Is it possible that in the future quantum algorithms find a better solution than their classical counterparts for every classical problem or maybe their usability is limited to just special problems?
By better solution, i meant if they provide speedup for any problem or they are just limited to certain problems. Because until now we see that there are just a few algorithms which are applicable to certain problems.
No. This was studied, for instance, here: Article A Limit on the Speed of Quantum Computation in Determining Parity
and here:Article A Limit on the Speed of Quantum Computation for Insertion in...
We do not have any particular result telling us that, for sure, every classical algorithm has a quantum homolgous that provide "better solution". Potentially, it depends on the faculty of humans to find a "quantum way" to do the same action as the classical algorithm, but in a quantum way, exploiting entaglement, or parallelisation of states, etc.
We can maybe find some algorithms, for which, we are sure that any other quantum algorithm homologous cannot be "better".
Dear Dr. Zomorodi
increasing of speed in quantum algorithms is related to feature of superposition of qubits. this feature can help to solving problems with exponential order and convert them to linear order. So, certainly, this feature can help us for problems in specific domain and threshold (well-known as P problems). if we want think about solving biggest problem such as analysis of the universe, So, we need to adding other features in computations that can help us to solving this problem very fast that still are unknown.
of course, it is important to notice that quantum science still is unknown. it means that, really we don't know that whats happen in quantum world? and in future, it is possible to discovery other features that can help us for solving this problem.
Regards
Moein
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