图的K着色问题的量子框架

中文摘要 AI 辅助

图着色是一个众所周知的NP完全问题，在调度、寄存器分配、频率分配和网络优化中有着广泛的应用。量子计算在特定问题实例中提供了多项式甚至超多项式加速的潜力，然而实用的量子图着色方法必须仔细平衡量子比特资源、电路深度和约束执行。我们提出了一个求解器无关的量子框架用于$K$-着色。该框架包含一种新颖的编码和高效的约束实现，用于通过Grover搜索实现精确着色，以及通过量子近似优化算法（QAOA）和量子退火实现几乎最优着色。与最先进方法（SOTA）中使用$O(NK)$个量子比特不同，我们将量子比特需求降低到$O(N \log_2 K)$，并优化了执行邻接约束的比较器电路。此外，我们还加入了一个基于对称性的图缩减作为可选的预处理步骤，以在量子执行前进一步减小实例规模。

英文摘要

Graph coloring is a well-known NP-complete problem with applications in scheduling, register allocation, frequency assignment, and network optimization. Quantum computing offers the potential for polynomial or even super-polynomial speedups in certain problem instances, yet practical quantum graph coloring methods must carefully balance qubit resources, circuit depth, and constraint enforcement. We proposed a solver agnostic quantum framework for $K$-coloring. Along with a novel encoding and efficient constraint implementation for its exact coloring exploiting Grover search and almost optimal coloring by the Quantum Approximate Optimization Algorithm \emph{(QAOA)}, and \emph{Quantum Annealing}. Unlike using $O(NK)$ qubits as in \emph{SOTA}, we reduced the qubit requirements to $O(N \log_2 K)$, along with optimized comparator circuits enforcing adjacency constraints. Further symmetry-based graph reduction is incorporated as an optional preprocessing step to further reduce the instance size before quantum execution.

发表机构

• National Institute of Technology Rourkela（印度国家技术学院鲁尔基拉分校）

机构由 AI 辅助整理，请以论文原文为准。