Improved Algorithm and Lower Bound for Variable Time Quantum Search

• URL: http://arxiv.org/abs/2302.06749v3
• Date: Wed, 2 Aug 2023 18:02:50 GMT
• Title: Improved Algorithm and Lower Bound for Variable Time Quantum Search
• Authors: Andris Ambainis, Martins Kokainis, Jevg\=enijs Vihrovs
• Abstract summary: 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 $O(sqrtTlog n)$. Our second result is a quantum lower bound of $Omega(sqrtTlog T)$.
• Score: 1.2246649738388389
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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