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arxiv: 2506.22394 · v4 · pith:W7A6XEZEnew · submitted 2025-06-27 · ❄️ cond-mat.mes-hall · quant-ph

Decoherence of Majorana qubits by 1/f noise

Abhijeet Alase , Marcus C. Goffage , Maja C. Cassidy , Susan N. Coppersmith This is my paper

Pith reviewed 2026-05-25 08:14 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords qubitsdecoherencenanowireincreasingmajoranananowiresnoisequasiparticles
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The pith

1/f charge noise excites quasiparticles that cause substantial decoherence in Majorana qubits even under ideal conditions, and increasing capacitance trades one decoherence source for another.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Majorana qubits are promoted because their protection should make errors drop exponentially as wires get longer or colder. The paper identifies that real materials produce 1/f charge noise whose fast wiggles can create unwanted quasiparticles inside the superconducting wire. These quasiparticles flip the qubit state and destroy coherence. Raising the wire capacitance reduces this internal effect but leaves the qubit open to quasiparticles arriving from outside. The net result is that the same noise-management strategies needed for ordinary superconducting qubits will also be required here.

Core claim

Qubits based on Majorana zero modes are subject to substantial decoherence resulting from the high-frequency components of 1/f charge noise, which excites quasiparticles in the bulk of the topological superconductor that cause qubit decoherence even under otherwise ideal conditions.

Load-bearing premise

The assumption that 1/f charge noise with sufficient high-frequency spectral density is present in the materials surrounding the nanowire and can couple to and excite quasiparticles in the bulk topological superconductor.

Figures

Figures reproduced from arXiv: 2506.22394 by Abhijeet Alase, Maja C. Cassidy, Marcus C. Goffage, Susan N. Coppersmith.

Figure 1
Figure 1. Figure 1: Quasiparticle generation in MZM nanowires by TLFs. a: Rendering of a superconducting￾semiconducting nanowire device hosting MZMs. Atomic scale defects found in the materials surrounding the nanowire give rise to two-level fluctuators (TLFs) with different transition frequencies. b: Each TLF undergoes a series of sudden transitions between its states, each causing an instantaneous step in the chem￾ical pote… view at source ↗
Figure 2
Figure 2. Figure 2: Excitation of quasiparticle pairs by a single two-level fluctuator (TLF) in a Kitaev chain. a: Sketch of the Hamiltonian of a Kitaev chain that hosts Majorana zero modes (MZMs). The parameters for the Kitaev chain (Eq. (46)), w = 350.8 µeV, ∆ = 110 µeV, N ∈ {159, 80, 48} (corresponding to nanowire lengths of L ∈ {10 µm, 5 µm, 3 µm}), µ1 = 0, and µ2 = 2.83 µeV are determined from recent experiments [2] (see… view at source ↗
Figure 3
Figure 3. Figure 3: Decoherence of tetron qubit architecture caused by pairs of quasiparticles excited by 1/f noise. a: Schematic of a tetron qubit together with the even parity qubit states and odd parity leakage states. Because the MZM state at one end can be viewed as holding half a fermion, it is not possible for a single nanowire to have one empty and one full state. b: Decoherence by excited quasiparticles in the tetron… view at source ↗
Figure 4
Figure 4. Figure 4: Probability of exciting at least one quasiparticle pair (PQPP, 1ns) by a single two-level fluctuator (TLF) over a time t = 1 ns, averaged over 50 different realizations of the TLF with superconducting gaps of ∆ = 11 µeV (∆/h = 2.7 GHz), ∆ = 36.7 µeV (∆/h = 8.9 GHz), ∆ = 110 µeV (∆/h = 26.6 GHz), ∆ = 330 µeV (∆/h = 80 GHz), and ∆ = 990 µeV (∆/h = 239 GHz), with a chain length of L = 3 µm, hopping amplitude … view at source ↗
Figure 5
Figure 5. Figure 5: Excitation of quasiparticle pairs (QPPs) by a single two-level fluctuator (TLF) in Kitaev chains with lengths L = 3 µm, 5 µm, 10 µm, hopping parameter w = 350.8 µeV, superconducting gap ∆ = 110 µeV, and one TLF switching the chemical potential at rate Γ between the values µ1 = 0 µeV and µ2 = 2.83 µeV. a: Probability of exciting at least one QPP over 1 ns as calculated numerically for a Kitaev chain, P num … view at source ↗
Figure 6
Figure 6. Figure 6: Construction of 1/f noise as the sum of Lorentzians from an ensemble of two-level fluctuators (TLFs). Left: Plot of changes in chemical potential due to switches of TLFs versus time for TLFs with different transition rates Γ. Right: Illustration of how 1/f noise emerges from the fluctuations of an ensemble of TLFs in which the frequencies are uniformly distributed in the logarithm of the frequency, in othe… view at source ↗
Figure 7
Figure 7. Figure 7: Majorana zero mode localization (MZM) length ζ versus hopping w in the Kitaev chain model, for L = 10 µm, ∆ = 110 µeV and µ = 0 µeV. In the numerical calculations all energies are normalized by ∆, to obtain ∆ = 1, e µe = µ/∆ and we = w/∆ and the lattice constant a = 63 nm gives the number of Kitaev chain lattice sites of N = 159. Numerically calculated localization lengths are denoted by dots and asterisks… view at source ↗
Figure 8
Figure 8. Figure 8: Hexon qubit and decoherence arising from quasiparticle excitations. a: Schematic of hexon qubit [18], which consists of six nanowires of topological superconductor along with a backbone of s-wave superconductor designed so that the MZM modes in the nanowires underneath exhibit strong mixing with each other. b: Qubit states of a hexon qubit. The top two and bottom two MZMs are constrained to be in an even-p… view at source ↗
Figure 9
Figure 9. Figure 9: Diagram of the region in k-space in two dimensions that contributes significantly to the integral yielding the number of quasiparticle pairs excited by a jump in the chemical potential. In d dimensions the density of points in k-space is (2π/L ) d , and the volume of the region that contributes significantly is proportional to k (d−1) F (∆/(ℏvF)), or, equivalently for free electrons, k d F∆/EF. Therefore, … view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that Majorana zero-mode qubits in superconductor-semiconductor nanowires suffer substantial decoherence from the high-frequency tail of ubiquitous 1/f charge noise. This noise excites bulk quasiparticles across the superconducting gap, producing errors even in otherwise ideal (infinite-length, zero-temperature) devices. Increasing nanowire capacitance is shown to suppress the mechanism but to expose the qubit to externally generated quasiparticles, leading the authors to conclude that MZM qubits will require engineering compromises comparable to those already faced by conventional superconducting qubits.

Significance. If the quantitative estimates of the high-frequency noise amplitude and the electrostatic coupling matrix elements to delocalized bulk states are realistic, the result is significant: it identifies a decoherence channel whose rate does not fall exponentially with wire length or temperature and therefore sets a practical limit independent of the usual topological-protection arguments. The paper supplies a concrete, physically motivated mechanism rather than an abstract bound, and it explicitly discusses the capacitance trade-off, which could guide device design. No machine-checked proofs or parameter-free derivations are presented, but the work is falsifiable through measurements of the high-frequency noise spectrum and quasiparticle generation rates.

major comments (2)
  1. [Introduction / Model section] The central claim rests on the premise that 1/f charge noise possesses sufficient spectral density at frequencies ~Δ/ℏ to drive quasiparticle excitations with matrix elements large enough to produce substantial decoherence. This assumption is load-bearing; if the actual high-frequency amplitude or the coupling to bulk states is orders of magnitude weaker, the headline conclusion does not follow. The manuscript should supply explicit numerical estimates (or references) for the noise power spectral density at the relevant frequencies together with the calculated or measured coupling strengths.
  2. [Theory / Calculation section] The derivation of the decoherence rate from the noise-driven quasiparticle excitation process must be shown in detail, including the Fermi-golden-rule expression, the assumed form of the noise spectrum, and the integration over the bulk density of states. Without these steps the quantitative claim of 'substantial decoherence' cannot be verified.
minor comments (1)
  1. [Abstract] The abstract states that the mechanism operates 'even under otherwise ideal conditions'; the manuscript should clarify whether this includes the limit of infinite wire length and zero temperature or whether residual finite-size or thermal effects are still present.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive suggestions. The two major comments correctly identify areas where additional explicit detail will strengthen the presentation. We will revise the manuscript to address both points directly.

read point-by-point responses

  1. Referee: [Introduction / Model section] The central claim rests on the premise that 1/f charge noise possesses sufficient spectral density at frequencies ~Δ/ℏ to drive quasiparticle excitations with matrix elements large enough to produce substantial decoherence. This assumption is load-bearing; if the actual high-frequency amplitude or the coupling to bulk states is orders of magnitude weaker, the headline conclusion does not follow. The manuscript should supply explicit numerical estimates (or references) for the noise power spectral density at the relevant frequencies together with the calculated or measured coupling strengths.

    Authors: We agree that explicit numerical values and references are needed for verifiability. In the revised manuscript we will add a dedicated paragraph (or table) in the Model section that quotes representative experimental values of the 1/f noise amplitude A at frequencies near Δ/ℏ (citing relevant literature on charge noise in semiconductor-superconductor devices) together with the electrostatic matrix elements |⟨ψ_bulk| n |ψ_MZM⟩| obtained from our electrostatic model of the nanowire. These numbers underpin the claim of substantial decoherence and will be presented with their uncertainties. revision: yes

  2. Referee: [Theory / Calculation section] The derivation of the decoherence rate from the noise-driven quasiparticle excitation process must be shown in detail, including the Fermi-golden-rule expression, the assumed form of the noise spectrum, and the integration over the bulk density of states. Without these steps the quantitative claim of 'substantial decoherence' cannot be verified.

    Authors: We will expand the Theory section to include the complete step-by-step derivation. The revised text will state the Fermi-golden-rule rate explicitly, specify the noise spectrum S(ω) = A/|ω| (with the high-frequency cutoff), and show the integral over the bulk quasiparticle density of states ρ(ω) that yields the decoherence rate. Although the essential expressions appear in the current version, we acknowledge they are not presented with full intermediate steps; the revision will make the calculation self-contained and reproducible. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses standard noise-quasiparticle modeling as input

full rationale

The paper derives decoherence rates from the high-frequency tail of ubiquitous 1/f charge noise coupling to bulk quasiparticles in the topological superconductor. This rests on conventional physical mechanisms (noise spectrum, excitation across gap Δ) treated as external inputs rather than fitted or self-defined quantities. No equations reduce a prediction to a fit by construction, and no load-bearing self-citation chain is evident from the provided text. The central result follows from applying known noise properties to the MZM setup; the assumption of sufficient high-frequency spectral density is an explicit premise, not smuggled in via renaming or ansatz. This is the normal case of a self-contained calculation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that 1/f charge noise is ubiquitous and possesses high-frequency components capable of quasiparticle excitation; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption 1/f charge noise is ubiquitous in the materials surrounding the nanowire and contains high-frequency components that excite quasiparticles in the bulk topological superconductor
    Invoked directly in the abstract as the source of decoherence under otherwise ideal conditions.

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