Quantum Dictionaries without QRAM

This paper presents an efficient gate-level implementation of a quantum dictionary: a data structure that can store a superposition of mappings from keys to values. The dictionary is stored as a fixed-length list of sorted address-value pairs, where the length of the list is the maximum number of entries that can be put in the dictionary. An addressed value can be extracted from (or injected into) the dictionary using $C \cdot (V + 2.5A) + O(V + A + C)$ expected Toffoli gates and $O(V + A)$ auxiliary qubits (where $C$ is the maximum capacity, $A$ is the address width, and $V$ is the value width).