Graph Coloring with Quantum Annealing

Constrained quantum annealing of graph coloring

We investigate a quantum annealing approach based on real-time quantum dynamics for graph coloring. In this approach, a driving Hamiltonian is chosen so that constraints are naturally satisfied without penalty terms, and the dimension of the Hilbert space is considerably reduced. The total Hamiltonian, which consists of driving and problem Hamiltonians, resembles a disordered quantum spin chain. The ground state of the problem Hamiltonian for graph coloring is degenerate. This degeneracy is advantageous and is characteristic of this approach. Real-time quantum simulations in a small system dem…

Localization in the constrained quantum annealing of graph coloring

Constrained quantum annealing (CQA) is a quantum annealing approach that is designed so that constraints are satisfied without penalty terms. There is an analogy between the model for the CQA of graph coloring and a set of disordered spin chains. In the model for the CQA of graph coloring, disorder corresponds to the fluctuation of effective local fields that increase in a CQA process. Numerical simulations of effective fields and entanglement demonstrate how localization appears in the CQA. Some notable features appear in the concurrence, which is a measure of entanglement, plotted as a funct…

由前向退火辅助的逆向量子退火

Reverse quantum annealing assisted by forward annealing

提出一种将前向退火低质量解作为初始状态的通用方法，通过D-Wave量子退火器求解图着色问题，显著提升了逆向退火的解质量与适用范围，有效扩展了传统前向退火的计算能力。

受Qudit启发的图着色优化方法

Qudit-inspired optimization for graph coloring

本研究提出一种受多能级量子比特（qudit）启发的图着色优化算法，设计了qudit梯度下降和局域量子退火两种策略，在标准基准上性能优于现有最优算法，以低计算资源实现高质量解，推动量子启发优化领域进展。

Disorder-assisted graph coloring on quantum annealers

We are at the verge of a new era, which will be dominated by Noisy Intermediate-Scale Quantum Devices. Prototypical examples for these new technologies are present-day quantum annealers. In the present work, we investigate to what extent static disorder generated by an external source of noise does not have to be detrimental, but can actually assist quantum annealers in achieving better performance. In particular, we analyze the graph coloring problem that can be solved on a sparse topology (i.e. chimera graph) via suitable embedding. We show that specifically tailored disorder can enhance the…

图的K着色问题的量子框架

A Quantum Framework for K Coloring of Graphs

本文提出一个求解器无关的量子框架用于图的K着色，通过新颖编码和优化比较器电路将量子比特需求从O(NK)降至O(N log₂K)，并支持Grover搜索、QAOA和量子退火，可选对称性图缩减进一步减小实例规模。