Iterative Partition Search Variational Quantum Algorithm for Solving Shortest Vector Problem

Abstract: The Partition Search Algorithm (PSA) and the Iterative Quantum Optimization with an Adaptive Problem (IQOAP) framework are two existing Variational Quantum Algorithms (VQAs) for solving the Shortest Vector Problem (SVP), but both suffer from certain limitations. In this work, we proposed the Iterative Partition Search Algorithm (IPSA), which is a targeted synthesis and refinement of these preceding methods. Our algorithm inherits the core idea of partitioning to circumvent the zero vector" from PSA and theiterative lattice basis reduction" framework from IQOAP. A key feature of IPSA is the ``1-tailed search spaces", which can be viewed as a highly constrained variant of PSA's partitioning strategy, specifically designed for optimal performance within IQOAP's iterative structure. We supplant IQOAP's fixed iteration count with a dynamic, stack-managed process and substitute a more expressive and shallower circuit structure for its original ansatz. Crucially, the 1-tailed design fundamentally ensures that every successful VQA execution yields an effective lattice basis update, thereby eliminating the issue of ineffective iterations in IQOAP. This evolutionary path of refinement allows IPSA to overcome the drawbacks of its predecessors precisely. Numerical simulations on 4- to 6-dimensional SVP instances demonstrate that IPSA achieves at least a 73\% improvement in success rate for finding optimal solutions and over a 35\% improvement in average solution quality compared with the methods above while maintaining comparable total circuit depth.