[Paper Review] NMR GHZ

Raymond Laflamme, Emanuel Knill+3 more|arXiv (Cornell University)|Sep 11, 1997

Biofield Effects and Biophysics70 citations

TL;DR

This paper demonstrates the experimental preparation of a three-qubit Greenberger-Horne-Zeilinger (GHZ) entangled state |000⟩+|111⟩ using nuclear magnetic resonance (NMR) in trichloroethylene molecules, employing proton and carbon nuclear spins. State tomography confirmed the state fidelity, marking a key advancement in multi-qubit entanglement for quantum information processing.

ABSTRACT

We describe the creation of a Greenberger-Horne-Zeilinger (GHZ) state of the form |000>+|111> (three maximally entangled quantum bits) using Nuclear Magnetic Resonance (NMR). We have successfully carried out the experiment using the proton and carbon spins of trichloroethylene, and confirmed the result using state tomography. We have thus extended the space of entangled quantum states explored systematically to three quantum bits, an essential step for quantum computation.

Motivation & Objective

• To extend the exploration of entangled quantum states to three qubits, a critical requirement for scalable quantum computation.
• To demonstrate the preparation of a genuine three-qubit GHZ state |000⟩+|111⟩ in a controlled physical system.
• To validate the state using quantum state tomography, ensuring high-fidelity preparation of the entangled state.
• To establish a systematic platform for generating and verifying complex entangled states in NMR-based quantum information systems.

Proposed method

• Utilized the proton and carbon nuclear spins of trichloroethylene as three qubits in an NMR quantum processor.
• Applied a sequence of radiofrequency pulses to prepare the initial state and implement unitary operations for entanglement generation.
• Employed a controlled unitary evolution to create the superposition |000⟩+|111⟩ from a product state.
• Performed quantum state tomography using a set of measurement bases to reconstruct the density matrix of the final state.
• Analyzed the reconstructed density matrix to verify the presence and fidelity of the GHZ state.
• Confirmed the entanglement by verifying the state's non-separability and fidelity against the ideal GHZ state.

Experimental results

Research questions

• RQ1 Can a three-qubit GHZ state be experimentally realized in an NMR system using nuclear spins?
• RQ2 What is the fidelity of the prepared three-qubit entangled state as measured by state tomography?
• RQ3 How can the entanglement in a three-qubit system be verified and characterized in a liquid-state NMR platform?
• RQ4 What are the experimental limitations in scaling NMR-based quantum states beyond two qubits?

Key findings

• The three-qubit GHZ state |000⟩+|111⟩ was successfully prepared using proton and carbon nuclear spins in trichloroethylene.
• State tomography confirmed the experimental state's fidelity to the ideal GHZ state, validating the entanglement.
• The experiment demonstrated a systematic extension of entangled state preparation to three qubits in an NMR system.
• The results show that NMR is a viable platform for generating and verifying complex multi-qubit entangled states.