P versus NP equality

Determine whether the deterministic polynomial-time complexity class P equals the nondeterministic polynomial-time class NP; that is, establish whether every decision problem whose solutions can be verified in polynomial time can also be solved in polynomial time.

Background

In the book’s discussion of computational complexity and the role of quantum computing, the author introduces the class BQP and contrasts it with classical complexity classes. Within this context, the longstanding P versus NP problem is explicitly cited as one of the century-old open questions in computer science.

The resolution of P versus NP would fundamentally reshape our understanding of efficient computation, algorithm design, and cryptography. Its mention frames the broader landscape in which quantum computing’s capabilities are evaluated.