arXiv subjects

Nicholas R. Allgood

Publications and source records attributed to Nicholas R. Allgood.

5 recordsLinked to original sources

arXiv2026

Kernel-Preserving Dynamics and Symmetry Classification for Synchronization Subspaces

We study the preservation and stability of synchronization subspaces in tensor products of finite-dimensional Hilbert spaces. Given self-adjoint operators $T_A$ and $T_B$ on local subsystems, the synchronization subspace is defined as the kernel of the difference operator $K = T_A \otimes I - I \otimes T_B$. We establish two main results: First for $ε$-compatible dynamics satisfying $||[H,K]|| \leq ε$, we prove a sharp drift bound where any initially synchronized state deviates from the kernel at a rate at most linear in time with slope $ε$. We show by explicit construction that this estimate is optimal to leading order. Second in the presence of finite group symmetry, we show that the synchronization subspace coincides with the diagonal isotypic component in the tensor product decomposition and we characterize the algebra of synchronization-preserving dynamics as the intersection of the commutants of the group action and synchronization operator.

math-ph↗

arXiv2026

Adaptive Quantum Optimized Centroid Initialization

Prototype-based clustering algorithms such as k-means are sensitive to the selection of initial cluster centroids, with poor initialization leading to slower convergence and suboptimal solutions trapped in local minima. We present Adaptive Quantum Optimized Centroid Initialization (AQOCI), a method that formulates the centroid initialization problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solves it using quantum annealing or quantum-inspired solvers. AQOCI extends a prior method (QOCI) by introducing an iterative refinement mechanism inspired by the Gauss-Seidel and Jacobi methods, enabling the recovery of real-valued centroid coordinates from binary solver outputs through adaptive scaling and offset adjustments. We evaluate AQOCI using three solver backends: TABU search, simulated annealing, and D-Wave's HybridBQM on synthetic Gaussian data with controlled sweeps over cluster separation, cluster count, dimensionality, and sample size, as well as on the MOTIF malware classification dataset, comparing against standard k-means with random initialization and k-means++ initialization. On the MOTIF dataset, AQOCI produces clusterings that are competitive with and, at smaller sample sizes, superior to k-means++, with V-measure improvements of up to 26\%. On synthetic data with heavily overlapping clusters, AQOCI--SimAnn outperforms k-means++ in V-measure. On well-separated synthetic data, k-means++ is clearly superior, and AQOCI exhibits a consistent performance plateau attributable to the binary encoding resolution. The dimensionality sweep demonstrates scalability to at least $d = 10$ without degradation.

quant-ph↗

arXiv2025

A Commuting Hamiltonian Framework for Quantum Time Transfer

We develop a mathematical framework for quantum time transfer based on commuting families of Hamiltonians and synchronization observables. The synchronization subspace is defined as the kernel of a difference operator between local clocks, and we show that this subspace is preserved exactly by a commutative $*$-subalgebra of Hamiltonians compatible with the clocks. Our first main result establishes \emph{perturbative stability}: for $ε$-compatible dynamics, where the commutator with the synchronization operator is bounded in norm by $ε$, we prove quantitative drift bounds showing that timing correlations degrade at most linearly in time with slope proportional to $ε$. Our second main result provides a \emph{representation-theoretic classification}: in the presence of a finite group symmetry, the synchronization subspace coincides with the diagonal isotypic component in the tensor product decomposition, and synchronization preservation is characterized by the commutant algebra of the group action. These results identify synchronization as a structural invariant of operator algebras, connecting approximate commutation, kernel-preserving dynamics, and symmetry protection. Beyond quantum time transfer, the framework suggests categorical and resource-theoretic generalizations and contributes to the broader study of operator-algebraic invariants in multipartite quantum dynamics.

quant-ph↗

arXiv2023

Quantum Optimized Centroid Initialization

One of the major benefits of quantum computing is the potential to resolve complex computational problems faster than can be done by classical methods. There are many prototype-based clustering methods in use today, and the selection of the starting nodes for the center points is often done randomly. Clustering often suffers from accepting a local minima as a valid solution when there are possibly better solutions. We will present the results of a study to leverage the benefits of quantum computing for finding better starting centroids for prototype-based clustering.

quant-ph↗

arXiv2022

A Quantum Algorithm To Locate Unknown Hashgrams

Quantum computing has evolved quickly in recent years and is showing significant benefits in a variety of fields, especially in the realm of cybersecurity. The combination of software used to locate the most frequent hashes and $n$-grams that identify malicious software could greatly benefit from a quantum algorithm. By loading the table of hashes and $n$-grams into a quantum computer we can speed up the process of mapping $n$-grams to their hashes. The first phase will be to use KiloGram to find the top-$k$ hashes and $n$-grams for a large malware corpus. From here, the resulting hash table is then loaded into a quantum simulator. A quantum search algorithm is then used search among every permutation of the entangled key and value pairs to find the desired hash value. This prevents one from having to re-compute hashes for a set of $n$-grams, which can take on average $O(MN)$ time, whereas the quantum algorithm could take $O(\sqrt{N})$ in the number of table lookups to find the desired hash values.

quant-ph↗