arXiv subjects

Sebastian Miles

Publications and source records attributed to Sebastian Miles.

12 recordsLinked to original sources

arXiv2026

Majorana parity qubit in coupled minimal Kitaev chains

Majorana zero modes provide a route to fault-tolerant qubits by encoding information non-locally in fermion parity. Their sensitivity to noise is expected to decrease exponentially with increasing separation between the Majoranas, a suppression known as topological protection. Kitaev chains engineered in quantum dot-superconductor arrays provide a tunable platform in which separated Majorana zero modes can emerge at the ends of the chain, even in two-site chains. These minimal-chain modes are known as poor man's Majoranas and retain characteristic Majorana properties, including near-zero energy and equal electron-hole character, but have only limited protection. A key outstanding challenge is to move beyond identifying such modes in electrical transport measurements and achieve coherent qubit control in the time domain. Here, we demonstrate a Majorana parity qubit by realizing coherent coupling between two-site Kitaev chains. Since total fermion parity is conserved, the system separates into global even and odd parity manifolds. We observe coherent parity oscillations in both manifolds with equal oscillation frequencies at the Majorana sweet spot, as predicted for isolated Majorana zero modes. We further show that the oscillation frequency and coherence depend systematically on inter-chain coupling and quantum-dot detunings, in close agreement with our model for short, partially protected chains. Our results establish the first coherent control of a Majorana qubit, encoded in the fermion parity of Majorana zero modes in minimal Kitaev chains.

cond-mat.mes-hall↗

arXiv2025

Probing ground-state degeneracies of a strongly interacting Fermi-Hubbard model with superconducting correlations

The Fermi-Hubbard model and its rich phase diagram naturally emerges as a description for a wide range of electronic systems. Recent advances in semiconductor-superconductor hybrid quantum dot arrays have allowed to realize degenerate quantum systems in a controllable way, e.g., allowing to observe robust zero-bias peaks in Kitaev chains, indicative for Majorana bound states. In this work, we connect these two domains. Noting the strong on-site Coulomb repulsion within quantum dots, we study small arrays of spinful hybrid quantum dots implemented in a two-dimensional electron gas. This system constitutes a Fermi-Hubbard model with inter-site superconducting correlations. For two electronic sites, we find robust zero-bias peaks indicative of a strongly degenerate spectrum hosting emergent Majorana Kramers pairs or $\mathbb{Z}_3$-parafermions. Extending to three sites, we find that these spinful systems scale very differently compared to spinless Kitaev chains. When the sweet-spot conditions are satisfied pairwise, we find that the ground state degeneracy of the full three-site system is lifted. This degeneracy can be restored by tuning the superconducting phase difference between the hybrid segments. However, these states are not robust to quantum dot detuning. Our observations are a first step towards studying degeneracies in strongly interacting Fermi-Hubbard systems with superconducting correlations.

cond-mat.mes-hall↗

arXiv2025

Effective Hamiltonians for Ge/Si core/shell nanowires from higher order perturbation theory

We theoretically explore the electronic structure of holes in cylindrical Germanium/Silicon core/shell nanowires using a perturbation theory approach. The approach yields a set of interpretable and transferable effective low-energy models for the lowest few sub-bands up to fifth order for experimentally relevant growth directions. In particular, we are able to resolve higher order cross terms e.g., the dependency of the effective mass on the magnetic field. Our study reveals orbital inversions of the lowest sub-bands for low-symmetry growth directions, leading to significant changes of the lower order effective coefficients. We demonstrate a reduction of the direct Rashba spin-orbit interaction due to competing symmetry effects for low-symmetry growth directions. Finally, we find that the effective mass of the confined holes can diverge yielding quasi flat bands interesting for correlated states. We show how one can tune the effective mass of a single spin band allowing one to tune the effective mass selectively to its divergent points.

cond-mat.mes-hall↗

arXiv2025

Quantifying robustness and locality of Majorana bound states in interacting systems

Protecting qubits from perturbations is a central challenge in quantum computing. Topological superconductors with separated Majorana bound states (MBSs) provide a strong form of protection that only depends on the locality of perturbations. While the link between MBS separation, robust degeneracy, and protected braiding is well understood in non-interacting systems, recent experimental progress in short quantum-dot-based Kitaev chains highlights the need to establish these connections rigorously for interacting systems. We do this by defining MBSs from many-body ground states and show how their locality constrains their coupling to an environment. This, in turn, quantifies the protection of the energy degeneracy and the feasibility of non-abelian braiding.

cond-mat.mes-hall↗

arXiv2025

Pareto-optimality of Majoranas in hybrid platforms

To observe Majorana bound states, and especially to use them as a qubit, requires careful optimization of competing quality metrics. We systematically compare Majorana quality in proximitized semiconductor nanowires and quantum dot chains. Using multi-objective optimization, we analyze the fundamental trade-offs between topological gap and localization length, two key metrics that determine MBS coherence and operational fidelity. We demonstrate that these quantities cannot be simultaneously optimized in realistic models, creating Pareto frontiers that define the achievable parameter space. Our results show that QD chains achieve both comparable quality as nanowires and a regime with a much shorter localization length, making them particularly promising for near-term quantum computing applications where device length and disorder are limiting factors.

cond-mat.mes-hall↗

arXiv2025

Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling

Exchanging the positions of two non-Abelian anyons transforms between many-body wavefunctions within a degenerate ground-state manifold. This behavior is fundamentally distinct from fermions, bosons and Abelian anyons. Recently, quantum dot-superconductor arrays have emerged as a promising platform for creating topological Kitaev chains that can host non-Abelian Majorana zero modes. In this work, we propose a minimal braiding setup in a linear array of quantum dots consisting of two minimal Kitaev chains coupled through an ancillary, normal quantum dot. We focus on the physical effects that are peculiar to quantum dot devices, such as interdot Coulomb repulsion and residual single electron tunneling. We find that the errors caused by either of these effects can be efficiently mitigated by optimal control of the ancillary quantum dot that mediates the exchange of the non-Abelian anyons. Moreover, we propose experimentally accessible methods to find this optimal operating regime and predict signatures of a successful Majorana braiding experiment.

cond-mat.mes-hall↗

arXiv2024

Scaling up a sign-ordered Kitaev chain without magnetic flux control

Quantum dot-superconductor arrays have emerged as a new and promising material platform for realizing topological Kitaev chains. So far, experiments have implemented a two-site chain with limited protection. Here we propose an experimentally feasible protocol for scaling up the chain in order to enhance the protection of the Majorana zero modes. To this end, we make use of the fact that the relative sign of normal and superconducting hoppings mediated by an Andreev bound state can be changed by electrostatic gates. In this way, our method only relies on the use of individual electrostatic gates on hybrid regions, quantum dots, and tunnel barriers, respectively, without the need for individual magnetic flux control, greatly simplifying the device design. Our work provides guidance for realizing a topologically protected Kitaev chain, which is the building block of error-resilient topological quantum computation.

cond-mat.mes-hall↗

arXiv2024

Interaction-induced strong zero modes in short quantum dot chains with time-reversal symmetry

We theoretically explore the emergence of strong zero modes in a two-site chain consisting of two quantum dots coupled due to a central dot that mediates electron hopping and singlet superconducting pairing. In the presence of time-reversal symmetry, the on-site Coulomb interaction leads to a three-fold ground-state degeneracy when tuning the system to a sweet spot as a function of the inter-dot couplings. This degeneracy is protected against changes of the dot energies in the same way as "poor man's'' Majorana bound states in short Kitaev chains. In the limit of strong interactions, this protection is maximal and the entire spectrum becomes triply degenerate, indicating the emergence of a ''poor man's'' version of a strong zero mode. We explain the degeneracy and protection by constructing corresponding Majorana Kramers-pair operators and $\mathbb{Z}_3$-parafermion operators. The strong zero modes share many properties of Majorana bound states in short Kitaev chains, including the stability of zero-bias peaks in the conductance and the behavior upon coupling to an additional quantum dot. However, they can be distinguished through finite-bias spectroscopy and the exhibit a different behavior when scaling to longer chains.

cond-mat.mes-hall↗

arXiv2024

Pymablock: an algorithm and a package for quasi-degenerate perturbation theory

A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer--Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, it is limited to two subspaces, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling and the ability to handle any number of subspaces with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.

quant-ph↗

arXiv2023

Kitaev chain in an alternating quantum dot-Andreev bound state array

We propose to implement a Kitaev chain based on an array of alternating normal and superconductor hybrid quantum dots embedded in semiconductors. In particular, the orbitals in the dot and the Andreev bound states in the hybrid are now on equal footing and both emerge as low-energy degrees of freedom in the Kitaev chain, with the couplings being induced by direct tunneling. Due to the electron and hole components in the Andreev bound state, this coupling is simultaneously of the normal and Andreev types, with their ratio being tunable by varying one or several of the experimentally accessible physical parameters, e.g., strength and direction of the Zeeman field, as well as changing proximity effect on the normal quantum dots. As such, it becomes feasible to realize a two-site Kitaev chain in a simple setup with only one normal quantum dot and one hybrid segment. Interestingly, when scaling up the system to a three-site Kitaev chain, next-nearest-neighbor couplings emerge as a result of high-order tunneling, lifting the Majorana zero energy at the sweet spot. This energy splitting is mitigated in a longer chain, approaching topological protection. Our proposal has two immediate advantages: obtaining a larger energy gap from direct tunneling and creating a Kitaev chain using a reduced number of quantum dots and hybrid segments.

cond-mat.mes-hall↗

arXiv2023

Fermionic quantum computation with Cooper pair splitters

We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. The device layout consists of quantum dots tunnel coupled by a hybrid superconducting island and a tunable capacitive coupling between the dots. We show that coherent control of Cooper pair splitting, elastic cotunneling, and Coulomb interactions allows us to implement the universal set of quantum gates defined by Bravyi and Kitaev. Due to the similarity with charge qubits, we expect charge noise to be the main source of decoherence. For this reason, we also consider an alternative design where the quantum dots have tunable coupling to the superconductor. In this second device design, we show that there is a sweetspot for which the local fermionic modes are charge neutral, making the device insensitive to charge noise effects. Finally, we compare both designs and their experimental limitations and suggest future efforts to overcome them.

cond-mat.mes-hall↗

arXiv2021

Universal properties of boundary and interface charges in continuum models of one-dimensional insulators

We study single-channel continuum models of one-dimensional insulators induced by periodic potential modulations which are either terminated by a hard wall (the boundary model) or feature a single region of dislocations and/or impurity potentials breaking translational invariance (the interface model). We investigate the universal properties of excess charges accumulated near the boundary and the interface, respectively. We find a rigorous analytic proof for the earlier observed linear dependence of the boundary charge on the phase of the periodic potential modulation as well as extend these results to the interface model. The linear dependence on the phase shows a universal value for the slope, and is intersected by discontinuous jumps by plus or minus one electron charge at the phase points where localized states enter or leave a band of extended states. Both contributions add up such that the periodicity of the excess charge in the phase over a $2\pi$-cycle is maintained. While in the boundary model this property is usually associated with the bulk-boundary correspondence, in the interface model a correspondence of scattering state and localized state contributions to the total interface charge is unveiled on the basis of the so-called nearsightedness principle.

cond-mat.mes-hall↗