Negative Hybridization: a Potential Cure for Braiding with Imperfect Majorana Modes

TL;DR

This paper proposes that negative hybridization of Majorana zero modes can mitigate hybridization errors, potentially restoring fault-tolerance in topological quantum computing with imperfect Majorana systems.

Contribution

It introduces the concept of negative hybridization energy in Majorana zero modes and demonstrates its potential to suppress gate errors below fault-tolerance thresholds.

Findings

Negative hybridization energy can reduce hybridization errors.

Examples show error suppression below fault-tolerance thresholds.

Negative hybridization restores functionality in imperfect Majorana systems.

Abstract

Majorana zero modes, the elementary building blocks for the quantum bits of topological quantum computers, are known to suffer from hybridization as their wavefunctions begin to overlap. This breaks the ground state degeneracy, splitting their energy levels and leading to an accumulation of error when performing topological quantum gates. Here we show that the energy splitting of the Majorana zero modes can become negative, which can be utilized to reduce the average hybridization energy of the total gate. We present two illustrative examples where negative hybridization suppresses gate errors to such an extent that they remain below the fault-tolerance threshold. As an intrinsic property of Majorana zero modes, negative hybridization enables systems based on imperfect Majorana zero modes to regain functionality for quantum information processing.