Number-conserving analysis of measurement-based braiding with Majorana zero modes

Abstract

Majorana-based quantum computation seeks to encode information non-locally in pairs of Majorana zero modes (MZMs), thereby isolating qubit states from a local noisy environment. In addition to long coherence times, the attractiveness of Majorana-based quantum computing relies on achieving topologically protected Clifford gates from braiding operations. Recent works have conjectured that mean-field BCS calculations may fail to account for non-universal corrections to the Majorana braiding operations. Such errors would be detrimental to Majorana-based topological quantum computing schemes. In this work, we develop a particle-number conserving approach for measurement-based topological quantum computing and investigate the effect of quantum phase fluctuations. We demonstrate that braiding transformations are indeed topologically protected in charge-protected Majorana-based quantum computing schemes. arXiv:1909.10521v2 [cond-mat.mes-hall]

Parity-to-charge conversion in Majorana qubit readout

“…Indeed, whereas braiding Majoranas locally in space is very challenging from an experimental perspective, see also Refs. [9,60], alternative schemes have been proposed which simulate braiding purely through parity measurements [19,[61][62][63]. In order to read out the parity of a MBS pair, however, parity has to be converted to a physically observable quantity, such as flux, charge, or capacitance [64].…”

Parity-to-charge conversion in Majorana qubit readout

“…Indeed, whereas braiding Majoranas locally in space is very challenging from an experimental perspective, see also Refs. [12,63], alternative schemes have been proposed which simulate braiding purely through parity measurements [22,[64][65][66]. In order to read out the parity of a MBS pair, however, parity has to be converted to a physically observable quantity, such as flux, charge, or capacitance [67].…”

Readout of Majorana bound states via Landau-Zener transition

“…These operations are also lying at the heart of Majorana based quantum information processing [20][21][22][23][24][25][26]. Moreover, braiding and other logical gates could be effectively implemented by a sequence of parity measurements [27][28][29][30][31]. Therefore, reading out the parity of MBSs is vital for both verifying the existence of MBSs and building a robust quantum computer.…”