5 - Implementation of quantum algorithms by NMR

Abstract

After the discovery of pseudo-pure states, a number of papers appeared in the literature reporting the practical implementation of quantum algorithms by nuclear magnetic resonance (NMR)—including Deutsch, Deutsch–Jozsa, Grover search, and Shor factorization algorithms—besides various examples of protocols to simulate quantum systems. There are also those experiments that implemented protocols to test quantum correlations such as entanglement. This chapter discusses various implementations of quantum algorithms by NMR. Quantum Fourier transform (QFT) is a key step for quantum algorithms, which exhibit exponential speed up. Its main application is in the Shor's factorization algorithm, which uses order finding and period finding. These are in turn variations of the general procedure known as phase estimation. For its importance in NMR quantum information processing (QIP), the chapter also includes some descriptions of quantum simulation experiments and discrete Wigner function measurements.