NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, computer science, biology, philosophy and cryptography. There are intensive research on proving ‘N...

2 A Brief Introduction to Theory of Computation 3 2.1 Some Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Modelling Computation Turing Machines . . . . . . . . . . . . 3 2.3 NP Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Sample NP Problems . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Optimizations for NP Problems . . . . . . . . . . . . ...

Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) a complexity class containing many important but intractable problems like the satisfiability of potentially conflict constraints (SAT). According well-founded exponential time hypothesis, verifying an SAT instance size $n$ requires generally c...