aiqbench analysis
This research proposes a hybrid architecture that integrates causal self-attention mechanisms from classical Transformers with Fully-Connected Variational Quantum Circuits to solve high-dimensional parabolic PDEs. By treating state trajectories as time-coordinate tokens, the method leverages quantum embeddings for compact hidden widths while retaining parameter-free structural operations in the attention layers. The study demonstrates that this specific hybrid approach effectively learns gradient-related control processes and outperforms non-attentive baselines on stochastic benchmarks relevant to computational finance and physics.
Quantum Transformer BSDE Solver via Multi-Layer Fully-Connected Variational Quantum Circuits
arXiv:2607.25162v1 Announce Type: new Abstract: Solving high-dimensional parabolic partial differential equations (PDEs) is important in engineering, physics, and stochastic control. Deep BSDE methods reformulate semilinear PDEs as backward stochastic differential equations and admit a model-based reinforcement learning interpretation, where trajectories are generated from known stochastic dynamics while a trainable model learns the gradient-related control process. We propose a Quantum Transformer BSDE solver based on Multi-Layer Fully-Connected Variational Quantum Circuits (FC-VQC). The method treats the normalized state trajectory as time--coordinate tokens and applies causal self-attention to learn interactions in the adapted BSDE gradient process. All trainable model parameters are contained within the FC-VQC embedding, projection, feed-forward, and decoder modules, while attention and structural operations remain classical and parameter-free. Experiments on three d=36 PDE benchmarks show that QTransformer consistently improves over the non-attentive FC-VQC baseline and outperforms the classical Transformer at compact hidden widths, while the wider classical Transformer achieves the best overall accuracy. These results demonstrate that combining causal attention with FC-VQC provides an effective quantum architecture for high-dimensional BSDE trajectory learning.
Abstract:Solving high-dimensional parabolic partial differential equations (PDEs) is important in engineering, physics, and stochastic control. Deep BSDE methods reformulate semilinear PDEs as backward stochastic differential equations and admit a model-based reinforcement learning interpretation, where trajectories are generated from known stochastic dynamics while a trainable model learns the gradient-related control process. We propose a Quantum Transformer BSDE solver based on Multi-Layer Fully-Connected Variational Quantum Circuits (FC-VQC). The method treats the normalized state trajectory as time--coordinate tokens and applies causal self-attention to learn interactions in the adapted BSDE gradient process. All trainable model parameters are contained within the FC-VQC embedding, projection, feed-forward, and decoder modules, while attention and structural operations remain classical and parameter-free. Experiments on three d=36 PDE benchmarks show that QTransformer consistently improves over the non-attentive FC-VQC baseline and outperforms the classical Transformer at compact hidden widths, while the wider classical Transformer achieves the best overall accuracy. These results demonstrate that combining causal attention with FC-VQC provides an effective quantum architecture for high-dimensional BSDE trajectory learning.
Quantum Physics (quant-ph); Computational Finance (q-fin.CP)
arXiv:2607.25162 [quant-ph]
(or arXiv:2607.25162v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.25162 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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