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arXiv:2610.07169

Proposing one-sided tetrons as topological qubits for Majorana-based quantum computation

Tudor D. Stanescu, Sumanta Tewari

Published Oct 5, 2026• 0 citations
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Abstract

One-dimensional SM-SC hybrid nanowires with Rashba spin-orbit coupling and applied Zeeman field can support Majorana zero modes (MZMs) at the ends of the wire. In finite-length systems, residual wave-function overlap between the end modes produces an energy splitting. In a two-sided tetron qubit, composed of a pair of parallel Majorana wires coupled by a trivial SC backbone in the middle, this splitting limits the parity lifetime associated with Majorana pairs involving both wires and the coherence of the qubit, adversely affecting measurement-based braiding and readout operations. Here, we propose a one-sided tetron made of four parallel Majorana wires connected at a common end by an SC backbone. In the topological phase, the free wire ends host four MZMs that define the topological qubit, while the Majoranas localized near the opposite ends hybridize through the backbone and acquire finite energy. To study the basic hybridization mechanism, we consider a simpler two-wire subsystem, i.e., half of a one-sided tetron, which we call a doublon. In a doublon, the backbone, or bridge, strongly hybridizes the two Majorana modes at the connected end and shifts them away from zero energy, while the modes at the free ends form a near-zero energy fermion. We show that the splitting of the surviving MZM pair can fall by about two orders of magnitude compared to the splitting energies in a two-sided tetron, thereby dramatically increasing the parity lifetimes. Thus, the one-sided tetron ensures a suppression of the Majorana overlap comparable to doubling the length of the corresponding two-sided tetron.

DOI
10.48550/arxiv.2610.07169

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One-dimensional SM-SC hybrid nanowires with Rashba spin-orbit coupling and applied Zeeman field can support Majorana zero modes (MZMs) at the ends of the wire. In finite-length systems, residual wave-function overlap between the end modes produces an energy splitting. In a two-sided tetron qubit, composed of a pair of parallel Majorana wires coupled by a trivial SC backbone in the middle, this splitting limits the parity lifetime associated with Majorana pairs involving both wires and the coherence of the qubit, adversely affecting measurement-based braiding and readout operations. Here, we propose a one-sided tetron made of four parallel Majorana wires connected at a common end by an SC backbone. In the topological phase, the free wire ends host four MZMs that define the topological qubit, while the Majoranas localized near the opposite ends hybridize through the backbone and acquire finite energy. To study the basic hybridization mechanism, we consider a simpler two-wire subsystem, i.e., half of a one-sided tetron, which we call a doublon. In a doublon, the backbone, or bridge, strongly hybridizes the two Majorana modes at the connected end and shifts them away from zero energy, while the modes at the free ends form a near-zero energy fermion. We show that the splitting of the surviving MZM pair can fall by about two orders of magnitude compared to the splitting energies in a two-sided tetron, thereby dramatically increasing the parity lifetimes. Thus, the one-sided tetron ensures a suppression of the Majorana overlap comparable to doubling the length of the corresponding two-sided tetron.
Finite-length one-dimensional topological superconductor wires host localized Majorana zero modes at their ends. In realistic models, these appear only after a topological quantum critical point is crossed by external tuning of parameters. Thus, there is a universal finite-size scaling, governed by the critical point, that dictates the evolution of the energy of the Majorana modes near the transition. We first describe this scaling, then apply it in detail to an explicit synthetic topological superconductor model. Our work not only connects Ising quantum criticality with realistic nanowires in the presence of spin-orbit coupling, Zeeman splitting, and superconductivity, but also provides a viable experimental route for discerning the existence of the topological quantum critical point.
Majorana-based topological qubits are expected to exploit the nonabelian braiding statistics of Majorana modes in topological superconductors to realize fault-tolerant topological quantum computation.Scalable qubit designs require several Majorana modes localized on quantum wires networks, with braiding operations relying on the presence of the groundstate degeneracy of the topologically nontrivial superconducting phase.However, this degeneracy is lifted due to the hybridization between Majorana modes localized at a finite distance.Here, we describe a braiding protocol in a trijunction where each branch consists of a lattice of Majorana modes overlapping at a finite distance.We find that the energy splitting between the groundstate and the lowest-energy state decreases exponentially with the number of Majorana modes if the system is in its topologically nontrivial regime.This result does not rely on the specific braiding geometry and on the details of the braiding scheme but is a consequence of the supersymmetry and nontrivial topology of the effective low-energy Hamiltonian describing the Majorana lattice.
Majorana zero modes, quasiparticles with non-Abelian statistics, have gained increasing interest for their fundamental role as building blocks in topological quantum computation. Previous studies have mainly focused on two well-separated Majorana zero modes, which could form two degenerate states serving as one nonlocal qubit for fault-tolerant quantum memory. However, creating and manipulating multiple Majorana zero modes, which could encode more qubits, remain an ongoing research topic. Here we report that multiple Majorana zero modes can exist in atomic Fermi double wires with spin-orbit coupling and perpendicular Zeeman field. This system belongs to the topological BDI class, thus all the topological superfluids are classified by integer numbers. Especially, diverse topological superfluids can be formed in a trap, where the zero energy modes can be found at the interfaces between different topological superfluids. The structure of these zero energy modes in the trap can be engineered by the trapping potential as well as other system parameters. This system would be a significant step towards utilization of Majorana zero modes in quantum computation.
Proximity-induced superconductivity in low-dimensional systems offers a powerful pathway to engineer topological superconducting phases in, otherwise, non-superconducting systems. These exotic phases are of fundamental and technological interest due to the presence of robust zero-energy modes, the Majorana bound states. In this work, we propose a theoretical framework to realize Majorana bound states from the edge states of a two-dimensional semi-Dirac system. This anisotropic system, under specific conditions, can host non-chiral edge states that propagate only along particular edges, effectively forming separated one-dimensional channels. We show that the interplay between Rashba spin-orbit coupling and a Zeeman field on this setup provides the right conditions to get an effective p-wave pairing between the edge states by proximity with a s-wave superconductor. In finite geometries, each edge can independently undergo a topological phase transition into a one-dimensional topological superconductor and give rise to four zero-energy modes localized at the strip corners. At low energies, the edge states subspace admits a description in terms of coupled Kitaev chains, providing a clear picture of the origin, robustness, and tunability of the corner Majorana modes. Our results establish semi-Dirac materials as a natural platform for realizing Majorana modes in two dimensions without relying on engineered nanostructures, vortices, or crystalline higher-order topology.
Majorana zero modes are emergent zero-energy quasiparticle excitations in certain superconducting systems that can be viewed as fractionalized or “half” electrons. These quasiparticles obey non-Abelian braiding statistics which is one manifestation of such half-electron character. Due to such non-Abelian braiding property, Majorana zero mode pairs hold promise as potential qubits for topological quantum computation. It is somewhat surprising that, at least theoretically, ordinary one-dimensional semiconductor systems can be induced to host such esoteric Majorana modes as edge states if some precise experimental conditions are satisfied. Because of the relative simplicity of material and experimental requirements to host Majorana modes, there has been a flurry of experimental effort to realize them in semiconductor nanowire systems. While experimental efforts have produced preliminary evidence for the presence of Majorana zero modes in these systems, a thorough confirmation is lacking. The experimental signature in question is the presence of a zero-bias conductance-peak that, while necessary, is not a sufficient criterion to establish the presence of underlying Majorana modes. Given the importance of Majorana braiding for topological quantum computation and skepticism over the presence of Majorana modes in these experimental systems, it would seem natural to attempt braiding these putative Majorana modes in the near future. In that case, an observation of non-Abelian statistics would provide the necessary and sufficient condition in favor of Majorana presence in the studied experimental systems. This thesis has three distinct parts. First, we assume perfect Majorana modes as given that can be successfully braided. In this case, we calculate the diabatic error due to the finite speed of braiding when the system is coupled to a Bosonic bath. Next, we grant that the mechanism for zero-bias conductance-peak is indeed topological, albeit the underlying Majorana modes may be imperfect (the modes are not precisely at zero energy). We study the interplay of dissipation and finite energy splitting of the Majorana modes and study its consequence regarding the probability of successful braiding. Lastly, we propose studying the correlation between independent left and right conductance measurements as a means to distinguish between a topological versus a non-topological the mechanism underlying the observed zero-bias conductance-peak.
We show that the microwave (MW) spectra in semiconductor-nanowire-based transmon qubits provide a strong signature of the presence of Majorana bound states in the junction.This occurs as an external magnetic field tunes the wire into the topological regime and the energy splitting of the emergent Majorana modes oscillates around zero energy owing to their wave function spatial overlap in finite-length wires.In particular, we discuss how these Majorana oscillations, and the concomitant fermion parity switches in the ground state of the junction, result in distinct spectroscopic features-in the form of an intermittent visibility of absorption lines-that strongly deviate from standard transmon behavior.In contrast, nonoscillating zero modes, such as topologically trivial Andreev bound states resulting from sufficiently smooth potentials, exhibit an overall standard transmon response.These differences in the MW response could help determine whether the junction contains topological Majoranas or not.