Conformalized Quantum DeepONet Ensembles for Scalable Operator Learning with Distribution-Free Uncertainty

• URL: http://arxiv.org/abs/2605.00330v1
• Date: Fri, 01 May 2026 01:13:59 GMT
• Title: Conformalized Quantum DeepONet Ensembles for Scalable Operator Learning with Distribution-Free Uncertainty
• Abstract summary: Operator learning enables fast surrogate modeling of high-dimensional dynamical systems.<n>Existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification.<n>We propose Conformalized Quantum DeepONet Ensembles, a framework that addresses both challenges simultaneously.
• Score: 7.889588152000197
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical settings. We propose Conformalized Quantum DeepONet Ensembles, a framework that addresses both challenges simultaneously. By leveraging Quantum Orthogonal Neural Networks (QOrthoNNs), we reduce operator inference complexity from O(n^2) to O(n), enabling scalable evaluation over fine discretizations. To provide rigorous uncertainty quantification, we combine ensemble-based epistemic modeling with adaptive conformal prediction, yielding distribution-free coverage guarantees. A key challenge in ensembling is that naive parallelism scales hardware resources linearly with the number of models. We resolve this by using Superposed Parameterized Quantum Circuits (SPQCs), which compress multiple ensemble members into a single circuit and enable simultaneous multi-model execution. Experiments on synthetic partial differential equations and real-world power system dynamics demonstrate that our approach achieves accurate predictions while maintaining calibrated uncertainty under realistic quantum noise. These results establish a practical pathway toward scalable, uncertainty-aware operator learning in quantum machine learning.

Related papers

• Learnable yet not simulable: a quantum resource theory of learning models [57.695822250391906]
  It remains unclear which quantum resource governs the classical learnability of quantum circuits.<n>We study the expectation-value functions of families of tunable quantum circuits.<n>These results establish a quantitative resource-theoretic framework for delineating the boundary between classical simulation and learning.
  arXiv  Detail & Related papers  (2026-08-03T14:48:03Z)
• Compositional Quantum Heuristics for Max-Clique Detection [0.0]
  In general, circuits that are sufficiently expressive to model complex behaviour often exhibit barren plateaus.<n>In this work we investigate a compositional approach to mitigate this trade-off by assembling larger quantum models from smaller subcomponents.<n>We use this framework to design permutation-equivariant quantum graph neural networks for identifying maximal cliques in graphs.
  arXiv  Detail & Related papers  (2026-05-08T11:38:57Z)
• Equivariant Evidential Deep Learning for Interatomic Potentials [55.6997213490859]
  Uncertainty quantification is critical for assessing the reliability of machine learning interatomic potentials in molecular dynamics simulations.<n>Existing UQ approaches for MLIPs are often limited by high computational cost or suboptimal performance.<n>We propose textitEquivariant Evidential Deep Learning for Interatomic Potentials ($texte2$IP), a backbone-agnostic framework that models atomic forces and their uncertainty jointly.
  arXiv  Detail & Related papers  (2026-02-11T02:00:25Z)
• Quantum LEGO Learning: A Modular Design Principle for Hybrid Artificial Intelligence [63.39968536637762]
  We introduce Quantum LEGO Learning, a learning framework that treats classical and quantum components as reusable, composable learning blocks.<n>Within this framework, a pre-trained classical neural network serves as a frozen feature block, while a VQC acts as a trainable adaptive module.<n>We develop a block-wise generalization theory that decomposes learning error into approximation and estimation components.
  arXiv  Detail & Related papers  (2026-01-29T14:29:21Z)
• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• A purely Quantum Generative Modeling through Unitary Scrambling and Collapse [6.647966634235082]
  Quantum Scrambling and Collapse Generative Model (QGen) is a purely quantum paradigm that eliminates classical dependencies.<n>We introduce a measurement-based training principle that decomposes learning into tractable subproblems, mitigating barren plateaus.<n> Empirically, QGen outperforms classical and hybrid baselines under matched parameter budget, while maintaining robustness under finite-shot sampling.
  arXiv  Detail & Related papers  (2025-06-12T11:00:21Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [50.95799256262098]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience.<n>We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise [49.97673761305336]
  Noise remains a major obstacle to achieving reliable quantum algorithms.<n>We present a provably noise-resilient training theory and algorithm to enhance the robustness of parameterized quantum circuit classifiers.
  arXiv  Detail & Related papers  (2025-05-24T02:51:34Z)
• Projective Quantum Eigensolver with Generalized Operators [0.0]
  We develop a methodology for determining the generalized operators in terms of a closed form residual equations in the PQE framework. With the application on several molecular systems, we have demonstrated our ansatz achieves similar accuracy to the (disentangled) UCC with singles, doubles and triples.
  arXiv  Detail & Related papers  (2024-10-21T15:40:22Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Attention to Quantum Complexity [21.766643620345494]
  We introduce the Quantum Attention Network (QuAN), a versatile classical AI framework. QuAN treats measurement snapshots as tokens while respecting their permutation invariance. We rigorously test QuAN across three distinct quantum simulation settings.
  arXiv  Detail & Related papers  (2024-05-19T17:46:40Z)
• Noise-Robust End-to-End Quantum Control using Deep Autoregressive Policy Networks [2.5946789143276447]
  Variational quantum eigensolvers have recently received increased attention, as they enable the use of quantum computing devices. We present a hybrid policy gradient algorithm capable of simultaneously optimizing continuous and discrete degrees of freedom in an uncertainty-resilient way. Our work exhibits the beneficial synergy between reinforcement learning and quantum control.
  arXiv  Detail & Related papers  (2020-12-12T02:13:28Z)
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation [5.668795025564699]
  We present an approach for tackling open quantum system dynamics. We compactly represent quantum states with autoregressive transformer neural networks. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator.
  arXiv  Detail & Related papers  (2020-09-11T18:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.