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arXiv:2609.25223

Scaling of qubit coherence in quantum dot based Majorana chains: Rabi and Ramsey oscillations of Majorana qubits formed by four and six quantum dots

Haining Pan, S. Das Sarma

Published Sep 21, 2026• 0 citations
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Abstract

We present a theoretical study of the Rabi and Ramsey coherence time of Majorana-based qubits formed by double $N$-site quantum-dot artificial Kitaev chains, following the recent experimental realization arXiv:2607.09511. We generalize the qubit to two chains of arbitrary length and compare the Rabi and Ramsey oscillations of the four-dot and six-dot qubits, simulated with realistic disorder for three sets of parameters: small and large superconducting gaps, and the experimental parameters. We find that, in the pristine limit, the Rabi oscillation is independent of the chain length, whereas the Ramsey oscillation of the six-dot qubit suffers from larger leakage, because the third site suppresses the unwanted energy splitting away from the sweet spot but at the same time makes the deliberate splitting difficult to achieve, which requires a larger detuning that could excite the bulk. In reality with disorder, neither coherence time improves universally with the chain length. The Rabi coherence is set by the competition of three dephasing channels, and the additional dots pay off only if the fluctuation of the interchain tunneling is suppressed; the Ramsey coherence is set by the fluctuation of the energy splitting during the $σ_z$ rotation, which for the four-dot qubit is fixed by the sweet-spot disorder alone and does not depend on the mean splitting, whereas for the six-dot qubit the detuning that generates the splitting adds a fluctuation growing with the splitting itself, so the additional dots pay off only for small splittings. This implies that a longer chain is thus a better quantum memory but not necessarily a better qubit under manipulation. Although topological protection is expected in a longer Kitaev chain qubit, observing it in the current Rabi and Ramsey measurement protocols remains an experimental challenge.

DOI
10.48550/arxiv.2609.25223

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We present a theoretical study of the Rabi and Ramsey coherence time of Majorana-based qubits formed by double NNN-site quantum-dot artificial Kitaev chains, following the recent experimental realization arXiv:2607.09511. We generalize the qubit to two chains of arbitrary length and compare the Rabi and Ramsey oscillations of the four-dot and six-dot qubits, simulated with realistic disorder for three sets of parameters: small and large superconducting gaps, and the experimental parameters. We find that, in the pristine limit, the Rabi oscillation is independent of the chain length, whereas the Ramsey oscillation of the six-dot qubit suffers from larger leakage, because the third site suppresses the unwanted energy splitting away from the sweet spot but at the same time makes the deliberate splitting difficult to achieve, which requires a larger detuning that could excite the bulk. In reality with disorder, neither coherence time improves universally with the chain length. The Rabi coherence is set by the competition of three dephasing channels, and the additional dots pay off only if the fluctuation of the interchain tunneling is suppressed; the Ramsey coherence is set by the fluctuation of the energy splitting during the σzσ_zσz​ rotation, which for the four-dot qubit is fixed by the sweet-spot disorder alone and does not depend on the mean splitting, whereas for the six-dot qubit the detuning that generates the splitting adds a fluctuation growing with the splitting itself, so the additional dots pay off only for small splittings. This implies that a longer chain is thus a better quantum memory but not necessarily a better qubit under manipulation. Although topological protection is expected in a longer Kitaev chain qubit, observing it in the current Rabi and Ramsey measurement protocols remains an experimental challenge.
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 NNN-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 authors address here the latest experimental platform for the topological Majorana qubit -- the artificial Kitaev chain -- and propose a new experimental direction to establish the topological qubit by evaluating its realistic qubit performance in Rabi and Ramsey oscillation experiments, including dephasing time, quality factor, leakage, and other key metrics. This work demonstrates that the qubit performance in the current experimental platform exhibits significantly enhanced coherence compared to conventional semiconductor quantum dot based charge qubits without superconductors, marking a crucial step toward realizing the first topological Majorana qubit in a solid-state system.
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.
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
Quantum bits based on Majorana zero modes are expected to be robust against certain noise types, and hence provide a quantum computing platform that is superior to conventional qubits. This robustness is not complete, though: imperfections can still lead to qubit decoherence and hence to information loss. In this work, we theoretically study Majorana-qubit dephasing in a minimal model: in a Kitaev chain with quasistatic disorder. Our approach, based on numerics as well as first-order nondegenerate perturbation theory, provides a conceptually simple physical picture and predicts Gaussian dephasing. We show that as system parameters are varied, the dephasing rate due to disorder oscillates out-of-phase with respect to the oscillating Majorana splitting of the clean system. In our model, first-order dephasing sweet spots are absent if disorder is uncorrelated. We describe the crossover between uncorrelated and highly correlated disorder, and show that dephasing measurements can be used to characterize the disorder correlation length. We expect that our results will be utilized for the design and interpretation of future Majorana-qubit experiments.
Topological quantum computation encodes quantum information nonlocally by nucleating non-Abelian anyons separated by distances LLL, typically spanning the qubit device size. This nonlocality renders topological qubits exponentially immune to dephasing from all sources of classical noise with operator support local on the scale of LLL. We perform detailed analytical and numerical analyses of a time-domain Ramsey-type protocol for noisy Majorana-based qubits that is designed to validate this coveted topological protection in near-term devices such as the so-called ``tetron'' design. By assessing dependence of dephasing times on tunable parameters, e.g., magnetic field, our proposed protocol can clearly distinguish a bona fide Majorana qubit from one constructed from semilocal Andreev bound states, which can otherwise closely mimic the true topological scenario in local probes. In addition, we analyze leakage of the qubit out of its low-energy manifold due to classical-noise-induced generation of quasiparticle excitations; leakage limits the qubit lifetime when the bulk gap collapses, and hence our protocol further reveals the onset of a topological phase transition. This experiment requires measurement of two nearby Majorana modes for both initialization and readout---achievable, for example, by tunnel coupling to a nearby quantum dot---but no further Majorana manipulations, and thus constitutes an enticing prebraiding experiment. Along the way, we address conceptual subtleties encountered when discussing dephasing and leakage in the context of Majorana qubits.