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Implementation of Quantum Computing Techniques on NMR Systems

Anurag Pallaprolu

Published Apr 1, 2014• 0 citations
OpenAlex

Abstract

This document is submitted as a partial requirement for the course Quantum Information and Computing, BITS Pilani. The phenomenon of NMR can be used to generate spin states of nuclei and these can be used as qubits for computational purposes, the speciality being, an ensemble of molecules must be utilized. This allows for an exponentiation in the processing power of the computer. The document explains about the setup, measurement and initialization of an NMR quantum computer.

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This document is submitted as a partial requirement for the course Quantum Information and Computing, BITS Pilani. The phenomenon of NMR can be used to generate spin states of nuclei and these can be used as qubits for computational purposes, the speciality being, an ensemble of molecules must be utilized. This allows for an exponentiation in the processing power of the computer. The document explains about the setup, measurement and initialization of an NMR quantum computer.
Nuclear Magnetic Resonance (NMR) forms a natural test-bed to perform quantum information processing (QIP) and has so far proven to be one of the most successful quantum information processors. The nuclear spins in a molecule treated as quantum bits or qubits which are the basic building blocks of a quantum computer. The development of NMR over half a century puts it in a platform where we can utilize its excellent control techniques over an ensemble of spin systems and perform quantum computation in a highly controlled way. Apart from a successful quantum information processor, NMR is also a highly powerful quantum platform where many of the potentially challenging quantum mechanical experiments can be performed.
The NMR quantum computer is one of the most established systems among many physical realizations of a quantum computer. In spite of its peculiar character associated with mixed states and lack of scalability, it still works as a prototypical quantum computer with at most 10 qubits. We should point out that it is the only quantum computer commercially available at the time of writing this book. For these reasons, an NMR quantum computer is introduced as one of the first examples of a physical system on which we can execute small-scale quantum algorithms. Qubits in this realization are nuclei with spin 1/2. Molecules with a certain number of such nuclei are employed as a quantum register. The system is made of a macroscopic number (∼ 1020) of moleclues in thermal equilibrium, and we have to take care of these aspects in preparation of a state and measurements as explained in this chapter. Our exposition follows [1] and [2]. Other useful review is [3].
This article reviews recent work done by us an some initial steps towards the implementation of quantum computation using liquid state NMR. We describe how special kinds of states required for such computation (called pseudo-pure states) can be created from a thermal ensemble of spins. We demonstrate the implementation of several quantum logic gates through one- and two-dimensional NMR methods, using transition- and spin- selective pulses. Finally, we discuss the implementation of the Deutsch-Jozsa algorithm using NMR.
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10-30 qubits.