While a minimal Kitaev chain is promised to host unprotected Majorana zero modes, its role for spin qubits is relatively underappreciated. Following recent breakthroughs in the fine control of transport behaviors, we propose to use minimal Kitaev chain as a robust coupling module between spin qubits. Long-distance, anisotropic exchange coupling can be mediated by the Andreev bound states (ABSs) in the hybrid segment. The chemical potential of ABS gives a simple way to selectively control the coupling strength and its response to local perturbations. Moreover, this additional control degree of freedom creates a unique sweet spot, allowing both strong coupling and first-order immunity against charge noise. The protected qubit encoded on the minimal Kitaev chain at the sweet spot is shown to boast over 200 fold improvement in decoherence time.
While a minimal Kitaev chain is promised to host unprotected Majorana zero modes, its role for spin qubits is relatively underappreciated. Following recent breakthroughs in the fine control of transport behaviors, we propose to use minimal Kitaev chain as a robust coupling module between spin qubits. Long-distance, anisotropic exchange coupling can be mediated by the Andreev bound states (ABSs) in the hybrid segment. The chemical potential of ABS gives a simple way to selectively control the coupling strength and its response to local perturbations. Moreover, this additional control degree of freedom creates a unique sweet spot, allowing both strong coupling and first-order immunity against charge noise. The protected qubit encoded on the minimal Kitaev chain at the sweet spot is shown to boast over 200 fold improvement in decoherence time.
Majorana zero modes provide a route to fault-tolerant qubits by encoding information non-locally in fermion parity. Their sensitivity to noise is expected to decrease exponentially with increasing separation between the Majoranas, a suppression known as topological protection. Kitaev chains engineered in quantum dot-superconductor arrays provide a tunable platform in which separated Majorana zero modes can emerge at the ends of the chain, even in two-site chains. These minimal-chain modes are known as poor man's Majoranas and retain characteristic Majorana properties, including near-zero energy and equal electron-hole character, but have only limited protection. A key outstanding challenge is to move beyond identifying such modes in electrical transport measurements and achieve coherent qubit control in the time domain. Here, we demonstrate a Majorana parity qubit by realizing coherent coupling between two-site Kitaev chains. Since total fermion parity is conserved, the system separates into global even and odd parity manifolds. We observe coherent parity oscillations in both manifolds with equal oscillation frequencies at the Majorana sweet spot, as predicted for isolated Majorana zero modes. We further show that the oscillation frequency and coherence depend systematically on inter-chain coupling and quantum-dot detunings, in close agreement with our model for short, partially protected chains. Our results establish the first coherent control of a Majorana qubit, encoded in the fermion parity of Majorana zero modes in minimal Kitaev chains.
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.
A recent experiment reported coherent parity oscillations between minimal Kitaev chains, demonstrating a Majorana parity qubit (arXiv:2607.09511). Operations on this qubit are controlled by coupling two Kitaev chains and are intrinsically unprotected against noise in the coupling strength. Here we show how the exponential protection in the underlying chains can nevertheless be revealed through unprotected qubit operations. To this end, we develop an analytical theory of quasistatic dephasing for two coupled N-site Kitaev chains at the sweet spot. In Rabi experiments, protection can be resolved by adapting the operating point with chain length: depending on the coupling architecture, it appears as an exponentially increasing optimized number of coherent oscillations or as a longer coherence time. Ramsey experiments show an exponentially increasing coherence time, provided the chains can be sufficiently decoupled. Our analytical theory takes into account the non-Gaussian splitting statistics of the Kitaev chains, allowing us to quantitatively predict the scaling with chain length. Moreover, we determine how residual noise and imperfections limit the range of chain lengths over which this scaling can be observed. Our results show how qubit dynamics can be used to probe Majorana protection in experimentally realistic devices.
The pursuit of fault-tolerant quantum computing necessitates qubit architectures that are inherently robust against environmental decoherence and operational errors. Spintronic qubits, leveraging the spin degree of freedom of electrons, offer a promising platform due to their long coherence times and compatibility with solid-state systems. However, even spintronic qubits remain susceptible to local noise. This paper explores the profound potential of Heisenberg-Kitaev interactions to confer topological protection upon spintronic qubits. By engineering materials and systems that exhibit these anisotropic, bond-directional interactions, it is theoretically possible to realize exotic quantum spin liquid states hosting non-Abelian anyons, such as Majorana zero modes. Encoding quantum information in the nonlocal properties of these anyons would render qubits immune to local perturbations, dramatically extending coherence times and simplifying error correction protocols. We provide a comprehensive review of the theoretical underpinnings of the Kitaev and Heisenberg-Kitaev models, survey candidate materials where such interactions are prevalent, and propose conceptual designs for topologically protected spintronic qubits. This work uniquely consolidates the theoretical framework of Heisenberg-Kitaev interactions with the practical demands of spintronic qubit design, offering a systematic conceptual pathway for their topological protection and predicting their robust characteristics. We further discuss the methodologies for theoretical modeling, the expected characteristics of such qubits, and the significant experimental challenges that must be overcome for their practical realization. This work highlights Heisenberg-Kitaev interactions as a crucial pathway towards the development of truly fault-tolerant and scalable quantum computing technologies.
Spin is typically traced out in the description of quantum-dot-based Kitaev chains to simplify the construction of Majorana fermions. Yet the intrinsic spin structure of poor-man's Majorana modes in minimal Kitaev chains under finite Zeeman fields offers a natural interface for the Kitaev parity qubit to interact with other spinful systems. Here, we establish such a platform to bridge the parity qubit and a quantum-dot spin qubit, with the effective coupling governed by the spin-dependent delocalization of the Majorana modes. Depending on whether the spin qubit is coupled to one or two chains constituting the parity qubit, the parity-spin coupling exhibits distinct forms: an anisotropic parity-conserving exchange interaction or a nontrivial exchange tensor tunable via the interchain superconducting-phase bias. Leveraging fast spin-qubit manipulation, we further demonstrate universal parity-qubit control, high-fidelity qubit-state readout, and entangling operations between the parity and spin qubits. These results turn the spinful structure of poor-man's Majoranas from a finite-field imperfection into a resource for hybrid quantum control.
In a recent breakthrough experiment [Nature (London) 614, 445 (2023)], signatures of Majorana zero modes have been observed in tunnel spectroscopy for a minimal Kitaev chain constructed from coupled quantum dots. However, as Ising anyons, Majoranas' most fundamental property of non-Abelian statistics is yet to be detected. Moreover, the minimal Kitaev chain is qualitatively different from topological superconductors in that it supports Majoranas only at a sweet spot. Therefore, it is not obvious whether non-Abelian characteristics such as braiding and fusion can be demonstrated in this platform with a reasonable level of robustness. In this work, we theoretically propose a protocol for detecting the Majorana fusion rules in an artificial Kitaev chain consisting of four quantum dots. In contrast with the previous proposals for semiconductor-superconductor hybrid nanowire platforms, here we do not rely on mesoscopic superconducting islands, which are difficult to implement in quantum dot chains. To show the robustness of the fusion protocol, we discuss the effects of three types of realistic imperfections on the fusion outcomes, e.g., diabatic errors, dephasing errors, and calibration errors. We also propose a fermion parity readout scheme using quantum capacitance. Our work will shed light on future experiments on detecting the non-Abelian properties of Majorana modes in a quantum dot chain.