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Efficient Preparation of Entangled States in Cavity QED with Grover's Algorithm.

Omar Nagib1, M Saffman1, K Mølmer2

  • 1University of Wisconsin-Madison, Department of Physics, 1150 University Avenue, Madison, Wisconsin 53706, USA.

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We propose a new method using Grover's search algorithm to create entangled quantum states in multiple qubits. This technique deterministically prepares complex atomic states with minimal photon interactions, advancing quantum information processing.

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Area of Science:

  • Quantum Information Science
  • Atomic Physics
  • Quantum Computing

Background:

  • Entangled states are crucial for quantum computing and communication.
  • Efficiently preparing entangled states, especially for ensembles of qubits, remains a challenge.
  • Existing methods often require individual atom addressing or complex experimental setups.

Purpose of the Study:

  • To develop an efficient method for preparing entangled states of atomic ensembles.
  • To leverage Grover's search algorithm for deterministic state preparation.
  • To explore the creation of specific multi-atom entangled states like Dicke, GHZ, and Schrödinger cat states.

Main Methods:

  • Utilizing the amplification mechanism of Grover's search algorithm.
  • Implementing conditional sign change via photon scattering on an optical cavity with an atomic ensemble.
  • Employing phase shifts of scattered photons to induce entanglement.

Main Results:

  • Deterministic preparation of collective Dicke states, Greenberger-Horne-Zeilinger states, and Schrödinger cat superpositions.
  • Achieving state preparation with a low number of photon scattering events (approximately N^{1/4}).
  • Demonstrating the feasibility without the need for individual atom addressing.

Conclusions:

  • The proposed method offers an efficient and deterministic route to multi-atom entanglement.
  • Grover's algorithm provides a powerful framework for quantum state preparation in atomic ensembles.
  • This approach has significant implications for building scalable quantum information processors.