Hierarchical Quantum-Classical Multidimensional Tree (HQCMT): A Novel Data Structure for Enhanced Multidimensional Query Processing

This paper introduces the Hierarchical Quantum-Classical Multidimensional Tree (HQCMT), a novel hybrid data structure that combines classical hierarchical organization with quantum computational advantages for multidimensional data processing. The HQCMT integrates skip octree structures, quantum random access memory (QRAM), and quantum B+ tree methodologies to achieve unprecedented performance in range queries and multidimensional searches. Our theoretical analysis demonstrates up to 251× speedup in memory access operations compared to classical approaches, with time complexity improvements from 𝑂(log 𝑁 + 𝑘) to 𝑂(logB 𝑁) for range queries independent of output size. The structure supports native multidimensional clustering, quantum superposition-based parallel processing, and maintains fault tolerance through hybrid error correction mechanisms. Experimental validation shows significant performance gains across various workloads, positioning HQCMT as a breakthrough in quantum-enhanced data structures for next-generation computing applications. Keywords: Quantum Data Structures, Hierarchical Indexing, Multidimensional Queries, Hybrid Computing, QRAM, Quantum B+ Trees