Experimental implementation of quantum gates with one and two qubits using Nuclear Magnetic Resonance

TL;DR

This paper demonstrates the experimental implementation of fundamental one- and two-qubit quantum gates using Nuclear Magnetic Resonance (NMR), showcasing the technique's practicality for quantum computing despite some scalability challenges.

Contribution

It presents a successful NMR-based experimental realization of key quantum gates with detailed procedures and quantum state tomography, highlighting NMR's potential in quantum information processing.

Findings

Implementation of single-qubit gates (Pauli-Z, Pauli-X, Hadamard) in NMR.

Realization of two-qubit gates using NMR techniques.

Quantum state tomography confirmed the accurate reconstruction of quantum states.

Abstract

Nuclear Magnetic Ressonance (NMR) is a widely used technique, with a long history of applications in chemestry, medicine, and material science. Twenty years ago, it emerged as a reliable source for quantum computing too, since the work of Cory. One of its major advantage is the ease with which arbitrary unitary transformations can be implemented, together with its experimental simplicity, that can be traced back to very simple NMR routines, which were being extensively used long before. However, some disadvantages came along, mostly related to experimental effort in the initialisation and measure processes, and scalability. In this work, we have successfully probed some simple quantum gates (Pauli-Z, Pauli-X and Hadamard) in one and two-qubit systems, realised in a NMR experiment. The work comprised a pseudo-pure state preparation, followed by the application of the gates, and a quantum tomography method, necessary to reconstruct the density matrix. The experiments were conducted with a chloroform sample, placed in a 300 MHz Bruker Avance II spectrometer, equipped with a superconducting magnet with a 7 T magnetic field.