Graph-VQE: A CUDA-Q Multi-QPU Simulation Framework for Hamiltonian-Aware Protein-Folding VQE

Abstract: The Variational Quantum Eigensolver (VQE) is essential for molecular simulation in drug discovery, but hardware noise and algorithmic limits restrict its precision. While the NVIDIA CUDA-Q platform mitigates some hardware issues via exact simulation, it lacks Qiskit support and restricts parallelization. To solve this, we introduce Graph-VQE, a novel framework that extends CUDA-Q with optimization-level parallelism. Graph-VQE leverages amino acid sequence structures by partitioning Hamiltonian interaction graphs into weakly coupled clusters using Louvain community detection. These clusters undergo restricted updates on the full-Hamiltonian objective, followed by a global refinement stage utilizing Hamiltonian batching. Furthermore, a custom Qiskit-CUDA-Q integration layer enables standard workflows with GPU acceleration. Evaluations on protein folding tasks prove that Graph-VQE outperforms baselines, achieving lower final energies. It delivers competitive RMSD and binding affinity compared to AlphaFold3 and IBM quantum processors while maintaining stable quality across multi-GPU environments, thereby providing a highly practical path toward high-fidelity biomolecular simulations.

• The paper introduces a novel Hamiltonian-aware graph partitioning method within a multi-QPU VQE framework to accelerate protein folding simulations.
• It employs a hardware-efficient ansatz and Louvain community detection with CUDA-Q acceleration, ensuring improved optimization and binding affinity outcomes.
• Performance scaling is achieved through hierarchical parallelization, demonstrating lower energy minima and linear time reduction across computational resources.

Graph-VQE: Hamiltonian-Aware Multi-QPU VQE for Protein Folding on CUDA-Q

Introduction and Motivation

Variational Quantum Eigensolver (VQE) is foundational for quantum molecular simulation but remains bottlenecked by both quantum hardware limitations and classical optimization scale, precluding routine traversal into "biological size" conformation spaces required for practical applications in drug discovery and protein engineering. The "Graph-VQE" framework addresses both aspects synergistically, introducing a Hamiltonian-informed graph partitioning method paired with hierarchical, multi-QPU simulation, all within a CUDA-Q backend augmented via a Qiskit interoperability layer.

Unlike prior parallelized or batched VQE approaches that fail to respect interaction topology or only accelerate measurement steps, Graph-VQE performs optimization-level parallelization on biologically motivated, modular communities, ensuring that the structure of amino acid coupling is reflected in the decomposition and thereby improving both fidelity and performance. Results demonstrate strong improvement in both solution energy and end-task proxies such as RMSD and binding affinity, with stable scaling behavior as the number of GPUs increases.

Figure 1: Binding affinity of Graph-VQE-predicted folds versus AlphaFold3 and IBM quantum processors for key protein fragments; lower energies reflect stronger binding.

Methodological Innovations

Hamiltonian Construction and Encoding

The system Hamiltonian incorporates both physical (Miyazawa-Jernigan interactions) and geometric penalty terms mapped onto a tetrahedral lattice. Each conformation is parameterized as a sequence of turns, reducing spatial degrees of freedom and enabling an encoding on $N = 2(L-1)$ qubits for a sequence of length $L$.

Figure 2: The pipeline from sequence input to lattice-based Hamiltonian suitable for VQE mapping.

Hardware-Efficient Ansatz and CUDA-Q Kernels

Graph-VQE utilizes a hardware-efficient EfficientSU2 ansatz, supporting flexible entanglement layouts (linear, circular, all-to-all), mapped directly to CUDA-Q's JIT-compiled quantum circuits to accelerate variational updates and expectation value evaluations. Measurement overhead is mitigated through shot parallelization.

Figure 3: Layered EfficientSU2 ansatz structure with variable entanglement; depth and entangling topology are tuned to balance expressibility and trainability.

Hamiltonian-Aware Partitioning and Louvain Community Detection

A Pauli-operator-based weighted interaction graph is constructed from Hamiltonian coefficients. The Louvain algorithm partitions this graph into weakly coupled communities, aligning with biochemically meaningful motif boundaries and ensuring strongly interacting residues and their encoding qubits are co-optimized. The modularity criterion guarantees dense intra-block and weak inter-block edge weights.

Hierarchical Parallelization Protocol

The optimization is split into two tiers: an initial phase of block-wise parameter optimization in which each GPU runs a VQE loop for a distinct community with remaining parameters fixed, followed by a global refinement phase wherein all parameters are updated jointly, with Hamiltonian term batching utilized to distribute the expectation calculation across GPUs.

Figure 4: Workflow of Graph-VQE: partitioning by Louvain community detection, concurrent block-wise optimization (task parallelism), followed by global refinement utilizing Hamiltonian batching (data parallelism) on multiple QPUs.

Structure Decoding

Post-optimization, the dominant computational basis state is decoded into a 3D lattice walk, enabling direct pipeline output to 3D coordinates for external docking and RMSD analysis.

Figure 5: Bitstring-to-structure decoding flow, reconstructing the folded geometry on the tetrahedral lattice.

Experimental Analysis

Shot Count Optimization

A shot-budget analysis establishes that higher measurement counts yield significantly deeper minima, with a transition from suboptimal local solutions ($-183$ at 2048 shots) to near-optimal values ($-390$ at 8192 shots), confirming the need for large estimation budgets in noisy VQE settings.

Figure 6: Average best energy as a function of measurement shots for Graph-VQE (circular entanglement); higher shot counts systematically improve minima.

Comparative Benchmarking Across Methods

Graph-VQE consistently achieves lower energy minima across multiple peptide motifs and diverse ansatz entanglement configurations. Its advantage is especially marked in hexapeptide cases, outperforming baselines such as SeqVQE, EQC, ADAPT-VQE, and CVaR-VQE by factors of 2.5×--4× in solution energy, reaching beneath $-640$ in the most challenging conformational regimes. Notably, Graph-VQE not only beats global baselines but, via ablation, is shown to require both the community-based parallel phase and the global refinement for optimal convergence: in a subset of cases, omitting refinement leads to superior block-level results, hinting at entanglement-topology-specific landscape structure. In the head-to-head with ADAPT-VQE, Graph-VQE's Hamiltonian-informed partitioning clearly induces deeper minima.

Figure 7: Energy minima comparison between ADAPT-VQE and Graph-VQE under circular entanglement for both stabilizing and competing interaction peptides.

Scaling and Efficiency

Scalability analysis demonstrates near-linear reduction in time-to-solution with increasing GPU count, with negligible regression in final solution energy, even as the computational load increases.

Figure 8: Graph-VQE shows linear decrease in wall-clock time per iteration with more GPUs while maintaining solution quality.

Trajectory and End-Task Proxy Results

Energy-versus-time curves show that baselines rapidly stall in energy minimization even given equal wall time, while Graph-VQE infractions continue descending to deeper minima, especially in more complex motif classes. Structural RMSD and predicted binding affinity against AlphaFold3 and IBM quantum-procured folds show Graph-VQE to be competitive or superior (see especially the more negative binding energies, as in Figure 1, and the RMSD table).

Figure 9: Comparison of energy convergence dynamics; Graph-VQE continues to find lower-energy states over time, especially on challenging competing-interaction motifs, whereas baselines plateau much earlier.

Backend Implementation and Practical Considerations

Graph-VQE chooses the CUDA-Q multi-QPU backend, eschewing memory pooling and tensor network approaches to avoid truncation-induced errors and maximize entanglement handling. Attempts to overlap multi-GPU memory pooling with multi-QPU partitioning are infeasible due to backend conflicting assumptions regarding amplitude ownership.

Figure 10: CUDA-Q backend designs—memory pooling (left, for single large state vectors) cannot be combined with independent QPU simulation (right, as used by Graph-VQE for parallel optimization of disjoint blocks).

Hyperparameter spaces—Louvain resolution, ansatz depth, measurement shots, early stopping and patience—require tuning contingent on both system scale and motif class; e.g., larger block counts accelerate partial minimizations but risk missing inter-block couplings.

Implications and Outlook

The Graph-VQE framework yields practical advances for quantum biomolecular simulation, especially in mapping physical system modularity to optimization and hardware parallelism. This approach demonstrably closes the gap between specialized quantum simulation and mainstream computational drug discovery: the combination of Hamiltonian-aware block optimization and efficient global refinement allows scale-out to complex motifs. Importantly, the achieved RMSD/binding affinity metrics are competitive with established classical (AlphaFold3) and experimental (IBM QPU) baselines, indicating the physical plausibility of the folded conformations.

In principle, this framework generalizes beyond tetrahedral lattice models and, with increased qubit capacity, is well-poised to address larger, more realistic biomolecular systems. The demonstrated Qiskit-CUDA-Q translation further lowers the barrier for adoption in quantum chemistry workflows.

Conclusion

Graph-VQE introduces a robust, parallelizable, and biologically grounded approach to scaling VQE for protein folding and related quantum chemical problems. Its combination of community detection-based Hamiltonian partitioning, hierarchical multi-QPU scheduling, and high-efficiency simulation within CUDA-Q—backstopped by domain-proven ansatzes and Qiskit compatibility—yields superior optimization quality and wall-time scaling. These results point toward a path through which quantum algorithms may soon tackle challenging, real-world biological and medicinal chemistry systems with accuracy competitive with or superior to leading classical methods (2607.02749).