The key insights and highlights of the content are:
Quantum algorithms often perform better when given a promise about the input structure, such as the number of marked items in Grover's search algorithm. However, requiring this promise can be limiting.
The authors develop a modified approach for span program and state conversion algorithms that achieves improved average query complexity on easier inputs, without needing to know the input structure ahead of time.
The core idea is to run subroutines with exponentially increasing query complexities, and use novel techniques to flag when the computation should halt. This allows the algorithm to match the asymptotic performance of existing bounded error algorithms on the hardest inputs, while achieving better average performance on easier inputs.
As applications, the authors prove exponential and superpolynomial quantum advantages in average query complexity for several search problems, generalizing prior work on quantum search with advice.
The authors also discuss directions for future work, such as extending their techniques to prove average-case quantum advantages for other problems, and improving the error scaling in their state conversion algorithms.
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by Noel T. Ande... kl. arxiv.org 04-03-2024
https://arxiv.org/pdf/2303.00217.pdfDybere Forespørgsler