Note on (active-)QRAM-style data access as a quantum circuit

TL;DR

This paper demonstrates how an active QRAM-like effect can be implemented as a quantum circuit with depth scaling as O(n + sqrt m), providing insights into quantum data access mechanisms.

Contribution

It introduces a method to realize active QRAM-like effects efficiently within quantum circuits, highlighting depth scaling and control operation requirements.

Findings

Realization of QRAM-like effect with depth O(n + sqrt m)

Analysis of controlled-U operations in the circuit

Insights into quantum data access mechanisms

Abstract

We observe how an active (i.e., requring $2^n$ parallel control operations) QRAM-like effect $$\sum_{y=0}^{N-1} |y\rangle\langle y| \otimes U^y_{\text{result},\text{memory}_y}$$ can be realized, as a quantum circuit of depth $O(n+\sqrt m)$ (where $m$ is the size of the result register) plus the maximum over all~$z$ of the circuit depths of controlled-$U^z$ operations.