchmarking study for the Variational Quantum Eigensolver (VQE), combining Bayesian optimization with Metropolis-Hastings refinement to search a backend conditioned VQE landscape and characterizing each backend by its best observed energy, evaluations to target, objective dispersion, and Sobol sensitivity fingerprint. On a 92 parameters LiH VQE across seven IBM fake backends, Brisbane wins overall (best energy 1.0207, top normalized quality), Kyoto matches its energy but converges five times more slowly, and Osaka trades a modest energy penalty for near optimal speed and low dispersion. The Sobol fingerprints further show that the dominant VQE parameters differ across backends, indicating backend specific robust regions rather than a universal calibration. Uncertainty quantification therefore provides a practical application level view of backend quality for near term variational workloads.
Variational Quantum Algorithms (VQAs) are promising methods for solving combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) devices. However, benchmarking VQAs is difficult due to their stochastic behavior and the lack of standardized performance criteria. This work introduces a general framework for evaluating VQAs applied to Quadratic Unconstrained Binary Optimization (QUBO) problems. The framework uses three complementary metrics: feasibility, quality, and reproducibility. It also introduces a quality diagram that visualizes trade-offs between success probability and computational resources. Reproducibility is formalized using Shannon entropy, and a decision rule is defined for selecting algorithms under resource constraints. As a demonstration, the framework is applied to several VQAs using Conditional Value at Risk (CVaR) cost functions and different shot counts on a 16-qubit QUBO instance. The results show how the framework supports systematic benchmarking and provides a foundation for adaptive algorithm selection in hybrid quantum-classical workflows.
Quantum fidelity estimation is a fundamental task in quantum information and computing to benchmark the quality of quantum states, and hence of quantum processes, on noisy quantum hardware. Point estimates of fidelity by existing methods generally lack the rigorous uncertainty quantification required for reliable preparation and verification of these tasks. While Bayesian and bootstrap frameworks are widely used for uncertainty quantification, they are sensitive to model misspecification or lack formal coverage guarantees in non-asymptotic regimes. This paper introduces a hybrid "Bayesian-informed" conformal prediction-based framework to provide distribution-free, rigorous prediction intervals for quantum state fidelity estimation which can be used, with care, to approximate confidence intervals with respect to the quantum randomness of Born's rule. The framework requires a point estimator, and we consider both classical point estimators as well as data-driven neural net estimators. We evaluate the robustness of the methodology across a diverse range of experimental challenges, including finite-sample noise, tomographic incompleteness, physical model error, and out-of-distribution data. Our results demonstrate that conformalized estimators maintain statistical validity where traditional methods fail, offering a scalable and reliable approach for the verification of modern quantum systems. The best performing variant of our methodology is based on a class-conditional conformal prediction, as this most closely approximates the conditional coverage desired for a true confidence interval.
Quantum machine learning (QML) models introduce unique sources of uncertainty arising from finite measurement shots, hardware noise, and variational optimization instability. Despite rapid progress in quantum algorithms, systematic uncertainty quantification (UQ) in QML remains largely underexplored and lacks standardized tooling. We present Quan-tumUQ, an open-source Python library for uncertainty quantification in quantum machine learning with native support for PennyLane and Qiskit. QuantumUQ provides shot-based uncertainty estimation, ensemble-based epistemic uncertainty, measurement-budget stability profiling, and calibration metrics for classification and regression tasks. We formalize the uncertainty decomposition in QML, describe the architectural design of the library, and demonstrate its capabilities through reproducible experiments. Our results show that measurement-induced uncertainty exhibits predictable scaling behavior and that calibration analysis reveals systematic overconfidence in variational quantum classifiers. QuantumUQ aims to make robustness, reliability, and trustworthiness first-class citizens in quantum ML research.
Quantum sensing offers sensitivities surpassing classical limits, yet practical deployment is often constrained by noise and inefficient signal extraction. This systematic review synthesizes literature from 2015 to 2025 and maps the landscape of data-driven signal processing across diverse platforms, including nitrogen-vacancy (NV) centers and cold atom interferometers. Emerging methodologies are categorized and emphasis is placed on the dominance of hybrid quantum-classical architectures where classical machine learning manages high-dimensional data processing while quantum processors execute specific primitives like feature mapping. Our findings demonstrate that advanced statistical frameworks such as Variational Bayesian Inference (VBI) enable scalable multi-parameter estimation with polynomial complexity, allowing dozens of sensor parameters to be estimated within minutes. Meanwhile, quantum sensing missions in GPS-denied navigation have achieved operational gains through AI-automated software designed to manage quantum hardware drifts and environmental noise, despite a persistent reality gap for generalized quantum machine learning. We further analyze the critical sensitivity-robustness dilemma inherent in entangled sensors and discuss mitigation strategies such as covariant quantum error-correcting codes. We also distinguish between theoretical Quantum Fisher Information (QFI) and realized Mean Squared Error (MSE) of sensor outputs to resolve benchmarking inconsistencies in quantum metrology, and propose a "Gold Standard" reproducibility framework tailored for the Noisy Intermediate-Scale Quantum (NISQ) era to promote automated workflows and hardware calibration transparency. This review provides a strategic roadmap for researchers to bridge the gap between theoretical sensitivity and reliable, software-defined operational utility in quantum sensing.