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arXiv:2205.03843 · Physical review. B./Physical review. B

Coupled superconducting spin qubits with spin-orbit interaction

Maria Spethmann, Xianpeng Zhang, Jelena Klinovaja, Daniel Loss

Published Sep 12, 2022• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.106.115411

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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.
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 NNN flux lines are required to perform any single- and two-qubit gate among NNN 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.
Hybrid semiconductor-superconductor qubits have recently emerged as a promising alternative to traditional platforms, combining material advantages with device-level tunability. A defining feature is their gate-tunable Josephson coupling, enabling superconducting qubit architectures with full electric-field control and offering a path toward scalable, low-crosstalk quantum processors. This approach seeks to merge benefits of superconducting and semiconductor qubits, for instance by encoding quantum information in the spin of a quasiparticle occupying an Andreev bound state, thus combining long coherence times with fast, flexible control. Progress has accelerated through bottom-up engineering of Andreev states in coupled quantum dot arrays, leading to architectures such as minimal Kitaev chains hosting Majorana zero modes. In parallel, Hamiltonian-protected designs aim to enhance resilience against local noise and decoherence by exploiting superconducting phase dynamics and discrete charge or flux degrees of freedom. This article reviews recent theoretical and experimental advances in hybrid qubits, providing an overview of physical mechanisms, device implementations, and emerging architectures, with emphasis on their potential for (topologically) protected quantum information processing. While many designs remain at proof-of-concept stage, rapid progress suggests practical demonstrations may soon be achievable.
We propose and theoretically investigate superconducting spin qubits. Superconducting spin qubit consists of a single spin confined in a Josephson junction. We show that owing to spin-orbit interaction, superconducting phase difference across the junction can polarize this spin. We demonstrate that this enables single-qubit operations and more complicated quantum gates, where spins of different qubits interact via a mutual inductance of the superconducting loop where the junctions are embedded. Recent experimental realizations of Josephson junctions made of semiconductor quantum dots in contact with superconducting leads have shown that the number of electrons in the quantum dot can be tuned by a gate voltage. Superconducting spin qubit is realized when the number of electrons is odd. We discuss the qubit properties at phenomenological level. We present a microscopic theory that enables us to make accurate estimations of the qubit parameters by evaluating the spin-dependent Josephson energy in the framework of fourth-order perturbation theory.
Hybrid systems comprising superconducting and semiconducting materials are promising architectures for quantum computing. Superconductors induce long-range interactions between the spin degrees of freedom of semiconducting quantum dots. These interactions are widely anisotropic when the semiconductor material has strong spin-orbit interactions. We show that this anisotropy is tunable and enables fast and high-fidelity two-qubit gates between singlet-triplet (ST) spin qubits. Our design is immune to leakage of the quantum information into noncomputational states and removes always-on interactions between the qubits, thus resolving key open challenges for these architectures. Our ST qubits do not require additional technologically demanding components nor fine-tuning of parameters. They operate at low magnetic fields of a few millitesla and are fully compatible with superconductors. By suppressing systematic errors in realistic devices, we estimate infidelities below ${10}^{\ensuremath{-}3}$, which could pave the way toward large-scale hybrid superconducting-semiconducting quantum processors.
Entangling two quantum bits by letting them interact is the crucial requirement for building a quantum processor. For qubits based on the spin of the electron, these two qubit gates are typically performed by exchange interaction of the electrons captured in two nearby quantum dots. Since the exchange interaction relies on tunneling of the electrons, the range of interaction for conventional approaches is severely limited as the tunneling amplitude decays exponentially with the length of the tunneling barrier. Here, we present an approach to couple two spin qubits via a superconducting coupler. In essence, the superconducting coupler provides a tunneling barrier for the electrons which can be tuned with exquisite precision. We show that as a result exchange couplings over a distance of several microns become realistic, thus enabling flexible designs of multiqubit systems.
We investigate thermal quantum correlations in a system of two coupled superconducting spin qubits described by an effective Andreev spin-qubit Hamiltonian in the presence of spin-orbit interaction. Using Local Quantum Fisher Information (LQFI) and Local Quantum Uncertainty (LQU) as quantum-correlation quantifiers, we analyze the effects of the superconducting phase difference, tunneling amplitude, spin-orbit coupling, and temperature on the nonclassical properties of the system. Analytical expressions for the thermal density matrix are obtained and employed to evaluate both quantities. Our results show that quantum correlations decrease monotonically with increasing temperature, while stronger tunneling and spin-orbit interaction significantly enhance their robustness. Moreover, the superconducting phase introduces a pronounced periodic behavior through the modulation of the effective exchange couplings, leading to constructive and destructive interference regimes that strongly influence the correlations. By analyzing the energy spectrum of the effective Hamiltonian, we demonstrate that the enhancement of quantum correlations is closely associated with an increased energy gap between the ground and first excited states, which suppresses thermal excitations and stabilizes the correlated ground state. Furthermore, LQFI is consistently larger than LQU throughout the investigated parameter space, reflecting its higher sensitivity to quantum fluctuations and local parameter estimation. These findings reveal the microscopic mechanism governing thermal quantum correlations in Andreev spin qubits and highlight the important roles of phase engineering, spin-orbit interaction, and tunneling in protecting quantum resources in hybrid superconducting quantum devices.