Generalized Jaynes-Cummings model as a quantum search algorithm

TL;DR

This paper introduces a continuous-time quantum search algorithm based on a generalized Jaynes-Cummings model, which mimics Grover's algorithm with optimal search time proportional to the square root of the search space size.

Contribution

It presents a novel quantum search algorithm derived from a generalized Jaynes-Cummings model, connecting quantum optics with quantum search techniques.

Findings

The algorithm achieves quadratic speedup similar to Grover's algorithm.

Resonances between initial and target states enable efficient search.

The standard Jaynes-Cummings model is a special case of this quantum search framework.

Abstract

We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states. This algorithm behaves like Grover's algorithm; the optimal search time is proportional to the square root of the size of the search set and the probability to find the searched state oscillates periodically in time. In this frame, it is possible to reinterpret the usual Jaynes-Cummings model as a trivial case of the quantum search algorithm.