Complexity continuum within Ising formulation of NP problems
Abstract
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 NPhard 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 kregular 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 NPhard class of problems can be a starting point in developing a standardised procedure for the performance evaluation of emerging physical simulators and physicsinspired algorithms.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 DOI:
 10.48550/arXiv.2008.00466
 arXiv:
 arXiv:2008.00466
 Bibcode:
 2020arXiv200800466K
 Keywords:

 Quantum Physics;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Computational Complexity;
 Computer Science  Emerging Technologies;
 Physics  Computational Physics
 EPrint:
 11 pages, 4 figures