Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quasiparticle Poisoning of Majorana Qubits due to Changes in Chemical Potential and Charge Noise

Marcus Goffage

Published Oct 25, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.26190/unsworks/32807

Related papers

Leakage at zero temperature from changes in chemical potential in Majorana qubits

M. C. Goffage, Abhijeet Alase, Maja C. Cassidy +1 more

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.

arXiv:2504.17485•Physical review. B./Physical review. B•Sep 5, 2025•0 citations

Decoherence of Majorana qubits by 1/f noise

Abhijeet Alase, M. C. Goffage, Maja C. Cassidy +1 more

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.

arXiv:2506.22394•Jun 27, 2025•0 citations

Topological Quantum Computing with Majorana Zero Modes and Beyond

Christina Knapp

Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Information encoded in the degenerate state space of pairs of non-Abelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. However, topological quantum computing faces significant challenges, not least of which is identifying an experimentally accessible platform supporting non-Abelian topological physics. In this thesis, we critically analyze topological quantum computing with Majorana zero modes, non-Abelian defects of a topological superconductor. We identify intrinsic error sources for Majorana-based systems and propose quantum computing architectures that minimize their effects. Additionally, we consider a new approach for realizing and detecting non-Abelian topological defects in fractional Chern insulators. Topological quantum computing is predicated on the idea that braiding non-Abelian anyons adiabatically can implement quantum gates fault tolerantly. However, any braiding experiment will necessarily depart from the strict adiabatic limit. We begin by analyzing the nature of diabatic errors for anyon braiding, paying particular attention to how such errors scale with braiding time. We find that diabatic errors are unfavorably large and worryingly sensitive to details of the time evolution. We present a measurement-based correction protocol for such errors, and illustrate its application in a particular Majorana-based qubit design. We next propose designs for Majorana-based qubits operated entirely by a measurement-based protocol, thereby avoiding the diabatic errors discussed above. Our designs can be scaled into large two dimensional arrays amenable to long-term quantum computing goals, whose core components are testable in near-term devices. These qubits are robust to quasiparticle poisoning, anticipated to be one of the dominant error sources coupling to Majorana zero modes. We demonstrate that our designs support topologically protected Clifford operations and can be augmented to a universal gate set without requiring additional control parameters.While topological protection greatly suppresses errors, residual coupling to noise limits the lifetimes of our proposed Majorana-based qubits. We analyze the dephasing times for our quasiparticle-poisoning-protected qubits by calculating their charge distribution using a particle number-conserving formalism. We find that fluctuations in the electromagnetic environment couple to an exponentially suppressed topological dipole moment. We estimate dephasing times due to $1/f$ noise, thermal quasiparticle excitations, and phonons for different qubit sizes.The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a $C=2$ Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.

•Jan 1, 2019•2 citations

Transport of Majorana zero modes in topological superconducting wires

Bill P. Truong

Majorana zero modes (MZMs) appear as edge states in topological superconductors and are envisioned as promising candidates for application towards fault-tolerant quantum computation. Quantum information may be stored in a degenerate ground state subspace constructed from MZMs while quantum gates may be performed by braiding MZMs and exploiting their non-Abelian properties. While the topological protection of MZMs ensures that they are robust against decoherence, their dynamical manipulation can nonetheless induce undesirable transitions to excited states, manifesting as a “diabatic error.”This thesis studies the diabatic error accumulated as MZMs are transported across a superconducting wire, which is an essential building block for physical braiding schemes. The transport protocol considered relies on appropriately tuning sections (“piano keys”) of a wire between distinct topological phases via electric gates to control local chemical potentials. First, the diabatic error is examined for transport which uses multiple piano keys. The error is calculated through numerical simulation of the transport protocol and is complemented by approximate analytical expressions calculated using an effective, low-energy model. It is found that an optimal number of keys can be used to reduce the error. Furthermore, this thesis explores transport protocols performed on wires which feature disorder on the chemical potential and noise in the piano key tuning. The rise in the diabatic error due to these additional effects with respect to parameters-of-interest including the disorder strength, disorder correlation length, noise amplitude, and noise frequency cut-offs is characterized using numerical methods. For disorder, it is found that the error’s behaviour is principally controlled by the statistics of the minimum bulk energy gap. Spatially correlated disorder is also studied which presents non-monotonic behaviour for the error. Finally, for noise, it is found that optical transitions can cause a substantial increase in the error as the frequency modes within the noise approach the minimum energy gap.

•Jan 1, 2026•0 citations

Parity-Resolved Many-Body Kinetics of a Topological Qubit under Nonequilibrium Phonon Pulses

Han Huang

Phonon bursts from ionizing radiation cause correlated errors in superconducting quantum processors. We study prescribed nonequilibrium phonon pulses in a Majorana qubit formed by two $2\,μ\mathrm{m}$ proximitized nanowires. Combining the lattice Lutchyn--Oreg model, microscopic electron--phonon coupling, and parity-resolved many-body dynamics, we track excitation, relaxation, and logical coherence. Without quasiparticle escape, recombination restores the initial Majorana occupations in about 130 ns, while phonons exchanged during excitation and recovery can retain logical-state information, leaving permanent coherence loss. For mirror-symmetric wires, the fractional coherence loss per wire is 0.75--1.0 times the excitation probability averaged over the two logical states, even at zero Majorana splitting; breaking mirror symmetry can suppress dephasing at small splitting. Factorized Boltzmann kinetics neglects quasiparticle correlations and overestimates residual parity flips. At equal deposited energy density, phonon spectra yield different excitation probabilities and coherence losses. Comparisons with Kitaev chains matched to the wire's gap and Majorana decay length reveal that low electron density suppresses excitation by energetic phonons, whereas hard-wall boundaries in a high-density control increase excitation efficiency by a factor of $5\times10^4$ relative to the wire for pulses centered at 1 meV. Magnetic-field and chemical-potential tuning yield different phonon sensitivities at the same bulk gap through changes in spin and electron--hole structure. Including hybrid states' semiconductor weights reduces near-threshold excitation rates fourfold when the tunnel coupling equals the parent superconducting gap. Our framework connects phonon spectra to leakage, poisoning, and coherence loss to guide Majorana-device design.

cond-mat.supr-conCross-listedarXiv:2610.37793•Oct 29, 2026

Erasure conversion in Majorana qubits via local quasiparticle detection

Abhijeet Alase, Kevin D. Stubbs, Barry C. Sanders +1 more

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

arXiv:2307.08896•Physical Review Research•Dec 20, 2024•2 citations
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.
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.
Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Information encoded in the degenerate state space of pairs of non-Abelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. However, topological quantum computing faces significant challenges, not least of which is identifying an experimentally accessible platform supporting non-Abelian topological physics. In this thesis, we critically analyze topological quantum computing with Majorana zero modes, non-Abelian defects of a topological superconductor. We identify intrinsic error sources for Majorana-based systems and propose quantum computing architectures that minimize their effects. Additionally, we consider a new approach for realizing and detecting non-Abelian topological defects in fractional Chern insulators. Topological quantum computing is predicated on the idea that braiding non-Abelian anyons adiabatically can implement quantum gates fault tolerantly. However, any braiding experiment will necessarily depart from the strict adiabatic limit. We begin by analyzing the nature of diabatic errors for anyon braiding, paying particular attention to how such errors scale with braiding time. We find that diabatic errors are unfavorably large and worryingly sensitive to details of the time evolution. We present a measurement-based correction protocol for such errors, and illustrate its application in a particular Majorana-based qubit design. We next propose designs for Majorana-based qubits operated entirely by a measurement-based protocol, thereby avoiding the diabatic errors discussed above. Our designs can be scaled into large two dimensional arrays amenable to long-term quantum computing goals, whose core components are testable in near-term devices. These qubits are robust to quasiparticle poisoning, anticipated to be one of the dominant error sources coupling to Majorana zero modes. We demonstrate that our designs support topologically protected Clifford operations and can be augmented to a universal gate set without requiring additional control parameters.While topological protection greatly suppresses errors, residual coupling to noise limits the lifetimes of our proposed Majorana-based qubits. We analyze the dephasing times for our quasiparticle-poisoning-protected qubits by calculating their charge distribution using a particle number-conserving formalism. We find that fluctuations in the electromagnetic environment couple to an exponentially suppressed topological dipole moment. We estimate dephasing times due to 1/f1/f1/f noise, thermal quasiparticle excitations, and phonons for different qubit sizes.The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a C=2C=2C=2 Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.
Majorana zero modes (MZMs) appear as edge states in topological superconductors and are envisioned as promising candidates for application towards fault-tolerant quantum computation. Quantum information may be stored in a degenerate ground state subspace constructed from MZMs while quantum gates may be performed by braiding MZMs and exploiting their non-Abelian properties. While the topological protection of MZMs ensures that they are robust against decoherence, their dynamical manipulation can nonetheless induce undesirable transitions to excited states, manifesting as a “diabatic error.”This thesis studies the diabatic error accumulated as MZMs are transported across a superconducting wire, which is an essential building block for physical braiding schemes. The transport protocol considered relies on appropriately tuning sections (“piano keys”) of a wire between distinct topological phases via electric gates to control local chemical potentials. First, the diabatic error is examined for transport which uses multiple piano keys. The error is calculated through numerical simulation of the transport protocol and is complemented by approximate analytical expressions calculated using an effective, low-energy model. It is found that an optimal number of keys can be used to reduce the error. Furthermore, this thesis explores transport protocols performed on wires which feature disorder on the chemical potential and noise in the piano key tuning. The rise in the diabatic error due to these additional effects with respect to parameters-of-interest including the disorder strength, disorder correlation length, noise amplitude, and noise frequency cut-offs is characterized using numerical methods. For disorder, it is found that the error’s behaviour is principally controlled by the statistics of the minimum bulk energy gap. Spatially correlated disorder is also studied which presents non-monotonic behaviour for the error. Finally, for noise, it is found that optical transitions can cause a substantial increase in the error as the frequency modes within the noise approach the minimum energy gap.
Phonon bursts from ionizing radiation cause correlated errors in superconducting quantum processors. We study prescribed nonequilibrium phonon pulses in a Majorana qubit formed by two 2 μm2\,μ\mathrm{m}2μm proximitized nanowires. Combining the lattice Lutchyn--Oreg model, microscopic electron--phonon coupling, and parity-resolved many-body dynamics, we track excitation, relaxation, and logical coherence. Without quasiparticle escape, recombination restores the initial Majorana occupations in about 130 ns, while phonons exchanged during excitation and recovery can retain logical-state information, leaving permanent coherence loss. For mirror-symmetric wires, the fractional coherence loss per wire is 0.75--1.0 times the excitation probability averaged over the two logical states, even at zero Majorana splitting; breaking mirror symmetry can suppress dephasing at small splitting. Factorized Boltzmann kinetics neglects quasiparticle correlations and overestimates residual parity flips. At equal deposited energy density, phonon spectra yield different excitation probabilities and coherence losses. Comparisons with Kitaev chains matched to the wire's gap and Majorana decay length reveal that low electron density suppresses excitation by energetic phonons, whereas hard-wall boundaries in a high-density control increase excitation efficiency by a factor of 5×1045\times10^45×104 relative to the wire for pulses centered at 1 meV. Magnetic-field and chemical-potential tuning yield different phonon sensitivities at the same bulk gap through changes in spin and electron--hole structure. Including hybrid states' semiconductor weights reduces near-threshold excitation rates fourfold when the tunnel coupling equals the parent superconducting gap. Our framework connects phonon spectra to leakage, poisoning, and coherence loss to guide Majorana-device design.
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