Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length

Abstract

Realizing Majorana bound states (MBSs) in short, well-controllable chains of coupled quantum dots sidesteps the problem of disorder, but requires fine-tuning and does not give the true topological protection inherent to long chains. Here, we introduce a new quality measure that is applicable also in the presence of strong electron-electron interactions and that quantifies the closeness to topological protection of finetuned MBSs in short quantum-dot chains. We call this measure local distinguishability because it puts a bound to the degree an arbitrary local measurement can distinguish between two states. We study the local distinguishability for quantum-dot chains of different length. The three-dot chain is studied in detail, and we find that it may not always be an improvement over the two-dot case, a fact that can be understood within an effective model derived from perturbation theory. For longer chains, the local distinguishability vanishes exponentially, signalling a transition to a topological phase with two ground states that cannot be distinguished by any local measurement.

arXiv comment11 pages, 9 figures. Minor changes to more closely match the published version

References in corpus (62)

• Non-Abelian Anyons and Topological Quantum Computation
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Majorana Zero Modes and Topological Quantum Computation
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Introduction to topological superconductivity and Majorana fermions
• Majorana fermions in chains of magnetic atoms on a superconductor
• Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states
• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks
• Evidence of topological superconductivity in planar Josephson junctions
• Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement
• Transport spectroscopy of NS nanowire junctions with Majorana fermions
• Topological Superconductivity in a Phase-Controlled Josephson Junction
• Realization of a minimal Kitaev chain in coupled quantum dots
• Density-Matrix Spectra of Solvable Fermionic Systems
• Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
• Topological Superconductivity in a Planar Josephson Junction
• How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
• Two-dimensional platform for networks of Majorana bound states
• Reproducing topological properties with quasi-Majorana states
• Physical mechanisms for zero-bias conductance peaks in Majorana nanowires
• Parity qubits and poor man's Majorana bound states in double quantum dots
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• Quantized zero bias conductance plateau in semiconductor-superconductor heterostructures without non-Abelian Majorana zero modes
• Flux-induced topological superconductivity in full-shell nanowires
• Flux-induced Majorana modes in full-shell nanowires
• Topological superconductivity in full shell proximitized nanowires
• Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires
• Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires
• Search for non-Abelian Majorana braiding statistics in superconductors
• Supercurrent detection of topologically trivial zero-energy states in nanowire junctions
• Adaptive tuning of Majorana fermions in a quantum dot chain
• Majorana nanowires for topological quantum computation
• Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor-superconductor nanowires
• Extended Kitaev chain with longer-range hopping and pairing
• Topologically trivial zero bias conductance peak in semiconductor Majorana wires from boundary effects
• A two-site Kitaev chain in a two-dimensional electron gas
• Roadmap towards Majorana qubits and nonabelian physics in quantum dot-based minimal Kitaev chains
• Visualising Majorana bound states in 1D and 2D using the generalized Majorana polarization
• Local and non-local quantum transport due to Andreev bound states in finite Rashba nanowires with superconducting and normal sections
• Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
• Majorana bound states in open quasi-1D and 2D systems with transverse Rashba coupling
• Probing Majorana localization in minimal Kitaev chains through a quantum dot
• Fusion protocol for Majorana modes in coupled quantum dots
• Strong Coulomb interactions in the problem of Majorana modes in a wire of the nontrivial topological class BDI
• Many-body Majorana operators and the equivalence of parity sectors
• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Minimal quantum dot based Kitaev chain with only local superconducting proximity effect
• Multi-particle content of Majorana zero-modes in the interacting p-wave wire
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Kitaev chain in an alternating quantum dot-Andreev bound state array
• Zero modes of the Kitaev chain with phase-gradients and longer range couplings
• Robustness of Majorana edge states of short-length Kitaev chains coupled with environment
• Localized Many-Particle Majorana Modes with Vanishing Time-Reversal Symmetry Breaking in Double Quantum Dots
• Many-particle Majorana bound states: derivation and signatures in superconducting double quantum dots

Cited by in corpus (10)

• Observation of edge and bulk states in a three-site Kitaev chain
• Fate of poor man's Majoranas in the long Kitaev chain limit
• Majorana sweet spots in 3-site Kitaev chains
• Majorana modes in quantum dots coupled via a floating superconducting island
• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• Quantifying robustness and locality of Majorana bound states in interacting systems
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward