Diabatic errors in Majorana braiding with bosonic bath

Abstract

Majorana mode based topological qubits are potentially subject to diabatic errors that in principle can limit the utility of topological quantum computation. Using a combination of analytical and numerical methods we study the diabatic errors in Majorana-based topological Y-junction that are coupled to a Bosonic bath in the Markovian approximation. From the study we find analytically that in the absence of a bath, the error rate can be made exponentially small in the braiding time only for completely smooth pulse shapes. Thus, pristine topological systems can reach exponentially small errors even for finite braid times. The presence of a dominantly dissipative Markovian bath is found to eliminate this exponential scaling of error to a power-law scaling as $T^{-1}$ with $T$ being the braiding time. However, the inclusion of relaxation imroves this scaling slightly to go as $T^{-2}$. Thus, coupling of topological systems to Bosonic baths can lead to powerlaw in braiding time diabatic errors that might limit the speed of topologically protected operations.

12 pages, 7 figures

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Cited by in corpus (16)

• Fusion protocol for Majorana modes in coupled quantum dots
• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Effects of decoherence on diabatic errors in Majorana braiding
• Demonstrating Majorana non-Abelian properties using fast adiabatic charge-transfer
• Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors
• Influence of long-range interaction on Majorana zero modes
• Transport probe of nonadiabatic transition caused by Majorana moving
• Dynamics of a Majorana trijunction in a microwave cavity
• Bath-induced decoherence in finite-size Majorana wires at non-zero temperature
• Effects of dynamical noises on Majorana bound states
• Transport of Majorana Bound State in the presence of telegraph noise
• Transport and fusion of Majorana zero modes in the presence of nonadiabatic transitions
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Dynamical simulation of the injection of vortices into a Majorana edge mode
• Monte Carlo studies of modified scalable designs for quantum computation