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

Marco Baioletti, Fabrizio Fagiolo, Angelo Oddi, Riccardo Rasconi

TL;DR

This work tackles the Qubit Routing Problem (QRP) on NISQ architectures by introducing DIRSH, a divide-and-conquer search that partitions circuits into chunks and uses a stochastic, heuristic-guided gate selection moderated by a multi-armed bandit to adapt parameters. The method balances global search via restarts and local pruning, while updating the qubit assignment as swaps are added. Empirical results on RevLib circuits mapped to the 20-qubit IBMQ Tokyo topology show that DIRSH consistently outperforms LightSABRE variants across budgets $T ightarrow ig"{10,20,30,60}$ seconds, achieving shorter depths $de$ and fewer swaps $sw$. This demonstrates that chunk-based decomposition combined with bandit-driven heuristics is effective for quantum circuit routing on NISQ devices, with future directions including noise-aware cost models, better initial qubit allocations, and dynamic chunking.

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.

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

TL;DR

This work tackles the Qubit Routing Problem (QRP) on NISQ architectures by introducing DIRSH, a divide-and-conquer search that partitions circuits into chunks and uses a stochastic, heuristic-guided gate selection moderated by a multi-armed bandit to adapt parameters. The method balances global search via restarts and local pruning, while updating the qubit assignment as swaps are added. Empirical results on RevLib circuits mapped to the 20-qubit IBMQ Tokyo topology show that DIRSH consistently outperforms LightSABRE variants across budgets seconds, achieving shorter depths and fewer swaps . This demonstrates that chunk-based decomposition combined with bandit-driven heuristics is effective for quantum circuit routing on NISQ devices, with future directions including noise-aware cost models, better initial qubit allocations, and dynamic chunking.

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.

Paper Structure

This paper contains 9 sections, 6 equations, 5 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem definition
  4. Proposed Algorithm
  5. Empirical Evaluation
  6. Setup
  7. Results
  8. Conclusions and Future Work
  9. Additional Material

Figures (5)

  • Figure 1: Values of $\Delta$ for Depth and SWAP with time budget $T = 10$s. Positive values indicate that DIRSH outperforms LightSABRE.
  • Figure 2: Values of $\Delta$ for Depth and SWAP with time budget $T = 20$s. Positive values indicate that DIRSH outperforms LightSABRE.
  • Figure 3: Values of $\Delta$ for Depth and SWAP with time budget $T = 30$s. Positive values indicate that DIRSH outperforms LightSABRE.
  • Figure 4: Values of $\Delta$ for Depth and SWAP with time budget $T = 60$s. Positive values indicate that DIRSH outperforms LightSABRE.
  • Figure 5: Average of the percentage deviations across all instances, in the depth minimization case (blue) and in the swap minimization case (orange).