A Simplicial Quantum Search

栖 小栗, Kaname Matsue, Osamu Ogurisu +1 more

Kaname Matsue, Osamu Ogurisu, Etsuo Segawa

Kaname Matsue, Osamu Ogurisu, Etsuo Segawa

Roberto Zucchini

In this paper, a quantum computational framework for algebraic topology based on simplicial set theory is presented. This extends previous work, which was limited to simplicial complexes and aimed mostly at topological data analysis. The proposed set-up applies to any parafinite simplicial set and proceeds by associating with it a finite dimensional simplicial Hilbert space, whose simplicial operator structure is studied in some depth. It is shown in particular how the problem of determining the simplicial set’s homology can be solved within the simplicial Hilbert framework. Further, the conditions under which simplicial set theoretic algorithms can be implemented in a quantum computational setting with finite resources are examined. Finally a quantum algorithmic scheme capable of computing the simplicial homology spaces and Betti numbers of a simplicial set combining a number of basic quantum algorithms is outlined.

Hossein Mehri‐Dehnavi, Hasan Dashtianeh, Hossein Yahyavi Kuchaksaraei +3 more

Sujay Gejji, Rashmi S, Thanuj Kumar M +3 more

Autonomous vehicle navigation requires finely calibrated environmental awareness, resilient onboard deliberation, and continual, near-instantaneous adaptation to evolving roadway behaviours. Current deep learning frameworks achieve strong scores on perception benchmarks, yet their propensity to overlook nonlinear spatial–temporal couplings—coupled with mandated low-latency constraints—remains a fundamental safety liability in actual driving contexts. To mitigate this gap, the present work introduces a hybrid architecture that overlays a Quantum Simplicial Classical Attention Convolutional Network (QSCACN2Net) with a Brown Bear Optimization Algorithm (BBOA), thereby achieving dual improvements in navigational efficacy and reliability. The QSCACN2Net component leverages quantum-classical hybrid propagation and simplicial attention blocks to isolate multidimensional environmental couplings. By combining sub-millisecond feature resolution with coherent ingestion of panoramic vehicular and atmospheric context, the architecture assimilates relevant information across disparate magnitudes of environmental structure. Simultaneously, the BBOA mimics seasonal hibernation metabolic patterns to design hyperparameter search; this biologically inspired mechanism secures accelerated convergence and pronounced robustness with minimal expansion of the hyperparameter search space. Validate the proposed architecture on the benchmarking KITTI dataset, reporting statistically relevant improvements in absolute error, quantifiable reductions in mean pixel perturbation measurements, and tightened end-to-end latency regimes that exceed existing state-of-the-art solutions. Combinatorial analysis of the experimental results substantiates scalable deployment, illustrating that the architecture satisfies the stringent maintainability, safety, and resource operability criteria demanded by future production-grade autonomous driving frameworks.