Parity-to-charge conversion for readout of topological Majorana qubits

TL;DR

This paper proposes a theoretical scheme for reading out Majorana qubits by converting their parity states into charge states, analyzing error mechanisms, and optimizing parameters to improve fidelity in topological superconductors.

Contribution

It introduces a parity-to-charge conversion method for Majorana qubits and analyzes error sources to enhance readout accuracy in topological superconductors.

Findings

Error mechanisms can be minimized with smooth, optimally strong tunnel pulses.

Slow charge noise dominates errors with weak pulses.

Leakage errors are significant with strong tunnel pulses.

Abstract

We theoretically study a scheme to distinguish the two ground states of a one-dimensional topological superconductor, which could serve as a basis for the readout of Majorana qubits. The scheme is based on parity-to-charge conversion, i.e., the ground-state parity of the superconductor is converted to the charge occupation on a tunnel-coupled auxiliary quantum dot. We describe how certain error mechanisms degrade the quality of the parity-to-charge conversion process. We consider (i) leakage due to a strong readout tunnel pulse, (ii) incomplete charge Rabi oscillations due to slow charge noise, and (iii) charge relaxation due to phonon emission and absorption. To describe these effects, we use simple model Hamiltonians based on the ideal Kitaev chain, and draw conclusions to generic one-dimensional topological superconductors wherever possible. In general, the effects of the error mechanisms can be minimized by choosing a smooth shape and an optimal strength for the readout tunnel pulse. In a case study based on InAs heterostructure device parameters, we estimate that the parity-to-charge conversion error is mainly due to slow charge noise for weak tunnel pulses and leakage for strong tunnel pulses.