Quantum computers are known to perform extremely well on a limited number of problems at this time. For real applications, such as path planning and search in graph analytics, are quantum computers expected to perform well? What are the advantages and disadvantages of using such machines for such applications?
Hello Ahmed
It will depend on the nature of problem you deal with. If you consider Graph isomorphism problem (GI), it seems to be in P (cf. Babai's work : Article Graph Isomorphism in Quasipolynomial Time
) but no definitive proof is given yet. However in Quantum algorithms research, GI is feasible in polynomial time :Article A proposal for an efficient quantum algorithm solving the gr...
Preprint The quantum algorithm for graph isomorphism problem
The intuition is : for problems that are in NP but not NP-complete, quantum algorithms will provide interesting solutions. For NP-complete problems, the intuition is speedup will not be much better than square root (as for Grover's algorithm) ... please read Scott Aaronson's research statement, it will give you much more insights/ideas : https://www.scottaaronson.com/research.pdf
Best wishes
1-If your Problem can be modeled and can be solved through Grover's algorithm then the problem will be favorite for Quantum Computer like breaking of cryptography.
2- The Simulation Problems of chemical structure and the discovery of new organic compounds will be the major application of Quantum Computer.
3-Teleportation through Quantum entanglement will be an other application of QCs.
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