The vast majority of real-life optimization problems with a large number of degrees of freedom are intractable by classical computers, since their complexity grows exponentially fast with the number of variables. Many of these problems can be mapped into classical spin models, such as the Ising, the XY or the Heisenberg models, so that optimization problems are reduced to finding the global minimum of spin models. Here, we propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model. By imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites and read out the result of the global minimization through the relative phases. Besides solving optimization problems, polariton graphs can simulate a large variety of systems undergoing the U(1) symmetry-breaking transition. We realize various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on a linear chain, the unit cells of square and triangular lattices, a disordered graph, and demonstrate the potential for size scalability on an extended square lattice of 45 coherently coupled polariton condensates. Our results provide a route to study unconventional superfluids, spin liquids, Berezinskii–Kosterlitz–Thouless phase transition, and classical magnetism, among the many systems that are described by the XY Hamiltonian.

古典计算机很难解决绝大多数具有大量自由度的现实优化问题，因为它们的复杂度随着变量数量的增加而呈指数增长。这些问题中的许多问题都可以映射到经典的自旋模型中，例如Ising，XY或Heisenberg模型，以便将优化问题减少到找到自旋模型的全局最小值。在这里，我们提出并研究了极化子图作为寻找XY全局最小值的有效模拟模拟器的潜力。模型。通过刻印定制几何形状的极化子凝聚晶格，我们表明我们可以设计晶格位点之间的各种耦合强度，并通过相对相读出全局最小化的结果。除解决优化问题外，极化子图还可以模拟经历U的多种系统（1）打破对称的过渡。我们实现了各种磁性相，例如线性链上的铁磁性，反铁磁性和受挫自旋结构，正方形和三角形晶格的晶胞，无序图，并展示了在45的扩展正方形晶格上尺寸可扩展性的潜力相干耦合的极化子冷凝物。我们的结果为研究XY哈密​​顿量描述的许多系统中的非常规超流体，自旋液体，贝雷津斯基-科斯特利茨-不思议的相变和经典磁性提供了一条途径。