Scalable Quantum-Inspired Optimization through Dynamic Qubit Compression

TL;DR

This work tackles the qubit-count bottleneck in near-term quantum optimization by mapping large Ising problems to Ising Hamiltonians and compressing them with GRANITE, a quantum-inspired framework that uses a physics-informed Graph Neural Network to predict ground-state spin alignments and iteratively contract spins. By learning contraction rules and employing a hybrid loss to prioritize high-confidence merges, GRANITE achieves tunable, multi-level reductions while preserving solution quality, enabling larger instances to fit on quantum hardware such as the D-Wave Pegasus system and potentially benefiting gate-based approaches like QAOA. Empirical results across multiple graph topologies show substantial qubit reductions (down to a few percent of the original qubits) with minimal loss in optimal energy, outperforming random reduction baselines and offering a flexible preprocessing step for quantum optimization. The approach broadens the practical reach of quantum-inspired optimization on current devices and paves the way for applying dynamic qubit compression to real-world large-scale graphs and diverse quantum architectures.

Abstract

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.

Figures (2)

• Figure 1: GRANITE: Graph Neural Ising Transformer for Efficient Quantum Optimization. The model comprises three key components: a, A GNN that learns edge ($e_{uv}$) and node ($h_v$) representations, capturing the Ising model's structure and interactions. b, A prediction layer using logistic regression with softmax to calculate weighted binary cross-entropy, assigning confidence scores to potential actions. c, A link contraction process that executes the highest-confidence merge or flip-merge operation. During inference, the contracted graph is iteratively fed back into GRANITE until the desired reduction ratio is achieved, enabling the transformation of large-scale Ising problems into quantum-compatible formats.
• Figure 2: GRANITE vs. random, the random merge and flip-merge of edge for n = 200 across three different topologies.

Theorems & Definitions (8)

• Theorem 1
• Definition 1: TAUTOLOGY
• Definition 2: All-SAT-EQUAL
• Lemma 1
• proof
• Lemma 2: 3-SAT Clause Encoding
• proof
• proof