Kernelized Decoded Quantum Interferometry Article Swipe

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Wang, Fumin · YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2511.20016

Decoded Quantum Interferometry (DQI) promises superpolynomial speedups for structured optimization; however, its practical realization is often hindered by significant sensitivity to hardware noise and spectral dispersion. To bridge this gap, we introduce Kernelized Decoded Quantum Interferometry (k-DQI), a unified framework that integrates spectral engineering directly into the quantum circuit architecture. By inserting a unitary kernel prior to the interference step, k-DQI actively reshapes the problem's energy landscape, concentrating the solution mass into a ``decoder-friendly'' low-frequency head. We formalize this advantage through a novel robustness metric, the noise-weighted head mass $Σ_K$, and prove a Monotonic Improvement Theorem, which establishes that maximizing $Σ_K$ guarantees higher decoding success rates under local depolarizing noise. We substantiate these theoretical gains in Optimal Polynomial Interpolation (OPI) and LDPC-like problems, demonstrating that kernel tuning functions as a ``spectral lens'' to recover signal otherwise lost to isotropic noise. Crucially, we provide explicit, efficient circuit realizations using Chirp and Linear Canonical Transform (LCT) kernels that achieve significant boosts in effective signal-to-noise ratio with negligible depth overhead ($\tilde{O}(n)$ to $\tilde{O}(n^2)$). Collectively, these results reframe DQI from a static algorithm into a tunable, noise-aware protocol suited for near-term error-corrected environments.

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preprint

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https://doi.org/10.48550/arxiv.2511.20016

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green

OpenAlex ID

https://openalex.org/W7106801916

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https://openalex.org/W7106801916

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DOI

https://doi.org/10.48550/arxiv.2511.20016

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Title

Kernelized Decoded Quantum Interferometry

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Type

preprint

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Publication year

2025

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2025-11-25

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Authors

Wang, Fumin

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https://doi.org/10.48550/arxiv.2511.20016

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green

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https://doi.org/10.48550/arxiv.2511.20016

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Concepts

Algorithm, Decoding methods, Mathematics, Chirp, Quantum Fourier transform, Robustness (evolution), Computer science, Quantum, Overhead (engineering), Qubit, Polynomial interpolation, Interferometry, Polynomial, Quantum computer, Unitary state, Kernel (algebra), Electronic engineering, Interpolation (computer graphics), Fourier transform, Quantum error correction, Erasure, Sensitivity (control systems), Realization (probability), Topology (electrical circuits), Upper and lower bounds, Adder, Orthogonality, Hadamard transform, Noise (video)

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