aiqbench analysis
This research introduces FC-VQC, a scalable framework for variational quantum circuits that eliminates trainable classical components to address the expressivity-trainability dilemma in high-dimensional function approximation. By successfully modeling complex spatio-temporal PDEs up to 144 spatial dimensions, the study demonstrates significant performance gains over classical baselines like neural networks and tensor networks while providing empirical diagnostics for noise sensitivity.
Scalable Quantum Machine Learning via Multi-layer Fully-Connected Variational Quantum Circuits
arXiv:2602.16623v3 Announce Type: replace Abstract: Variational quantum circuits (VQCs) face an expressivity-trainability dilemma and scalability challenges. We propose Multi-Layer Fully-Connected Variational Quantum Circuits (FC-VQC), a general-purpose quantum machine learning framework that connects local VQC blocks through measurement, deterministic parameter-free routing, and re-encoding. All trainable model parameters reside within the quantum blocks, without trainable classical neural components. We study fully connected, sliding-window, and parallel block mixing and analyze computational costs, conditional error propagation, and block information exchange. Using classical simulation, we evaluate tabular regression and classification, with our main comparison addressing spatio-temporal function approximation for the Black--Scholes, Burgers, and time-dependent oscillatory PDEs with up to $144$ spatial dimensions. Comparisons include neural-network, explicit angle-feature, tensor-network, and gradient-boosted-tree baselines. The results show that FC-VQC achieves the lowest trajectory relative MAE for all PDEs at the higher dimensions $d\in\{81,144\}$. Gradient-dynamics and depolarizing-noise experiments provide complementary empirical diagnostics of trainability and preliminary noise sensitivity.
Abstract:Variational quantum circuits (VQCs) face an expressivity-trainability dilemma and scalability challenges. We propose Multi-Layer Fully-Connected Variational Quantum Circuits (FC-VQC), a general-purpose quantum machine learning framework that connects local VQC blocks through measurement, deterministic parameter-free routing, and re-encoding. All trainable model parameters reside within the quantum blocks, without trainable classical neural components. We study fully connected, sliding-window, and parallel block mixing and analyze computational costs, conditional error propagation, and block information exchange. Using classical simulation, we evaluate tabular regression and classification, with our main comparison addressing spatio-temporal function approximation for the Black--Scholes, Burgers, and time-dependent oscillatory PDEs with up to $144$ spatial dimensions. Comparisons include neural-network, explicit angle-feature, tensor-network, and gradient-boosted-tree baselines. The results show that FC-VQC achieves the lowest trajectory relative MAE for all PDEs at the higher dimensions $d\in\{81,144\}$. Gradient-dynamics and depolarizing-noise experiments provide complementary empirical diagnostics of trainability and preliminary noise sensitivity.
54 pages, 11 figures, 29 tables. Main text: 9 pages
arXiv:2602.16623 [quant-ph]
(or arXiv:2602.16623v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2602.16623 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 243 words
