# Scalable Quantum-Inspired Optimization through Dynamic Qubit Compression

arXiv: https://arxiv.org/abs/2412.18571 · HTML: https://mlsanity.com/paper/2412.18571/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Builds on (most cited first, 14 of 14)

- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [A practical heuristic for finding graph minors](https://mlsanity.com/paper/1406.2741/) (2014)
- [On the Emerging Potential of Quantum Annealing Hardware for Combinatorial Optimization](https://mlsanity.com/paper/2210.04291/) (2022)
- [Noise-Resilient Quantum Machine Learning for Stability Assessment of Power Systems](https://mlsanity.com/paper/2104.04855/) (2021)
- [Ising Model Optimization Problems on a FPGA Accelerated Restricted Boltzmann Machine](https://mlsanity.com/paper/2008.04436/) (2020)
- [Optimising Rolling Stock Planning including Maintenance with Constraint Programming and Quantum Annealing](https://mlsanity.com/paper/2109.07212/) (2021)
- [FastHare: Fast Hamiltonian Reduction for Large-scale Quantum Annealing](https://mlsanity.com/paper/2205.05004/) (2022)

## Built on by (most cited first, 1 of 1)

- [Binarizing Physics-Inspired GNNs for Combinatorial Optimization](https://mlsanity.com/paper/2507.13703/) (2025)

## Abstract (arXiv)

Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework that dynamically compresses large Ising models to fit available quantum hardware of different sizes. Thus, we aim to bridge the gap between large-scale optimization and current hardware capabilities. Our method leverages a physics-inspired GNN architecture to capture complex interactions in Ising models and accurately predict alignments among neighboring spins (aka qubits) at ground states. By progressively merging such aligned spins, we can reduce the model size while preserving the underlying optimization structure. It also provides a natural trade-off between the solution quality and size reduction, meeting different hardware constraints of quantum computing devices. Extensive numerical studies on Ising instances of diverse topologies show that our method can reduce instance size at multiple levels with virtually no losses in solution quality on the latest D-wave quantum annealers.