It is proved in this paper that to every underdetermined linear system Ax = b there corresponds a constant p(A, b) > 0 such that every solution to the lp-norm minimization problem also solves the l0-norm minimization problem whenever 0 < p < p(A, b). This phenomenon is named NP/CLP equivalence.

Understanding NP-complete problems is a central topic in computer science (NP stands for nondeterministic polynomial time). This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer. The efficiency of this approach is limited by small spectral gaps between the ground and excited states of the...