We present new designs for quantum random access memory. More precisely, for each function, f:F2n→F2d, we construct oracles, Of, with the property \begin{equation} \mathcal{O}_f \left| x \right\rangle_n \left| 0 \right\rangle_d = \left| x \right\rangle_n \left| f(x) \right\rangle_d. \end{equation} Our methods are based on the Walsh-Hadamard Transform of f, viewed as an integer valued function. In general, the complexity of our method scales with the sparsity of the Walsh-Hadamard Transform and not the sparsity of f, yielding more favorable constructions in cases such as binary optimization problems and function with low-degree Walsh-Hadamard Transforms. Furthermore, our design comes with a tuneable amount of ancillas that can trade depth for size. In the ancilla-free design, these oracles can be ε-approximated so that the Clifford + T depth is O((n+log2(εd))Wf), where Wf is the number of nonzero components in the Walsh-Hadamard Transform. The depth of the shallowest version is O(n+log2(εd)), using n+dWf qubit. The connectivity of these circuits is also only logarithmic in Wf. As an application, we show that for boolean functions with low approximate degrees (as in the case of read-once formulas) the complexities of the corresponding QRAM oracles scale only as 2O(nlog2(n)).