A unitary whose first row is uniform over M entries is built as the inverse of a prior uniform-superposition circuit, placing the partial sum of the first M amplitudes in the |0> amplitude with O(log M) gates.
Solving nonlinear di fferential equations with differentiable quantum circuits
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Efficient quantum algorithm for weighted partial sums and numerical integration
A unitary whose first row is uniform over M entries is built as the inverse of a prior uniform-superposition circuit, placing the partial sum of the first M amplitudes in the |0> amplitude with O(log M) gates.