## NMR Quantum Computing

Nuclear magnetic resonance (NMR) spectroscopy has become well established as a tool for exploratory experimental investigations of quantum computation. Fundamental gates, algorithms, error correction and other issues in quantum information theory have been demonstrated at the level of a few qubits using room temperature, solution state NMR systems.

Recently we successfully implemented the N = 3 case of the Deutsch-Jozsa algorithm using room temperature solution state NMR. This implementation was characterized by the choice of qubits, namely the C13 nuclei of alanine, and the resulting methods for processing the quantum information. The homonuclear nature of the qubits (henceforth qubit and spin are used interchangeably) demands qubit selective pulses throughout the realization, thus greatly complicating the experimental effort in comparison to a heteronuclear system. Furthermore the arrangement of couplings between qubits in alanine is such that the only reliable method for processing quantum information is along a chain of qubits, whose pattern of couplings is effectively A-B-C (the A-C coupling is too weak). This demands indirect" gate realizations using swapping techniques via intermediate spins and is more difficult than direct" realizations, possible in the fully coupled case. Although these restrictions are artificial at the level of a few qubits there is reason to believe that they will become important as the number of qubits increases. Therefore the ability to implement the associated information processing techniques will become crucial; hence our choice of this restrictive qubit system. Even at the low level of three qubits the resulting experiments were sufficiently complicated to motivate the development and use of a host of simplification techniques and experimental methods to construct the appropriate pulse sequence. Much of the literature bypasses or only briefly describes such details, which will become increasingly important as the number of qubits in NMR quantum computation implementations grows.

The results of this investigation are shown below for the C13 output spectra for alanine: (a) Fiducial spectrum, (b) f1 spectrum, (c) f42 spectrum,(d) f3 spectrum, (e) f4 spectrum, (f ) f5 spectrum, (g) f6 spectrum, (h) f7 spectrum, (i) f8 spectrum, (j) f9 spectrum, and (k) f10 spectrum. In each spectrum the leftmost multiplet corresponds to qubit 2, the central to qubit 1 and the rightmost to qubit 0. Insets provide enlargements of all antiphase and doubly antiphase multiplets. Details are provided in "arXiV:quant-ph/0105015 10 May 2001"