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arXiv:2608.18042

Dynamics of Majorana tetron qubits under quasiparticle poisoning

Sauri Bhattacharyya, Bernard van Heck

cond-mat.mes-hallquant-phSubmitted Aug 18, 2026• Announced Aug 19, 2026• 0 citations
v1 · Aug 18, 2026v2 · Aug 30, 2026
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Abstract

We study the dissipative dynamics of a Majorana tetron qubit in the presence of extrinsic quasiparticle poisoning due to the coupling to external leads. From the Bloch-Redfield equation describing a finite-size topological superconductor hosting four Majorana zero modes, we recover analytical expressions for the steady state, the parity leakage rate, and the decoherence rate of a Majorana qubit at arbitrary values of the charging energy. The analysis shows that the exponential suppression of the dephasing rate is gradually removed by the energy splitting of the qubit states. These results can be useful to understand time-domain experimental data in Majorana qubit prototypes.

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17 pages, 3 figures

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We study the dissipative dynamics of a Majorana tetron qubit in the presence of extrinsic quasiparticle poisoning due to the coupling to external leads. From the Bloch-Redfield equation describing a finite-size topological superconductor hosting four Majorana zero modes, we recover analytical expressions for the steady state, the parity leakage rate, and the decoherence rate of a Majorana qubit at arbitrary values of the charging energy. The analysis shows that the exponential suppression of the dephasing rate is gradually removed by the energy splitting of the qubit states. These results can be useful to understand time-domain experimental data in Majorana qubit prototypes.
Building a fault-tolerant quantum computer requires physical qubits with exceptionally low error rates. An exciting proposal for achieving this goal is to employ Majorana-based qubits, which may have error rates that are exponentially suppressed in macroscopic system parameters. Specifically, for Majorana qubits based on topological superconducting nanowires, errors are expected to be exponentially suppressed in the nanowire length, superconducting gap, and decreasing temperature. This thesis investigates errors in Majorana-based qubits from excited quasiparticles due to changes in chemical potentials and 1/f charge noise, and shows that such errors are not exponentially suppressed and can be quite substantial. In the first study of this thesis, we show that small temporal variations of the chemical potential can cause errors that grow linearly with the length of the nanowire. These errors stem from leakage into excited bulk quasiparticle states, which poison Majorana modes at opposite ends of the nanowire. We further demonstrate that the dynamics of this leakage are captured by the half Landau-Zener effect, which dictates its dependence on key parameters such as the superconducting gap, chemical potential variations, and dynamic changes in the spatial profile of Majorana modes. In the second study we investigate quasiparticle excitations due to high-frequency components of 1/f charge noise, which is ubiquitous in the materials surrounding the nanowire. We model 1/f noise as arising from two level fluctuators which cause chemical potential fluctuations following random telegraph noise. We demonstrate that 1/f noise causes error rates which grow linearly with the system size and are not exponentially suppressed in the superconducting gap. For existing tetron qubit designs, we estimate decoherence times to be an order of magnitude shorter than the target 1μs measurement time. This thesis also develops an algorithmic framework for applying the covariance matrix method to the time-dependent Kitaev chain model. This extends upon existing approaches, providing a key numerical tool used throughout this thesis. This work motivates engineering strategies to reduce coupling to two level systems in Majorana qubits, such as increasing the nanowire capacitance. Beyond Majoranas, a promising avenue is to investigate the impact of this quasiparticle excitation mechanism on superconducting circuits, such as superconducting qubits, resonators, and single-photon detectors.
Majorana zero modes have been attracting considerable attention because of their prospective applications in fault-tolerant topological quantum computing. In recent years, some schemes have been proposed to detect and manipulate Majorana zero modes using superconducting qubits. However, manipulating and reading the Majorana zero modes must be kept in the time window of quasiparticle poisoning. In this work, we study the problem of quasiparticle poisoning in a split transmon qubit containing hybrid Josephson junctions involving Majorana zero modes. We show that Majorana coupling will cause parity mixing and 4π Josephson effect. In addition, we obtained the expression of qubit parameter-dependent parity switching rate and demonstrated that quasiparticle poisoning can be greatly suppressed by reducing E_J/E_C via qubit design.
Qubits based on Majorana zero modes are a promising path towards topological quantum computing. Such qubits, though, are susceptible to quasiparticle poisoning which does not have to be small by topological argument. We study the main sources of the quasiparticle poisoning relevant for realistic devices-nonequilibrium above-gap quasiparticles and equilibrium localized subgap states. Depending on the parameters of the system and the architecture of the qubit either of these sources can dominate the qubit decoherence. However, we find in contrast to naive estimates that in moderately disordered, floating Majorana islands the quasiparticle poisoning can have timescales exceeding seconds.
Building a fault-tolerant quantum computer requires physical qubits with exceptionally low error rates. Majorana-based tetron qubits are predicted to exhibit error rates that decrease exponentially with inverse temperature and length of each topological superconducting wire in the tetron. In contrast to this prediction, we show that small temporal variations of the chemical potential can cause errors that grow linearly with tetron length at zero temperature. These errors stem from leakage into excited quasiparticle states, which ultimately poison Majorana modes at opposite ends of the tetron, causing errors. We further demonstrate that the dynamics of this leakage is captured by the half Landau-Zener effect, which dictates its dependence on key system parameters such as the superconducting gap, chemical potential variations, and dynamic changes in the spatial profile of Majorana modes. These results motivate further investigations into the impact of leakage on qubit performance and potential mitigation strategies.
Qubits based on Majorana zero modes (MZMs) in superconductor-semiconductor nanowires have attracted intense interest due to claims that their error rates are suppressed exponentially with increasing nanowire length or decreasing temperature. However, here we show that these qubits are subject to substantial decoherence resulting from the high-frequency components of 1/f charge noise, which is ubiquitous in the materials surrounding the nanowire. This process excites quasiparticles in the bulk of the topological superconductor that cause qubit decoherence even under otherwise ideal conditions. Increasing nanowire capacitance suppresses this mechanism but exposes the qubits to decoherence from externally-generated quasiparticles. Therefore, achieving high-fidelity MZM qubits using superconductor-semiconductor nanowires will require engineering strategies and compromises very similar to those needed for conventional superconducting qubits.
Quasiparticle poisoning errors in Majorana-based qubits are not suppressed by the underlying topological properties, which undermines the usefulness of this proposed platform. This work tackles the errors originating from intrinsically excited quasiparticles by developing an erasure conversion scheme based on local quasiparticle detection. To model such measurements, we begin by constructing the quasiparticle position operator for the Kitaev chain. A measurement probe coupling to this operator is shown to allow projective measurements in the Wannier quasiparticle basis. Detection of quasiparticles in a region of width d adjacent to each Majorana zero-energy mode allows implementation of an error-detecting Majorana stabilizer code C d based on microscopic fermionic (nontopological) physical degrees of freedom. The implementation of C d converts a large fraction of Pauli errors to erasure errors, thus achieving “erasure conversion” in Majorana qubits. We show that the fraction of Pauli errors escaping conversion to erasure errors is exponentially small in d , a result tied to the exponential localization of Wannier functions which we prove rigorously. The suppression in Pauli error rate comes at the cost of the erasure rate increasing sublinearly with d , but this can be readily compensated for by a suitable outer code, with the net effect being a higher threshold rate of quasiparticle poisoning. The framework developed here serves as a basis for understanding how realistic measurements, such as conductance measurements, could be utilized for achieving fault tolerance in these systems. Published by the American Physical Society 2024