A Novel Approach to Quantum Heuristics for Structured Database Search

Quantum search in structured database using local adiabatic evolution and spectral methods

Since Grover's seminal work which provides a way to speed up combinatorial search, quantum search has been studied in great detail. We propose a new method for designing quantum search algorithms for finding a marked element in the state space of a graph. The algorithm is based on a local diabatic evolution of the Hamiltonian associated with the graph. The main new idea is to apply some techniques such as Krylov bspace projection methods, Lanczos algorithm and spectral distribution methods. Indeed, using these techniques together with the second-order perturbation theory, we give a systematic …

Controlled quantum search on structured databases

We present quantum algorithms to search for marked vertices in structured databases with low connectivity. Adopting a multi-stage search process, we achieve a success probability close to $100\%$ on Cayley trees with large branching factors. We find that the number of stages required is given by the height of the Cayley tree. At each stage, the jumping rate should be chosen as different values. The dominant term of the runtime in the search process is proportional to $N^{(2r-1)/2r}$ for the Cayley tree of height $r$ with $N$ vertices. We further find that one can control the number of stages b…

A Framework for Structured Quantum Search

A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to the underlying structure of abstract search spaces, and is analytically simpler than previous structured search methods. The algorithm is evaluated empirically with a variety of search problems, and shown to be particularly effective for searches with many constraints. Furthermore, the algorithm provides a simple framework for utilizing search heuristics. It…

A new adiabatic quantum search algorithm

We present a new adiabatic quantum algorithm for searching over structured databases. The new algorithm is optimized using a simplified complexity analysis.

QCE'24 教程：量子退火——数据库优化的新兴探索

QCE'24 Tutorial: Quantum Annealing -- Emerging Exploration for Database Optimization

本教程系统介绍量子退火技术，并演示其在数据库优化中的应用，包括连接顺序优化、事务调度和虚拟机分配，旨在为数据库领域提供量子计算优化的理论与实践指导。