Construction and implementation of NMR quantum logic gates for two spin systems

Area of Science:

• Quantum Computing
• Nuclear Magnetic Resonance (NMR) Spectroscopy
• Quantum Information Science

Background:

• Ensemble quantum computing using NMR measurements is a key method for studying small quantum computer prototypes.
• Access to a diverse set of logic gates is crucial for laboratory-based quantum computing research.
• Developing efficient methods to translate quantum logic operations into experimental protocols is essential.

Purpose of the Study:

• To introduce a systematic approach for reducing quantum logic gates into NMR pulse sequences.
• To provide a method for generating pulse sequences for all permutations of a four-level quantum system.
• To experimentally implement representative quantum logic operations using NMR.

Main Methods:

• Representing quantum logic operations as permutation matrices derived from their truth tables.
• Utilizing these permutation matrices as propagators for NMR transitions.
• Deriving NMR pulse sequences from the calculated propagators.
• Implementing derived pulse sequences on a 13C-labeled chloroform system (a two spin-1/2 system).

Main Results:

• A systematic methodology for deriving NMR pulse sequences from quantum logic gates was established.
• Pulse sequences for all permutations of a four-level system were successfully derived.
• Experimental implementations of selected quantum logic operations were demonstrated on a NMR system.

Conclusions:

• The developed approach provides a direct and systematic route from quantum logic operations to NMR pulse sequences.
• This method facilitates the construction and testing of quantum logic gates for NMR-based quantum computing.
• The experimental validation confirms the feasibility and effectiveness of the proposed technique for quantum information processing.