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arXiv:2511.09591 · Annalen der Physik

Quantum Frustration as a Protection Mechanism in Non-Topological Majorana Qubits

E. Novais

quant-phcond-mat.mes-hallSubmitted Nov 12, 2025• Announced Nov 13, 2025• 0 citations• Revised Apr 7, 2026 (v2)
v1 · Nov 12, 2025v2 · Apr 7, 2026
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Abstract

I analyze the decoherence of a $π$-junction qubit encoded by two co-located Majorana modes. Although not topologically protected, the qubit leverages distinct spatial profiles to couple to two independent environmental baths, realizing the phenomenon of quantum frustration. This mechanism is tested against the threat of quasiparticle poisoning (QP). I show that frustration is effective against Ohmic noise ($s=1$) and has some protection for $0.76<s<1$ sub-Ohmic noise. However, the experimentally prevalent $1/f$ noise ($s\to0$) falls deep within the model's localized phase, where frustration is insufficient. This causes spontaneous symmetry breaking and catastrophic decoherence. The qubit's viability depends on what the effective environment is that these local Majorana wave functions experience.

DOI
10.1002/andp.202500581
Comments
12 pages, 4 figures, improved discussion and two new appendices

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I analyze the decoherence of a πππ-junction qubit encoded by two co-located Majorana modes. Although not topologically protected, the qubit leverages distinct spatial profiles to couple to two independent environmental baths, realizing the phenomenon of quantum frustration. This mechanism is tested against the threat of quasiparticle poisoning (QP). I show that frustration is effective against Ohmic noise (s=1s=1s=1) and has some protection for 0.76<s<10.76<s<10.76<s<1 sub-Ohmic noise. However, the experimentally prevalent 1/f1/f1/f noise (s→0s\to0s→0) falls deep within the model's localized phase, where frustration is insufficient. This causes spontaneous symmetry breaking and catastrophic decoherence. The qubit's viability depends on what the effective environment is that these local Majorana wave functions experience.
We investigate the decoherence patterns of topological qubits in contact with the environment using a novel way of deriving the open system dynamics, rather than using the Feynman–Vernon approach. Each topological qubit is made up of two Majorana modes of a 1D Kitaev chain. These two Majorana modes interact with the environment in an incoherent way which yields peculiar decoherence patterns of the topological qubit. More specifically, we consider the open system dynamics of topological qubits which are weakly coupled to fermionic/bosonic Ohmic-like environments. We find atypical patterns of quantum decoherence. In contrast to the case for non-topological qubits—which always decohere completely in all Ohmic-like environments—topological qubits decohere completely in Ohmic and sub-Ohmic environments but not in super-Ohmic ones. Moreover, we find that the fermion parities of the topological qubits, though they cannot prevent the qubit states from exhibiting decoherence in sub-Ohmic environments, can prevent thermalization turning the state into a Gibbs state. We also study the cases in which each Majorana mode can couple to different Ohmic-like environments, and the time dependence of concurrence for two topological qubits.
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.
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.
We show that the electromagnetic or phononic environment of a topological quantum device can be engineered to actively suppress decoherence. For a Majorana qubit in a superconducting wire, the exponentially small splitting ε∼e−L/ξε\sim e^{-L/ξ}ε∼e−L/ξ that provides topological protection also makes the qubit vulnerable to low-frequency noise. From a microscopic local interaction, we derive the effective low-energy coupling between the Majorana parity operator and a bosonic field; the coupling strength itself is proportional to εεε, reflecting the qubit's non-local nature. The resulting pure-dephasing rate scales as Γϕ∝ε2S(ε)Γ_ϕ\propto ε^2 S(ε)Γϕ​∝ε2S(ε), with S(ε)S(ε)S(ε) the environmental noise power at frequency εεε. In the experimentally relevant high-temperature regime (kBT≳ℏεk_B T \gtrsim \hbarεkB​T≳ℏε), this gives Γϕ∝ερ(ε)TΓ_ϕ\propto ερ(ε) TΓϕ​∝ερ(ε)T, where ρ(ε)ρ(ε)ρ(ε) is the environmental density of states. By engineering an environment with a suppressed low-frequency density of states, ρeng(ω)=ρ0(ω/ωc)αρ_{\text{eng}}(ω) = ρ_0 (ω/ω_c)^αρeng​(ω)=ρ0​(ω/ωc​)α for ω<ωcω< ω_cω<ωc​ (α>0α> 0α>0), the dephasing rate drops to Γϕeng∝εα+1∝e−(α+1)L/ξΓ_ϕ^{\text{eng}} \propto ε^{α+1} \propto e^{-(α+1)L/ξ}Γϕeng​∝εα+1∝e−(α+1)L/ξ. Thus, longer wires yield exponentially better coherence---a direct synergy with topological protection. This "inverse Purcell" effect, which suppresses the density of states at the qubit frequency, provides a quantitative design principle for environmental engineering. Our work establishes spectral density shaping as a practical method for enhancing coherence in topological quantum devices.
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 and tunnel-coupled to fermionic reservoirs, we recover analytical expressions for the decoherence rate of a Majorana qubit at arbitrary values of the charging energy. The analysis shows that the exponential suppression of the decoherence 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.
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.