Synthesis of fast qudit gates by a train of coincident pulses

Abstract

We propose an exact analytical method for the production of fast quantum gates in a system of d degenerate states, using a technique of a train of coincident pulses. It is an alternative to the adiabatic passage technique. This study exploits the Morris-Shore transformation and generalized quantum Householder reflection in which each of Householder reflection is implemented by n + m (n and m are arbitrary integers) sets of coincident pulses. Decoherence due to the population of the upper state is efficiently suppressed as the number of pulse sets (n and m ) increases. It is remarkable that the upper state population is damped considerably, even for a small number of pulse sets, despite the fact that all the fields applied were on resonance with their transitions. In this method, simple Gaussian pulses with minimal pulse areas were used, which is easy to achieve experimentally. As a case study to validate the method, we implement the quantum Fourier transform in qutrit and ququad by a proper pulse train.