arXiv subjects

Higinio Mora Mora

Publications and source records attributed to Higinio Mora Mora.

2 recordsLinked to original sources

arXiv2026

When Does a Quantum Speedup Survive End-to-End?

Primitive quantum speedups are interface-relative: they depend on the input access used to run the primitive and on the output contract used to consume its state or samples. This paper introduces a transcript-level admissibility relation \(A_M\preceq_{\mathrm{int}}A_Q\), defined relative to the declared implementation package of the quantum interface. It identifies which adaptive classical access transcripts that same package licenses, with all setup, transcript-generation, and precision overheads charged. The main application is an operational audit for normalized-Betti estimation in clique-complex TDA, separating three declared-interface regimes. Reversible indexed simplex interfaces certify matched classical simplex sampling and local Laplacian row access by evaluating their reversible routines on single computational branches. Membership-based preparations induce a rejection route of overhead \(\binom{n}{k+1}/|S_k|\). Abstract spectral or block-encoding interfaces require an accompanying implementation package, transcript reduction, or shared representation. Under the indexed certificate and interface closure, the end-to-end cost is fixed by the imported estimator's spectral dependence on the gap \(γ\); the concretely realized bounded-treewidth family already admits exact \(\mathrm{poly}(n)\) classical Betti computation by rank over \(\mathbb{Q}\). A low-rank separation supports the role of access and output contracts.

quant-ph↗

arXiv2026

Spectral Phase Encoding for Quantum Kernel Methods

Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive noise. We introduce Spectral Phase Encoding (SPE), a hybrid construc- tion combining a discrete Fourier transform (DFT) front-end with a diagonal phase-only embedding aligned with the geometry of diagonal quantum maps. Within a unified framework, we compare QK-DFT against alternative quantum variants (QK-PCA, QK-RP) and classi- cal SVM baselines under identical clean-data hyperparameter selection, quantifying robustness via dataset fixed-effects regression with wild cluster bootstrap inference across heterogeneous real-world datasets. Across the quantum family, DFT-based preprocessing yields the smallest degradation rate as noise increases, with statistically sup- ported slope differences relative to PCA and RP. Compared to classical baselines, QK-DFT shows degradation comparable to linear SVM and more stable than RBF SVM under matched tuning. Hardware exper- iments confirm that SPE remains executable and numerically stable for overlap estimation. These results indicate that robustness in quan- tum kernels depends critically on structure-aligned preprocessing and its interaction with diagonal embeddings, supporting a robustness-first perspective for NISQ-era quantum machine learning.

cs.LG↗