A Simple and Convenient Measure of NMR Rotor Fidelity

Composite pulses [1, 2, 3] play an important role in many NMR experiments, as they allow the effects of experimental imperfections, such as pulse length errors and off-resonance effects, to be reduced. In conventional NMR experiments these pulses are used to implement particular transformations on the Bloch sphere, such as inversion, and their quality can be easily assessed by determining the efficiency with which some known starting state is transferred to the desired final state. Furthermore the transfer efficiency can be both calculated and measured, allowing a simple comparison between theory and experiment. An alternative approach to composite pulses, developed by Tycko [4], seeks to design general rotors, that is pulses which perform well for any initial starting state. Composite pulses of this kind, which are sometimes called Class A composite pulses [2], are rarely (if ever) needed for conventional NMR experiments, but are useful in NMR implementations of quantum computation [5, 6, 7, 8, 9], where they act to reduce systematic errors in quantum logic gates [10]. With pulses of this kind conventional measures of transfer efficiency are inappropriate, and it is necessary to consider the overall fidelity of the composite pulse sequence when viewed as a general rotor.