NP问题伊辛公式内的复杂性连续统
Complexity continuum within Ising formulation of NP problems
摘要：
一个有前途的方法，以实现计算霸权的经典冯诺依曼架构探索经典和量子硬件作为伊辛机。伊辛哈密顿量的最小化是已知的NP-困难的问题，某些相互作用矩阵类，但不是所有的问题实例都同样难以优化。我们建议确定计算简单的情况下，一个“优化简单性标准”。这种优化的简单性，可以发现广泛的模型，从自旋玻璃k-正则最大切割问题。许多光学，光子和电子系统的神经形态架构，可以自然地操作，以优化满足这一标准的问题，因此，这些问题往往被选择来说明新的伊辛机的计算优势。我们进一步探讨了稀疏和密集模型的中间复杂性，通过分析循环耦合矩阵，可以“重新布线”，以引入更大的复杂性。一个令人信服的方法来区分容易和困难的情况下，在同一个NP难类的问题可以是一个起点，在开发一个标准化的程序，新兴的物理模拟器和物理启发的算法的性能评估。
英文摘要：
A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for certain interaction matrix classes, yet not all problem instances are equivalently hard to optimise. We propose to identify computationally simple instances with an `optimisation simplicity criterion'. Such optimisation simplicity can be found for a wide range of models from spin glasses to k-regular maximum cut problems. Many optical, photonic, and electronic systems are neuromorphic architectures that can naturally operate to optimise problems satisfying this criterion and, therefore, such problems are often chosen to illustrate the computational advantages of new Ising machines. We further probe an intermediate complexity for sparse and dense models by analysing circulant coupling matrices, that can be `rewired' to introduce greater complexity. A compelling approach for distinguishing easy and hard instances within the same NP-hard class of problems can be a starting point in developing a standardised procedure for the performance evaluation of emerging physical simulators and physics-inspired algorithms.
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