Majorana braiding without an exponential Hilbert space
ORAL
Abstract
Qubits built with Majorana zero modes are the primary path towards topologically protected quantum computing. However, braiding errors can be introduced from sources such as quasiparticle poisoning, Majorana hybridization, and diabatic processes. It is not fully understood how these error rates behave in a full quasiparticle background, which is often included using the full exponential Hilbert space. We present a method to calculate expectation values, <ψ(t)|Â|ψ(t)>, and overlaps of time evolved many-body states from single-particle states in a superconductor. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to quantify the braiding errors. We show how error rates depend on the timescale and smoothness of the time dependence, as well as the energy gap and distance between Majorana zero modes. This method is a powerful tool to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any superconducting system.
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Publication: J. Bedow, E. Mascot, D. K. Morr, Emergence and Manipulation of non-equilibrium Yu-Shiba-Rusinov states. arXiv:2112.07733 (2021).<br><br>J. Bedow, E. Mascot, T. Hodge, S. Rachel, D. K. Morr, Non-equilibrium braiding of Majorana fermions and the implementation of a $sigma_x$ quantum gate in magnet-superconductor hybrid structures. Manuscript in preparation.<br><br>E. Mascot, T. Hodge, D. Crawford, S. Rachel, Classical simulation of topological quantum computing. Manuscript in preparation.
