用于蛋白质-蛋白质相互作用网络对齐的量子优化

中文摘要 AI 辅助

蛋白质-蛋白质相互作用（PPI）网络对齐结合拓扑结构与序列信息，以识别跨物种的保守模块，但全局对齐仍具挑战性：启发式算法牺牲最优性，而精确方法缺乏可扩展性。我们将该对齐建模为加权最大公共诱导子图问题，并通过模积图将其重新表述为补图上的最小权重顶点覆盖，其中节点权重携带序列相似性信息。为解决此问题，我们开发了一种混合框架，结合核化、分支定界法及7种量子近似优化算法（QAOA）公式。这些公式在覆盖约束的实施方式上存在差异，从代价哈密顿量中的惩罚项到限制在可行子空间的混合器。对于单轮QAOA，我们推导了4种循环混合器变体的期望代价闭式表达式，无需电路模拟即可实现性能表征。将其应用于简化为KEGG通路的合成与真实网络，QAOA公式在对齐核心上实现了高拓扑保守性，同时至少保持与领先经典对齐器相当的生物保守性，但节点覆盖有所降低。在选定的KEGG通路中，对齐的子网保留了疾病相关蛋白质，维持了生物相关信息。成本较低的公式会留下更多未覆盖的边，而在混合器中实施可行性会使电路深度提高1至2个数量级。这些结果共同凸显了量子优化在PPI网络对齐中的潜力，以及随着量子硬件成熟将影响其可扩展性的资源权衡。

英文摘要

Protein-protein interaction (PPI) network alignment combines topological and sequence information to identify conserved modules across species, but global alignment remains challenging: heuristics sacrifice optimality, while exact methods lack scalability. We model the alignment as a weighted maximum common induced subgraph problem and reformulate it through the modular product graph to a minimum-weight vertex cover on the complement, with node weights carrying sequence similarity. To solve this problem, we develop a hybrid framework combining kernelisation, branch-and-bound, and seven Quantum Approximate Optimisation Algorithm (QAOA) formulations. These formulations differ in how the cover constraints are enforced, from penalty terms in the cost Hamiltonian to mixers confined to the feasible subspace. For single round QAOA, we derive closed-form expressions for the expected cost of four circulant mixer variants, enabling performance characterisation without circuit simulation. Applied to synthetic and real-world networks reduced to KEGG pathways, the QAOA formulations achieve high topological conservation on the aligned core while at least maintaining biological conservation comparable to leading classical aligners, at the cost of reduced node coverage. Across selected KEGG pathways, the aligned subnetworks retain disease-associated proteins, preserving biologically relevant information. Cheaper formulations leave more edges uncovered, while enforcing feasibility in the mixer raises circuit depth by one to two orders of magnitude. Together, these results highlight the potential of quantum optimisation for PPI network alignment and the resource trade-offs that will shape its scalability as quantum hardware matures.

发表机构

• University of Hamburg（汉堡大学）
• Parity Quantum Computing Germany GmbH（帕里特量子计算德国有限公司）
• Parity Quantum Computing GmbH（帕里特量子计算有限公司）
• Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）
• Department of Mathematics and Computer Science, University of Southern Denmark（南丹麦大学数学与计算机科学系）

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