Connecting quantum dots through Andreev bound states in a semiconductor-superconductor hybrid provides a platform to create a Kitaev chain. Interestingly, in a double quantum dot, a pair of poor man’s Majorana zero modes can emerge when the system is fine-tuned to a sweet spot, where superconducting and normal couplings are equal in magnitude. Control of the Andreev bound states is crucial for achieving this, usually implemented by varying its chemical potential. In this work, we propose using Andreev bound states in a short Josephson junction to mediate both types of couplings, with the ratio tunable by the phase difference across the junction. Now a minimal Kitaev chain can be easily tuned into the strong coupling regime by varying the phase and junction asymmetry, even without changing the dot-hybrid coupling strength. Furthermore, we identify an optimal sweet spot at π phase, enhancing the excitation gap and robustness against phase fluctuations. Our proposal introduces a new device platform and a new tuning method for realizing quantum-dot-based Kitaev chains.

We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. The device consists of quantum dots tunnel-coupled by a hybrid superconducting island and a tunable capacitive coupling between the dots. We show that coherent control of Cooper pair splitting, elastic cotunneling, and Coulomb interactions implements the universal set of quantum gates defined by Bravyi and Kitaev [1]. Due to the similarity with charge qubits, we expect charge noise to be the main source of decoherence. For this reason, we also consider an alternative design where the quantum dots have tunable coupling to the superconductor. In this second device design, we show that there is a sweet spot for which the local fermionic modes are charge neutral, making the device insensitive to charge noise effects. Finally, we compare both designs and their experimental limitations and suggest future efforts to overcome them.