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arXiv:2507.01606 · Nature

Single-shot parity readout of a minimal Kitaev chain

Nick van Loo, Francesco Zatelli, Gorm O. Steffensen, Bart Roovers, Guanzhong Wang, Thomas Van Caekenberghe, Alberto Bordin, David van Driel, Yining Zhang, Wietze D. Huisman, Ghada Badawy, Erik P. A. M. Bakkers, Grzegorz P. Mazur, Ramón Aguado, Leo P. Kouwenhoven

Published Feb 11, 2026• 13 citations
arXivHTMLPDF
DOI
10.1038/s41586-025-09927-7

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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.

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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.
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.
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.