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Optimal T Counts under Sparsity: from QROM to State Preparation and Block Encoding
Many quantum algorithms require coherent access to classical data, often modeled by quantum read-only memory (QROM). We initiate the study of the $\mathrm{T}$ count of sparse QROM, in which only $s$ of the $2^n$ addresses store nonzero data. We prove that the optimal $\mathrm{T}$ count is $Θ\left(n+
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