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.
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.
Hybrid devices integrating quantum dots with Josephson junctions are gaining interest because they combine spin-based quantum computing with circuit quantum electrodynamics (circuit QED) methods. In particular, Andreev spin qubits have shown significant experimental progress including strong two-qubit coupling, and are predicted to exhibit all-to-all connectivity. Here we propose superconducting singlet-triplet (SST) qubits that rely on parallel-aligned double quantum dots in Josephson junctions. While Andreev spin qubits require spin-orbit interaction to unlock the spin degree-of-freedom, SST qubits do not require spin-orbit interaction, making the advantages of hybrid devices available to a wider range of materials. Similar to Andreev spin qubits, the qubit states couple to the superconducting phase across the junction, which allows for control and readout using circuit QED, and supports all-to-all connectivity. Only N flux lines are required to perform any single- and two-qubit gate among N qubits, and thus the overhead of control lines is small. Finally, linear protection from charge or flux noise makes these qubits interesting candidates for a future quantum processor.
Opportunités de manipulation directe d'un qubit de spin d'Andreev piloté en phase The research presented in this thesis delves into a theoretical exploration of Andreev bound states (ABS) hosted in Josephson junctions with spin-orbit coupling (SOC). ABS are fermionic bound states that appear at the junction between two superconducting electrodes forming a Josephson junction. These bound states are at the core of the microscopic description of the Josephson effect and provide an explanation for the transfer of Cooper pairs from one superconducting electrode to the other. Crucially, when the superconducting phase difference between the two electrodes is non-zero, a supercurrent can flow in the junction, depending on the occupancy of the ABS. The presence of this supercurrent facilitates the coupling between a microwave resonator and a junction due to its sensibility to the electromagnetic field. This coupling then allows for the detection and manipulation of ABS.Furthermore, in the presence of SOC along with a superconducting phase bias, the spin degeneracy of ABS can be lifted. Therefore such a junction provides a unique opportunity to realize a special kind of spin qubit known as Andreev spin qubit (ASQ). The qubit operation can be performed via an AC modulation of an electrostatic gate or magnetic flux, thanks to the sensitivity of the ABS to the electric potential or the phase difference, respectively. So far, the coherent manipulation of such qubits has been realized in gate-driven experiments as well as in flux-driven experiments with the use of additional Andreev levels. However, the direct transition between the two ABS forming the ASQ has remained out of reach in flux-driven experiments. In this thesis, we investigate two distinct types of Josephson junctions with SOC with the aim of estimating the amplitude of the matrix elements of the current operator between two ABS forming an ASQ. These elements characterize the coupling strength between the qubit and an external flux drive, indicating which transitions between ABS are within reach. Our first project focuses on a superconductor-normal-superconductor junction where the normal region consists of a nanowire with Rashba SOC. As a minimal model, we consider a generic scatterer located along the nanowire. Unless this scatterer possesses additional spatial (mirror) symmetries, it is responsible for inducing spin-flip transmission probability. Using the scattering formalism, we derive the energy spectrum of ABS and assess how SOC influences the spin-splitting between opposite spin states. We then obtain analytical expressions for the matrix elements of the current operator. Notably, our study reveals that SOC allows one to have finite elements between opposite spin states. In a second project, the system we study consists of a superconductor-double quantum dots-superconductor junction. A quantum dot consists of a tiny region defined by electrostatic gates or impurities. Due to its small size, Coulomb repulsion can be significant. However, in the simplest case of a quantum dot with a single level, even in the presence of SOC in the coupling between the dot and the leads, spin degeneracy of ABS is still preserved. However, recent experiments showed that additional levels allow to lift the spin degeneracy. Here, we introduce a second quantum dot which provides an additional level and offers more control on each level. By using an effective model, we identify the minimal ingredients that are necessary to lift the spin degeneracy. Our results reveal that this splitting is achievable through spin-dependent couplings with the leads and is reduced by the Coulomb repulsion. Additionally, the presence of a finite coupling between the two dots, combined with SOC in the couplings with the leads, allows one to have finite matrix elements of the current operator between opposite spin states, which we obtain numerically. In short, we present in this thesis two platforms for the realization of phase-driven ASQ.
We investigate the superconducting Anderson impurity model for interacting quantum dot Josephson junctions with spin-orbit coupling and a term accounting for tunnelling through higher-energy orbitals. These elements establish the conditions required for spin polarization in the absence of external magnetic field at finite superconducting phase bias. This Hamiltonian has been previously used to model the Andreev spin qubit, where quantum information is encoded in spinful odd-parity subgap states. Here we instead analyse the even-parity sector, i.e., the Andreev pair qubit based on Andreev bound states (ABS). The model is solved using the zero-bandwidth approximation and the numerical renormalization group, with further insight from variational calculations. Electron-electron interaction admixes single-occupancy Yu-Shiba-Rusinov (YSR) components into the ABS states, thereby strongly enhancing spin transitions in the presence of spin-orbit coupling. The ABS states can thus become sensitive to local magnetic field fluctuations, which has implications for decoherence in Andreev pair qubits. For strong interaction U U , especially in the cross-over region between the ABS and YSR regimes for U \sim 2\Delta U ∼ 2 Δ , charge, spin, and inductive transitions can all become strong, offering avenues for spin control and quantum transduction.
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.
Superconducting spin qubits, also known as Andreev spin qubits, promise to combine the benefits of superconducting qubits and spin qubits defined in quantum dots. While most approaches to control these qubits rely on controlling the spin degree of freedom via the supercurrent, superconducting spin qubits can also be coupled to each other via the superconductor to implement two-qubit quantum gates. We theoretically investigate the interaction between superconducting spin qubits in the weak tunneling regime and concentrate on the effect of spin-orbit interaction (SOI), which can be large in semiconductor-based quantum dots and thereby offers an additional tuning parameter for quantum gates. We find analytically that the effective interaction between two superconducting spin qubits consists of Ising, Heisenberg, and Dzyaloshinskii-Moriya interactions and can be tuned by the superconducting phase difference, the tunnel barrier strength, or the SOI parameters. The Josephson current becomes dependent on SOI and spin orientations. We demonstrate that this interaction can be used for fast controlled phase-flip gates with a fidelity >99.99%. We propose a scalable network of superconducting spin qubits which is suitable for implementing the surface code.
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.