Iterative Partition Search Variational Quantum Algorithm for Solving Shortest Vector Problem

TL;DR

This paper introduces the IPSA, a novel variational quantum algorithm that improves the efficiency and success rate of solving the Shortest Vector Problem by addressing limitations of previous algorithms through iterative, dynamic strategies validated on quantum hardware.

Contribution

The paper proposes IPSA, a new variational quantum algorithm that combines a 1-tailed search strategy with dynamic iteration to enhance performance on SVP, overcoming prior limitations.

Findings

IPSA achieves a 14-fold success rate increase over PSA.

IPSA reduces circuit depth by 82.7% compared to IQOAP.

Experimental results align with numerical simulations.

Abstract

The Partition Search Algorithm (PSA) and Iterative Quantum Optimization with an Adaptive Problem (IQOAP) are leading variational quantum algorithms for solving Shortest Vector Problem (SVP). However, each has limitations that restrict its practical impact. IQOAP suffers from ineffective iterations that fail to update the lattice basis, whereas PSA's static partitioning leads to oversized search spaces. In this work, we propose the Iterative Partition Search Algorithm (IPSA), which systematically addresses these drawbacks by integrating a "1-tailed search spaces" with a dynamic, stack-managed iterative process. Specifically, the "1-tailed" strategy ensures that every successful execution yields an effective lattice basis update, thereby eliminating the ineffective iterations associated with IQOAP. Concurrently, the dynamic iterative process reduces the required qubit count, thereby avoiding the limitation of an oversized search space inherent to PSA. We validate IPSA on the Baihua superconducting quantum processor via the Quafu platform. Small-scale real hardware experiments demonstrate that, compared to PSA, IPSA achieves a 14-fold increase in success rate at a cost of less than double the total circuit depth. Conversely, compared to IQOAP, IPSA reduces the total circuit depth by 82.7% while achieving approximately 2.5 times its success rate. Furthermore, we also conduct numerical simulations whose results are in good agreement with the experimental findings and extend our analysis.