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arXiv · 2302.06749

Improved Algorithm and Lower Bound for Variable Time Quantum Search

Andris Ambainis·Martins Kokainis·Jevgēnijs Vihrovs
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Abstract

We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where $T=\sum_{i=1}^n t_i^2$ with $t_i$ denoting the time to check the $i$-th item. Our second result is a quantum lower bound of $\Omega(\sqrt{T\log T})$. Both the algorithm and the lower bound improve over previously known results by a factor of $\sqrt{\log T}$ but the algorithm is also substantially simpler than the previously known quantum algorithms.

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Andris Ambainis, Martins Kokainis, Jevgēnijs Vihrovs. 2023-02-13. Improved Algorithm and Lower Bound for Variable Time Quantum Search. https://doi.org/10.4230/lipics.tqc.2023.7

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