The problem to find the ground state energy of an Ising-type Hamiltonian is known to be NP-hard . Recently, there have been two proposals in the community of quantum computing to tackle this problem. One is Yamamoto et al.'s coherent computing  that uses an injection-locked laser network; the other is the annealing machine using the commercial flux-qubit array cells produced by D-Wave System Inc . In this talk, I will explain my proof  of the existence of hard instances of the problem on the physical systems, which is based on known statistical properties of the problem (e.g., ). I will also discuss the possibility of error correction to mitigate the difficulty although this requires further investigations.