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I have just started reading the paper A Grand Unification of Quantum Algorithms. There is a claim on page 2 that "by simply adjusting the parameters of QSVT, one can construct nearly all known quantum algorithms".

On the same page, the paper states explicitly that algorithms for the search problem, factoring/phase estimation, Hamiltonian simulation, HHL can all be derived from the QSVT. So now I am wondering - what are some examples of known algorithms that are not encompassed by this framework?

Miriam K.
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1 Answers1

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Today I have reached page 24 of the above-linked paper and I found a sentence that partially answers the question:

Notably, various quantum algorithms have not yet been constructed from QSVT-based subroutines, such as variational algorithms like the variational quantum eigensolver or the quantum approximate optimization algorithm. It would be fascinating to see if QSVT can encompass, or perhaps even enhance, these hybrid quantum algorithms as well.

Miriam K.
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