Nonadiabatic conditional geometric phase shift with NMR - art. no. 097901

A conditional geometric phase shift gate, which is fault tolerant to certai n types of errors due to its geometric nature, was realized recently via nu clear magnetic resonance (NMR) under adiabatic conditions. However, in quan tum computation, everything must be completed within the decoherence time. The adiabatic condition makes any fast conditional Berry phase (cyclic adia batic geometric phase) shift gate impossible. Here we show that by using a newly designed sequence of simple operations with an additional vertical ma gnetic field, the conditional geometric phase shift gate can be run nonadia batically. Therefore geometric quantum computation can be done at the same rate as usual quantum computation.