Simple implementation of a quantum search with trapped ions

TL;DR

This paper presents a simple and efficient ion trap implementation of Grover's quantum search algorithm, reducing the physical steps to match the algorithm's theoretical complexity and demonstrating robustness to imperfections.

Contribution

It introduces a straightforward ion trap method for implementing Grover's algorithm with minimal steps, avoiding complex transformations and enabling both probabilistic and deterministic searches.

Findings

Physical steps scale as O(√N), matching theoretical complexity.

Implementation is simple and robust to initialization errors.

Allows demonstration of both probabilistic and deterministic Grover search.

Abstract

We propose an ion trap implementation of Grover's quantum search algorithm for an unstructured database of arbitrary length N. The experimental implementation is appealingly simple because the linear ion trap allows for a straightforward construction, in a single interaction step and without a multitude of Hadamard transforms, of the reflection operator, which is the engine of the Grover algorithm. Consequently, a dramatic reduction in the number of the required physical steps takes place, to just O(\sqrt{N}), the same as the number of the mathematical steps. The proposed setup allows for demonstration of both the original (probabilistic) Grover search and its deterministic variation, and is remarkably robust to imperfections in the register initialization.