Minimal Kitaev chains composed of two semiconducting quantum dots coupled via a superconductor have emerged as a promising platform to realize and study Majorana bound states (MBSs), which appear for fine-tuned configurations. We propose a hybrid qubit based on a Josephson junction between two such double quantum dots (DQDs) embedded in a superconducting qubit geometry. The qubit makes use of the $4\ensuremath{\pi}$-Josephson effect in the Kitaev junction to create a subspace based on the even/odd fermionic parities of the two DQD arrays hosting MBSs. Deep in the transmon regime, we demonstrate that by performing circuit QED spectroscopy on such a hybrid Kitaev-transmon ``Kitmon'' qubit, one could observe distinct MBS features in perfect agreement with precise analytical predictions in terms of DQD parameters only. This agreement allows us to extract the Majorana polarization in the junction from the microwave response.
Minimal Kitaev chains composed of two semiconducting quantum dots coupled via a superconductor have emerged as a promising platform to realize and study Majorana bound states (MBSs), which appear for fine-tuned configurations. We propose a hybrid qubit based on a Josephson junction between two such double quantum dots (DQDs) embedded in a superconducting qubit geometry. The qubit makes use of the 4\ensuremathπ-Josephson effect in the Kitaev junction to create a subspace based on the even/odd fermionic parities of the two DQD arrays hosting MBSs. Deep in the transmon regime, we demonstrate that by performing circuit QED spectroscopy on such a hybrid Kitaev-transmon ``Kitmon'' qubit, one could observe distinct MBS features in perfect agreement with precise analytical predictions in terms of DQD parameters only. This agreement allows us to extract the Majorana polarization in the junction from the microwave response.
The possibility of engineering artificial Kitaev chains in arrays of quantum dots coupled via narrow superconducting regions has emerged as an attractive way to overcome the disorder issues that complicate the realization and detection of topological superconducting phases in other platforms. Although a true topological phase would require long chains, a two-site chain realized in a double quantum dot can already be tuned to points in parameter space where it hosts zero-energy states that seem identical to the Majorana bound states that characterize a topological phase. These states have been named “poor man’s Majorana bound states” (PMMs) because they lack formal topological protection. In this work, we propose a pathway for next-generation experiments on PMMs. The pathway starts with experiments to characterize a single pair of PMMs by measuring the Majorana quality and then moves on to initialization and readout of the parity of a PMM pair, which allows the measurement of quasiparticle poisoning times. The next step is to couple two PMM systems to form a qubit. We discuss measurements of the coherence time of such a qubit, as well as a test of Majorana fusion rules in the same setup. Finally, we propose and analyze three different types of braidinglike experiments that require more complex device geometries. Our conclusions are supported by calculations based on a realistic model with interacting and spinful quantum dots, as well as by simpler models to gain physical insight. Our calculations show that it is indeed possible to demonstrate non-Abelian physics in minimal two-site Kitaev chains despite the lack of a true topological phase. However, our findings also reveal that doing so requires some extra care, appropriately modified protocols, and awareness of the details of this particular platform. Published by the American Physical Society 2024
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.
Abstract We investigate the effect of interatomic Coulomb repulsion V and particular states disregarded previously on the Kitaev-transmon system proposed by Pino et al (2024 Phys. Rev. B 109 075101) which consists of a Josephson junction connecting two double quantum dots (DQDs) modeled by the spinless Kitaev Hamiltonian. For an isolated DQD, we demonstrate that a ‘sweet spot’ hosting ‘poor man’s Majorana’ states persist in the presence of V , provided that system parameters are appropriately tuned. For the full system, we demonstrate that, at the sweet spots of both DQDs, all eigenstates are doubly degenerate. This degeneracy arises from the existence of an operator that maps between two decoupled Hilbert subspaces. Away from the sweet spots, the microwave spectrum becomes sensitive to the choice of initial state of the system. In our study, we consider transitions from the ground state (which depending on the flux alternates between the above mentioned subspaces) to all possible excited states. This scenario corresponds to a system initially in thermal equilibrium at low temperature.
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 realize a hybrid superconductor-semiconductor transmon device in which the Josephson effect is controlled by a gate-defined quantum dot in an InAs-Al nanowire.Microwave spectroscopy of the transition spectrum of the transmon allows us to probe the ground-state parity of the quantum dot as a function of the gate voltages, the external magnetic flux, and the magnetic field applied parallel to the nanowire.The measured parity phase diagram is in agreement with that predicted by a single-impurity Anderson model with superconducting leads.Through continuous-time monitoring of the circuit, we furthermore resolve the quasiparticle dynamics of the quantum dot Josephson junction across the phase boundaries.Our results can facilitate the realization of semiconductor-based 0-π qubits and Andreev qubits.
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.