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Grid-Partitioned MWIS Solving with Neutral Atom Quantum Computing for QUBO Problems

Soumyadip Das, Suman Kumar Roy, Rahul Rana, M Girish Chandra

TL;DR

The paper tackles NP-hard QUBO optimization by recasting it as a MWIS problem on unit disk graphs and solving at scale with neutral-atom quantum hardware. It introduces GP-NAQC, a four-step pipeline: map QUBO to MWIS, partition the layout with grids, solve subgraphs via Analog Hamiltonian Simulation, and greedily merge results into a global solution, enabling practical use on NISQ devices. Empirical results on a 50-asset portfolio show GP-NAQC achieving lower mean energies than classical simulated annealing with robust performance, highlighting hardware-aware gains from high qubit connectivity and Rydberg blockade physics. The framework provides a scalable, near-term path for quantum-accelerated optimization and lays groundwork for applying similar grid-partitioned quantum-classical hybrids to scheduling, clustering, and network design as hardware improves.

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in real-world applications, such as portfolio optimization, but pose significant computational challenges for large-scale instances. We propose a hybrid quantum-classical framework that leverages neutral atom quantum computing to address QUBO problems by mapping them to the Maximum Weighted Independent Set (MWIS) problem on unit disk graphs. Our approach employs spatial grid partitioning to decompose the problem into manageable subgraphs, solves each subgraph using Analog Hamiltonian Simulation (AHS), and merges solutions greedily to approximate the global optimum. We evaluate the framework on a 50-asset portfolio optimization problem using historical S&P 500 data, benchmarking against classical simulated annealing. Results demonstrate competitive performance, highlighting the scalability and practical potential of our method in the Noisy Intermediate-Scale Quantum (NISQ) era. As neutral atom quantum hardware advances, our framework offers a promising path toward solving large-scale optimization problems efficiently.

Grid-Partitioned MWIS Solving with Neutral Atom Quantum Computing for QUBO Problems

TL;DR

The paper tackles NP-hard QUBO optimization by recasting it as a MWIS problem on unit disk graphs and solving at scale with neutral-atom quantum hardware. It introduces GP-NAQC, a four-step pipeline: map QUBO to MWIS, partition the layout with grids, solve subgraphs via Analog Hamiltonian Simulation, and greedily merge results into a global solution, enabling practical use on NISQ devices. Empirical results on a 50-asset portfolio show GP-NAQC achieving lower mean energies than classical simulated annealing with robust performance, highlighting hardware-aware gains from high qubit connectivity and Rydberg blockade physics. The framework provides a scalable, near-term path for quantum-accelerated optimization and lays groundwork for applying similar grid-partitioned quantum-classical hybrids to scheduling, clustering, and network design as hardware improves.

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in real-world applications, such as portfolio optimization, but pose significant computational challenges for large-scale instances. We propose a hybrid quantum-classical framework that leverages neutral atom quantum computing to address QUBO problems by mapping them to the Maximum Weighted Independent Set (MWIS) problem on unit disk graphs. Our approach employs spatial grid partitioning to decompose the problem into manageable subgraphs, solves each subgraph using Analog Hamiltonian Simulation (AHS), and merges solutions greedily to approximate the global optimum. We evaluate the framework on a 50-asset portfolio optimization problem using historical S&P 500 data, benchmarking against classical simulated annealing. Results demonstrate competitive performance, highlighting the scalability and practical potential of our method in the Noisy Intermediate-Scale Quantum (NISQ) era. As neutral atom quantum hardware advances, our framework offers a promising path toward solving large-scale optimization problems efficiently.
Paper Structure (11 sections, 15 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 15 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Proposed Methodology
  4. QUBO-to-MWIS Mapping
  5. Grid Partitioning
  6. Analog Hamiltonian Simulation
  7. Greedy Merging
  8. Results and Discussion
  9. Dataset Description
  10. Conclusion
  11. Acknowledgement

Figures (2)

  • Figure 1: Workflow of the GP-NAQC framework: The QUBO problem is mapped to a unit disk graph, partitioned into subgraphs, solved via AHS, and merged greedily to obtain an approximate global solution.
  • Figure 2: Comparison of energies from GP-NAQC and simulated annealing across QUBO instances for portfolio optimization (left) and random QUBO problems (right). Error bars indicate standard deviation over five runs.