Parity qubits and poor man's Majorana bound states in double quantum dots

TL;DR

This paper proposes a method to realize non-topologically protected Majorana bound states in double quantum dots, enabling parity qubit encoding and potential for entanglement and measurement in quantum computing applications.

Contribution

It introduces a tunable double quantum dot system hosting 'poor man's Majorana states' with specific conditions for their existence and discusses their use as non-local parity qubits.

Findings

Majorana bound states can be realized in double quantum dots with magnetic field control.

The encoded fermionic state acts as a non-local parity qubit.

Inter-dot interactions lift the degeneracy of the Majorana states.

Abstract

We study a double quantum dot connected via a common superconducting lead and show that this system can be tuned to host one Majorana bound state (MBS) on each dot. We call them "poor man's Majorana bound states" since they are not topologically protected, but otherwise share the properties of MBS formed in topological superconductors. We describe the conditions for the existence of the two spatially separated MBS, which include breaking of spin degeneracy in the two dots, with the spins polarized in different directions. Therefore, we propose to use a magnetic field configuration where the field directions on the two dot form an angle. By control of this angle the cross Andreev reflection and the tunnel amplitudes can be tuned to be approximately equal, which is a requirement for the formation of the MBS. We show that the fermionic state encoded in the two Majoranas constitutes a parity qubit, which is non-local and can only be measured by probing both dots simultaneously. Using a many-particle basis for the MBS, we discuss the role of interactions and show that inter-dot interactions always lift the degeneracy. We also show how the MBS can be probed by transport measurements and discuss how the combination of several such double dot systems allows for entanglement of parity qubits and measurement of their dephasing times.