Andreev spin qubits bound to Josephson vortices in spin-orbit coupled planar Josephson junctions

We propose a variant of Andreev spin qubits (ASQs) defined in planar Josephson junctions based on spin-orbit coupled two-dimensional electron gases (2DEGs) in a weak out-of-plane magnetic field. The magnetic field induces a linear phase gradient across the junction, generating Josephson vortices that can host low-energy Andreev bound states (ABSs). We show that, in certain parameter regimes, the combined effect of the phase gradient and spin-orbit coupling stabilizes an odd-fermion parity ground state, where a single Josephson vortex binds a spinful low-energy degree of freedom that is energetically separated from the other ABSs. This low-energy degree of freedom can be exploited to define a special type of ASQ, which we dub the vortex spin qubit (VSQ). We show that single-qubit gates for VSQs can be performed via flux driving, while readout can be achieved by adapting standard circuit quantum electrodynamics (cQED) techniques developed for conventional ASQs. We further outline how an entangling two-qubit gate can be performed using an ac current drive. We argue that VSQs offer prospects for a substantial reduction in device complexity and hardware overhead compared to conventional ASQ implementations, while preserving key advantages such as supercurrent-based readout, single-qubit gates, and long-range two-qubit gates.

💡 Research Summary

This paper proposes a novel variant of Andreev spin qubits (ASQs), termed the vortex spin qubit (VSQ), which leverages the unique physics of Josephson vortices in planar Josephson junctions. The core concept involves a planar superconductor-semiconductor-superconductor junction fabricated on a two-dimensional electron gas (2DEG) with strong Rashba spin-orbit coupling. When a weak out-of-plane magnetic field is applied, it induces a linear gradient in the superconducting phase difference across the junction. This phase gradient generates an array of Josephson vortices, where the phase difference is an odd multiple of π.

The authors demonstrate through analytical arguments and numerical simulations using the Bogoliubov-de Gennes formalism that these Josephson vortices can host low-energy Andreev bound states (ABSs). In specific parameter regimes, particularly at sufficiently high chemical potential (µ), the combination of the phase gradient and spin-orbit coupling stabilizes an odd-fermion-parity ground state. Within a single vortex, this results in a spinful, low-energy doublet (states |⇑⟩ and |⇓⟩) that is energetically well-separated from the higher-lying Caroli-de Gennes-Matricon states. This doublet defines the two logical states of the VSQ. The energy splitting (ϵ_q) between these states arises from spin-orbit coupling and is calculated to be on the order of 25 µeV for realistic Nb/InAs/Nb junction parameters, which is sufficient for ground-state initialization at millikelvin temperatures.

A key advantage of the VSQ architecture is its inherent simplicity. The “vortex dot” that confines the qubit is defined not by electrostatic gates but by the superconducting phase profile itself, potentially eliminating the need for complex local gate electrodes to define the quantum dot. Furthermore, multiple vortices (and thus multiple VSQs) can be created within a single junction, offering a path toward reduced device complexity and hardware overhead compared to conventional ASQ implementations.

For qubit control and readout, the paper outlines methods that preserve the advantages of standard ASQs. Readout can be performed by adapting circuit quantum electrodynamics (cQED) techniques. By inductively coupling the junction’s flux loop to a microwave resonator, the qubit state can be dispersively read out via a shift in the resonator’s frequency (δf), which depends on the supercurrent matrix element (|J_⇑⇓|) between the two qubit states. Single-qubit gates can be executed via ac flux driving, where an oscillating magnetic flux modulates the global phase difference (φ₀) to drive Rabi oscillations between the |⇑⟩ and |⇓⟩ states. The authors also suggest the possibility of performing an entangling two-qubit gate between distant VSQs using an ac current drive, which would leverage the supercurrent-mediated interaction.

In summary, the vortex spin qubit represents a promising and potentially simplified architecture for Andreev spin qubits. It mitigates several experimental challenges of previous ASQ designs—such as the need for large charging energies or strong magnetic fields—by utilizing the natural phase structure of a Josephson junction in a magnetic field. While maintaining the desirable features of strong supercurrent coupling for fast manipulation and long-range coupling, the VSQ platform points toward a more scalable and less hardware-intensive future for hybrid semiconductor-superconductor quantum processors.