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arXiv:2506.13988

Resolving Andreev spin qubits in germanium-based Josephson junctions

Silas Hoffman, Charles Tahan

Published Jun 16, 2025• 0 citations
arXivHTMLPDF

Abstract

Andreev spin qubits (ASQs) are a promising platform for quantum information processing which benefit from both the small footprint of semiconducting spin qubits and the long range connectivity of superconducting qubits. While state-of-the-art experiments have developed ASQs in InAs nanowires, these realizations are coherence-time limited by nuclear magnetic noise which cannot be removed by isotopic purification. In Ge-based Josephson junctions, which can be isotopically purified, Andreev states have been experimentally observed but spin-resolved Andreev states remain elusive. Here, we theoretically demonstrate that the geometry of the Josephson junction can limit the qubit frequency to values below typical experimental temperatures and render the ASQ effectively invisible. ASQs could be experimentally resolved by judiciously choosing the geometry of the junction and filling of the underlying Ge. Our comprehensive study of ASQ frequency on in situ and ex situ experimentally controllable parameters provides design guidance of Ge-based Josephson junctions and paves the way towards realization of high-coherence ASQs.

DOI
10.48550/arxiv.2506.13988

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Andreev spin qubits (ASQs) are a promising platform for quantum information processing which benefit from both the small footprint of semiconducting spin qubits and the long range connectivity of superconducting qubits. While state-of-the-art experiments have developed ASQs in InAs nanowires, these realizations are coherence-time limited by nuclear magnetic noise which cannot be removed by isotopic purification. In Ge-based Josephson junctions, which can be isotopically purified, Andreev states have been experimentally observed but spin-resolved Andreev states remain elusive. Here, we theoretically demonstrate that the geometry of the Josephson junction can limit the qubit frequency to values below typical experimental temperatures and render the ASQ effectively invisible. ASQs could be experimentally resolved by judiciously choosing the geometry of the junction and filling of the underlying Ge. Our comprehensive study of ASQ frequency on in situ and ex situ experimentally controllable parameters provides design guidance of Ge-based Josephson junctions and paves the way towards realization of high-coherence ASQs.
We theoretically study the dephasing of an Andreev spin qubit (ASQ) due to electric and magnetic noise. Using a tight-binding model, we calculate the Andreev states formed in a Josephson junction where the link is a semiconductor with strong spin-orbit interaction. As a result of both the spin-orbit interaction and induced superconductivity, the local charge and spin of these states vary as a function of externally controllable parameters: the phase difference between the superconducting leads, an applied magnetic field, and filling of the underlying semiconductor. Concomitantly, coupling to fluctuations of the electric or magnetic environment will vary, which informs the rate of dephasing. We qualitatively predict the dependence of dephasing on the nature of the environment, magnetic field, phase difference between the junction, and filling of the semiconductor. Comparing the simulated electric- and magnetic-noise-induced dephasing rate to experiment suggests that the dominant source of noise is magnetic. Moreover, by appropriately tuning these external parameters, we find sweet spots at which we predict an enhancement in ASQ coherence times.
The spin of a quasiparticle trapped in a quantum dot Josephson junction forms the basis of an Andreev spin qubit (ASQ): a semiconductor-superconductor device where the interplay between a localized spin degree of freedom and superconductivity leads to a spin-resolved Josephson potential. In this work, we show that shunting an ASQ with a linear inductor enhances its relaxation time by separating the spin-qubit states into distinct potential wells in phase space, nearly eliminating wavefunction overlap. The resulting inductively protected Andreev (IPA) spin qubit is equivalent to two fluxoniums in the heavy regime, one for each spin. Thus, the IPA qubit combines the long coherence times, low-frequency ground-state manifold, and large anharmonicity of a protected superconducting qubit with the operational advantages of a spin degree of freedom.
Planar germanium heterostructures are promising hosts for hybrid quantum devices due to their compatibility with superconductors, low material disorder, and relaxed fabrication constraints. Also, the potentially low density of nuclear spins and strong spin-orbit interaction make germanium attractive for coherent spin physics. However, recent microwave spectroscopy experiments were unable to resolve a spin-splitting of bound states in germanium Josephson junctions, the prerequisite for defining and controlling Andreev spin qubits. Here, we argue that compressive strain is the key mechanism suppressing spin splitting in current devices. Furthermore, we propose unstrained and tensile-strained heterostructures, fully compatible with state-of-the-art growth technology, that significantly enhance the relevant spin-orbit effect. By numerically simulating ballistic Josephson junctions, we predict spin splittings comfortably in the GHz range, more than 2 orders of magnitude larger than compressively strained cases, and all-electric quantum gates in a hundred nanoseconds. Our results establish strain engineering as a key design principle for realizing Andreev spin qubits in germanium-based devices.
Andreev (or superconducting) spin qubits (ASQs) have recently emerged as a promising qubit platform that combines superconducting circuits with semiconductor spin degrees of freedom. While recent experiments have successfully coupled two ASQs, how to realize a scalable architecture for extending this coupling to multiple distant qubits remains an open question. In this work, we resolve this challenge by introducing an architecture that achieves all-to-all connectivity between multiple remote ASQs. Our approach enables selective connectivity between any qubit pair while keeping all other qubit pairs uncoupled. Furthermore, we demonstrate the feasibility of efficient readout using circuit quantum electrodynamics techniques and compare different readout configurations. Our architecture shows promise both for gate-based quantum computing and for analog quantum simulation applications by offering higher qubit connectivity than alternative solid-state platforms.
Abstract Josephson junctions based on semiconductor nanowires are potential building blocks for electrically tunable qubit structures, e.g., the gatemon or the Andreev qubit. However, an actual realization requires the thorough investigation of the intrinsic excitation spectrum. Here, we demonstrate the fabrication of low-loss superconducting microwave circuits that combine high quality factors with a well-controlled gate architecture by utilizing a flip-chip approach. This platform is then used to perform single-tone and two-tone experiments on Andreev states in in-situ grown InAs/Al core/half-shell nanowires with shadow mask defined Josephson junctions. In gate-controlled and flux-biased spectroscopic measurements we find clear signatures of single quasiparticle as well as quasiparticle pair transitions between discrete Andreev bound states mediated by photon-absorption. Our experimental findings are supported by simulations that show that the junction resides in the intermediate channel length regime.
Andreev-spin qubits are a new qubit platform that merges superconductivity with semiconductor physics. The mechanisms dominating observed energy relaxation remain unidentified. We report here on three steps taken to address these questions in an InAs\mathrm{In}\mathrm{As}InAs nanowire weak link. First, we designed a microwave readout circuit tuned to be directly sensitive to the spin-dependent inductance of the weak link so that higher orbital states are not necessary for readout---this resulted in larger windows in parameter space in which the spin-state properties can be probed. Second, we implemented a successful gap-engineering strategy to mitigate quasiparticle poisoning. Third, the weak link was fabricated by in situ shadow evaporation, which has been shown to improve atomic-scale disorder. We show how our design allows characterization of the spin stability and coherence over the full range of magnetic flux and gate voltage of an odd-parity bias point. The spin-relaxation and dephasing rates are comparable with those of the best devices previously reported, suggestive that surface atomic-scale disorder and quasiparticle poisoning are not linked to spin relaxation in InAs\mathrm{In}\mathrm{As}InAs nanowires. Our design strategies are transferrable to novel materials platforms for Andreev qubits, such as germanium and carbon.