Note on (active-)QRAM-style data access as a quantum circuit
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We observe how an active (i.e., requring 2^n parallel control operations) QRAM-like effect ∑_y=0^N-1 |y〉〈 y| ⊗ U^y_result,memory_y can be realized, as a quantum circuit of depth O(n+√(m)) (where m is the size of the result register) plus the maximum over all z of the circuit depths of controlled-U^z operations.
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