Alternative circuit ansatz for quantum spectral mixing

Develop and benchmark alternative variational quantum circuit architectures—such as hardware‑efficient or problem‑inspired designs—for the mode‑shared spectral mixer in the HQ‑LP‑FNO hybrid Fourier neural operator, and determine whether these designs better exploit quantum correlations for spectral channel mixing than the currently used QFT–mixer–inverse‑QFT VQC.

Background

HQ‑LP‑FNO replaces a fraction of dense mode‑wise spectral mixing in LP‑FNO with a mode‑shared VQC mixer to achieve parameter efficiency while maintaining accuracy on 3D laser‑processing surrogates. The implemented VQC uses a QFT–IsingXY–inverse‑QFT structure with learned pre/post linear projections.

While results show parameter reductions and competitive accuracy, the authors note that other circuit families might better leverage quantum correlations for spectral mixing, motivating a systematic exploration of alternative circuit ansatz designs.

References

Several directions remain open. Alternative circuit Ansatz, such as hardware-efficient or problem-inspired designs, may better exploit quantum correlations for spectral mixing.

— Hybrid Fourier Neural Operator for Surrogate Modeling of Laser Processing with a Quantum-Circuit Mixer  (2604.04828 - Papierz et al., 6 Apr 2026) in Conclusion (Section 6)

Whether they can be turned into a design principle with a useful inductive bias, rather than merely an unsimulable one, is the natural next question.

— Classical Limits of Spectral Filtering in Quantum Generative Models  (2608.14169 - Roth, 14 Aug 2026) in Section 6, Discussion and Conclusion