Introduction to NMR Quantum Information Processing

TL;DR

This paper introduces nuclear magnetic resonance (NMR) techniques for quantum information processing, explaining how qubits are realized, controlled, and measured, and demonstrating simple quantum algorithms with experimental results.

Contribution

It provides a comprehensive overview of NMR-based quantum computing, including methods to implement and measure quantum algorithms using room temperature liquid state NMR.

Findings

NMR can implement basic quantum algorithms successfully.

Pseudopure states enable quantum computation despite mixed initial states.

NMR QIP has promising prospects for future experiments.

Abstract

After a general introduction to nuclear magnetic resonance (NMR), we give the basics of implementing quantum algorithms. We describe how qubits are realized and controlled with RF pulses, their internal interactions, and gradient fields. A peculiarity of NMR is that the internal interactions (given by the internal Hamiltonian) are always on. We discuss how they can be effectively turned off with the help of a standard NMR method called ``refocusing''. Liquid state NMR experiments are done at room temperature, leading to an extremely mixed (that is, nearly random) initial state. Despite this high degree of randomness, it is possible to investigate QIP because the relaxation time (the time scale over which useful signal from a computation is lost) is sufficiently long. We explain how this feature leads to the crucial ability of simulating a pure (non-random) state by using ``pseudopure'' states. We discuss how the ``answer'' provided by a computation is obtained by measurement and how this measurement differs from the ideal, projective measurement of QIP. We then give implementations of some simple quantum algorithms with a typical experimental result. We conclude with a discussion of what we have learned from NMR QIP so far and what the prospects for future NMR QIP experiments are.