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Improved Algorithm and Lower Bound for Variable Time Quantum Search
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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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Cited by 1 Pith paper
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Faster quantum linear system solver beyond the condition number
Two quantum linear system solvers are presented with query complexity independent of the condition number, scaling instead with an effective condition number or a solution-norm ratio.
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