Divide-et-impera Heuristic-based Randomized Search for the Qubit Routing Problem

2025-11-18

AI Summary

This work addresses the Quantum Bit Routing Problem (QRP) on Noisy Intermediate-Scale Quantum (NISQ) devices. We propose a heuristic-guided randomized divide-and-conquer search algorithm that integrates circuit partitioning, a multi-armed bandit–driven adaptive heuristic strategy, depth-sensitive local pruning, and restart mechanisms to dynamically balance global exploration and local optimization. Our key contributions are threefold: (i) the first integration of a divide-and-conquer framework with multi-armed bandit–based parameter adaptation for QRP; (ii) the introduction of topology-aware randomized gate–SWAP co-optimization; and (iii) empirical validation on the IBM Q Tokyo 20-qubit architecture, demonstrating consistent reductions in circuit depth and SWAP count across diverse time budgets—outperforming three LightSABRE variants. The method achieves superior scalability and robustness under realistic NISQ constraints.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper introduces the DIRSH algorithm for the Qubit Routing Problem (QRP), using a heuristic-guided randomized divide-and-conquer strategy. The method splits the circuit into chunks and optimizes each one with a stochastic selection of gates and swaps. It balances global search, via restarts and adaptive tuning of bandit parameters with depth-sensitive local pruning. Tested on RevLib benchmarks mapped to the 20-qubit IBMQ Tokyo topology, DIRSH outperformed three LightSABRE variants across different time budgets, achieving shorter depths and fewer swaps. These results confirm that combining chunk-based decomposition with bandit-driven heuristics is effective for routing quantum circuits on NISQ devices.

Problem

• Developed heuristic algorithm for quantum circuit routing optimization
• Addressed qubit mapping challenges on NISQ device architectures
• Solved depth and swap reduction in quantum compiler design

Innovation

• Divide-and-conquer strategy for circuit splitting
• Heuristic-guided randomized search with bandit tuning
• Depth-sensitive local pruning for optimization