Quantum Dictionaries without QRAM

TL;DR

This paper introduces a gate-level implementation of quantum dictionaries that efficiently stores superpositions of key-value mappings without requiring QRAM, using a fixed-length sorted list and optimized gate complexity.

Contribution

It provides a novel, efficient quantum dictionary design that operates at the gate level without QRAM, with explicit resource estimates for gates and qubits.

Findings

Uses $C imes (V + 2.5A)$ expected Toffoli gates

Requires $O(V + A)$ auxiliary qubits

Stores superpositions of key-value mappings efficiently

Abstract

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).