No, quantum computing does not provide a promise of solving all NP-complete problems efficiently. While quantum computing has the potential to offer computational advantages over classical computers for certain problems, including some NP-complete problems, it does not imply that all NP-complete problems can be solved in polynomial time using quantum computers.
NP-complete problems are a class of computational problems that are believed to be intractable for classical computers, meaning that the best-known algorithms for solving these problems have exponential time complexity. The existence of a polynomial-time algorithm for any NP-complete problem would imply that P = NP, which is an unsolved problem in computer science.
Quantum computing does not fundamentally change the complexity class of NP-complete problems. While quantum algorithms, such as Grover's algorithm, can provide speedup over classical algorithms for certain types of searches, they do not offer a general polynomial-time solution to all NP-complete problems.
Furthermore, it is important to note that quantum algorithms have specific constraints and limitations. Quantum algorithms can potentially provide speedup for specific problem types, such as factoring large numbers with Shor's algorithm or solving optimization problems with the Quantum Approximate Optimization Algorithm (QAOA). However, these algorithms do not address the full class of NP-complete problems.
In summary, while quantum computing has the potential to offer computational advantages for some NP-complete problems, it does not guarantee a general polynomial-time solution for all NP-complete problems. The complexity class of NP-complete problems remains a challenge for both classical and quantum computing.