Modern quantum algorithms are increasingly formulated as coherent procedures for implementing polynomial transformations of operators and singular values. This perspective provides a powerful and unifying language for quantum algorithm design, connecting a wide range of distinct problems through five closely related ke...
Tal Gurfinkel, Kaushika De Silva, A. Mahasinghe et al.· 0 citations
The standard geometric derivation of neural scaling exponents takes the intrinsic dimension of a data manifold as its input. On modular addition in $\mathbb{Z}_p$ that derivation has no input. The exact algebraic solution is an orbit of $\mathbb{Z}_p$ acting by isometries. Transitivity alone makes the ratio statistic u...
Chon-Fai Kam, M. Bessafi, Frédéric Cadet· 0 citations
Xu, Vardi and Safran (ICML 2026) prove that over-parameterized ridge regression over an unstructured random Gaussian feature map groks, with the delay between memorization and generalization growing as $1/\lambda$ in the weight decay. We show that on a structured feature map the same delay does not appear. For a band-l...
Chon-Fai Kam, M. Bessafi, Frédéric Cadet· 0 citations
It is proved that the local ZX simplification layer (spider fusion and identity removal) computes exactly the free-product normal form of Z_2 * Z_8, giving exact per-instance compression and, under a calibrated ergodicity hypothesis, a depth-independent limit law confirmed on two independently constructed nets.
Chon-Fai Kam, A. Mahasinghe, Kaushika De Silva et al.· 0 citations
A measurement of what diagrammatic post-processing recovers from structural redundancy in the Solovay-Kitaev algorithm, which optimizes for numerical convergence rather than circuit economy, and its output carries structural redundancy that a gate-level compiler cannot see.
Dulari De Silva, A. Mahasinghe, Chon-Fai Kam et al.· 0 citations
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