Can we say that we've already have a lot quantum algorithms offer speed up over classical algorithms(at least polynomial)?

Question

The question is inspired by the comment of this link that people say we still don't have a lot of quantum algorithms that offer speed up over classical algorithms. While I found that on this website: Quantum Algorithm Zoo, it seems that there are already a lot of problems showing speed-up over classical algorithms(polynomial or exponential or more).

But rather strange thing is that the algorithm I often heard about is mainly these three: Grover's algorithm(Amplitude amplification), Hamiltonian Simulation, Phase estimation(Maybe I need to add Quantum Machine Learning? Not very familiar with that filed)$^{[1]}$. So the reason that we feel we don't have a lot of algorithms might be that a lot of algorithms are mainly based on these basic algorithms?

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$[1]$: The talk by Issac Chuang also mainly stated these several algorithms.

Answer 1

To have an algorithm is one thing, to be able to execute it is another thing. Think for example about HHL or Shor's algorithm, they have proven exponential speed up but to execute them successfuly is hard and maybe million qubits processor is needed for practical application. So, we have enough algorithms but the main issue on current quantum HW is to execute real world tasks successfuly. Moreover, in the cases above, we are still not sure how to efficiently implement a circuit for general case. In literature you can find many tailored examples but with known solution which is hardly something we want to do in practice where we are seeking unknown solutions.