Parity qubits and poor man's Majorana bound states in double quantum dots

Abstract

We study a double quantum dot connected via a common superconducting lead and show that this system can be tuned to host one Majorana bound state (MBS) on each dot. We call them "poor man's Majorana bound states" since they are not topologically protected, but otherwise share the properties of MBS formed in topological superconductors. We describe the conditions for the existence of the two spatially separated MBS, which include breaking of spin degeneracy in the two dots, with the spins polarized in different directions. Therefore, we propose to use a magnetic field configuration where the field directions on the two dot form an angle. By control of this angle the cross Andreev reflection and the tunnel amplitudes can be tuned to be approximately equal, which is a requirement for the formation of the MBS. We show that the fermionic state encoded in the two Majoranas constitutes a parity qubit, which is non-local and can only be measured by probing both dots simultaneously. Using a many-particle basis for the MBS, we discuss the role of interactions and show that inter-dot interactions always lift the degeneracy. We also show how the MBS can be probed by transport measurements and discuss how the combination of several such double dot systems allows for entanglement of parity qubits and measurement of their dephasing times.

7 pages, 3 figures. Published version

References in corpus (25)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• 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
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Majorana fermions in a tunable semiconductor device
• Majorana Fermion Induced Resonant Andreev Reflection
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Tunneling characteristic of a chain of Majorana bound states
• Andreev-Tunneling, Coulomb Blockade, and Resonant Transport of Non-Local Spin-Entangled Electrons
• Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor
• Carbon Nanotubes as Cooper Pair Beam Splitters
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Electronic Entanglement in the Vicinity of a Superconductor
• How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
• Non-Abelian operations on Majorana fermions via single charge control
• Majorana fermions in superconducting nanowires without spin-orbit coupling
• Quantum information transfer between topological and spin qubit systems
• Single Carbon Nanotube--Superconductor Entangler: noise correlations and EPR states
• Emerging Dirac and Majorana fermions for carbon nanotubes with proximity-induced pairing and spiral magnetic field
• Andreev reflection at half-metal-superconductor interfaces with non-uniform magnetization
• Using hybrid topological-spin qubit systems for two-qubit-spin gates

Cited by in corpus (138)

• Realization of a minimal Kitaev chain in coupled quantum dots
• Josephson ${\phi }_0$-junction in nanowire quantum dots
• Parity lifetime of bound states in a proximitized semiconductor nanowire
• Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires
• Adaptive tuning of Majorana fermions in a quantum dot chain
• Modulation of Majorana-Induced Current Cross-Correlations by Quantum Dots
• Majorana nanowires for topological quantum computation
• Anomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multi-level dots
• Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor-superconductor nanowires
• Tuning Yu-Shiba-Rusinov States in a Quantum Dot
• Quantifying wave-function overlaps in inhomogeneous Majorana nanowires
• 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
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Controlled crossed Andreev reflection and elastic co-tunneling mediated by Andreev bound states
• Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
• Mpemba effects in open nonequilibrium quantum systems
• Unconventional Superconductivity in Double Quantum Dots
• Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas
• Particle-hole symmetry protects spin-valley blockade in graphene quantum dots
• Crossed Andreev reflection and elastic co-tunneling in a three-site Kitaev chain nanowire device
• Quench dynamics and parity blocking in Majorana wires
• Probing Majorana localization in minimal Kitaev chains through a quantum dot
• Fusion protocol for Majorana modes in coupled quantum dots
• Signatures of Majorana protection in a three-site Kitaev chain
• Transport signatures of an Andreev molecule in a quantum dot -- superconductor -- quantum dot setup
• Minimal Kitaev-transmon qubit based on double quantum dots
• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Minimal quantum dot based Kitaev chain with only local superconducting proximity effect
• Fingerprints of Majorana bound states in Aharonov Bohm geometry
• Tunneling transport in NSN junctions made of Majorana nanowires across the topological quantum phase transition
• Phase-dependent heat and charge transport through superconductor-quantum dot hybrids
• Tunable Floquet Majorana Fermions in Driven Coupled Quantum Dots
• Parity-to-charge conversion for readout of topological Majorana qubits
• Observation of edge and bulk states in a three-site Kitaev chain
• Adversarial Hamiltonian learning of quantum dots in a minimal Kitaev chain
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in magnetic field
• Majorana mode leaking into a spin-charge entangled double quantum dot
• Interaction induced hybridization of Majorana zero-modes in a coupled quantum-dot hybrid-nanowire system
• Finite-frequency noise in a quantum dot with normal and superconducting leads
• Kitaev chain in an alternating quantum dot-Andreev bound state array
• Encrypting Majorana Fermions-qubits as Bound States in the Continuum
• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• Enhanced current noise correlations in a Coulomb-Majorana device
• From perfect to imperfect poor man's Majoranas in minimal Kitaev chains
• Fermion-parity qubit in a proximitized double quantum dot
• Majorana molecules and their spectral fingerprints
• Non-Hermitian multiterminal phase-biased Josephson junctions
• A quantum dot in germanium proximitized by a superconductor
• Probing Majorana-like states in quantum dots and quantum rings
• Phenomenology of Majorana zero modes in full-shell hybrid nanowires
• Strong nonlocal tuning of the current-phase relation of a quantum dot based Andreev molecule
• Fate of poor man's Majoranas in the long Kitaev chain limit
• Localized Many-Particle Majorana Modes with Vanishing Time-Reversal Symmetry Breaking in Double Quantum Dots
• Rabi and Ramsey oscillations of a Majorana qubit in a quantum dot-superconductor array
• Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length
• Driven Andreev molecule
• Detecting Majorana modes by readout of poisoning-induced parity flips
• Flux-tunable Kitaev chain in a quantum dot array
• Spin-degeneracy breaking and parity transitions in three-terminal Josephson junctions
• Fractional Josephson effect in a quadruple quantum dot
• Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor
• Non-collinear spin-orbit magnetic fields in a carbon nanotube double quantum dot
• Charge sensing the parity of an Andreev molecule
• Superconductor-quantum dot hybrid coolers
• Coupling of quantum-dot states via elastic-cotunneling and crossed Andreev reflection in a minimal Kitaev chain
• Majorana sweet spots in 3-site Kitaev chains
• Majorana modes in quantum dots coupled via a floating superconducting island
• Non-Hermitian minimal Kitaev chains
• Machine-learned tuning of artificial Kitaev chains from tunneling-spectroscopy measurements
• Adiabatic Cooper pair splitter
• Non local quantum state engineering with the Cooper pair splitter beyond the Coulomb blockade regime
• Emergent pair symmetries in systems with poor man's Majorana modes
• Two-impurity helical Majorana problem
• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
• Fano interference and a slight fluctuation of the Majorana hallmark
• Extracting entangled qubits from Majorana fermions in quantum dot chains through the measurement of parity
• Subgap dynamics of double quantum dot coupled between superconducting and normal leads
• Interaction-induced strong zero modes in short quantum dot chains with time-reversal symmetry
• Multiplicative Majorana zero-modes
• Floquet Majorana Fermions in superconducting quantum dots
• Full counting statistics in a Majorana single-charge transistor
• Majorana excitons in a Kitaev chain of semiconductor quantum dots in a nanowire
• Scaling up a sign-ordered Kitaev chain without magnetic flux control
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Flip-chip-based fast inductive parity readout of a planar superconducting island
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• A flux-controlled two-site Kitaev chain
• Design of a Majorana trijunction
• Many-particle Majorana bound states: derivation and signatures in superconducting double quantum dots
• Grain-boundary topological superconductor
• Fermionic quantum computation with Cooper pair splitters
• YSR Bond Qubit in a Double Quantum Dot with cQED Operation
• Autler-Townes Doublet observation via a Cooper-Pair Beam Splitter
• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Unified model for non-Abelian braiding of Majorana and Dirac fermion zero modes
• Josephson diode effect in nanowire-based Andreev molecules
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Spin-resolved nonlocal transport in proximitized Rashba nanowires
• Superconducting triangular islands as a platform for manipulating Majorana zero modes
• Phase-controlled minimal Kitaev chain in multiterminal Josephson junctions
• Flux-Tunable Hybridization in a Double Quantum Dot Interferometer
• Fractionalization of Majorana-Ising-type quasiparticles
• Exploring the energy spectrum of a four-terminal Josephson junction: Towards topological Andreev band structures
• Nonlocal Josephson diode effect in minimal Kitaev chains
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Complex-band-structure eigenvalue method adapted to Floquet systems: topological superconducting wires as a case study
• Characterizing local Majorana properties using Andreev states
• Non-Abelian holonomy of Majorana zero modes coupled to a chaotic quantum dot
• Fano fingerprints of Majoranas in Kitaev dimers of superconducting adatoms
• Super-Poissonian noise from quasiparticle poisoning in electron transport through a pair of Majorana bound states
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Superconducting Diode Effect in Double Quantum Dot Device
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• Nonreciprocal Equilibrium Josephson Effect of Arbitrary Periodicity from Poor Man's Majorana Zero Modes
• Spin dependent conductance of a quantum dot side attached to topological superconductors as a probe of Majorana fermion states
• AI-enhanced tuning of quantum dot Hamiltonians toward Majorana modes
• Majorana modes in a triple-terminal Josephson junction with embedded parallel-coupled double quantum dots
• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Quantifying robustness and locality of Majorana bound states in interacting systems
• Determination of the current-phase relation of an InAs 2DEG Josephson junction with a microwave resonator
• Creating and detecting poor man's Majorana bound states in interacting quantum dots
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward
• Entanglement dynamics in minimal Kitaev chains
• Andreev molecule in parallel InAs nanowires
• Directional conductance of Andreev crystals in hybrid Josephson junction arrays
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States
• Slave-spin approach to the Anderson-Josephson quantum dot
• Quantum capacitance and parity switching of a quantum-dot-based Kitaev chain
• Spin splitting, Kondo correlation and singlet-doublet quantum phase transition in a superconductor-coupled InSb nanosheet quantum dot
• Parity readout in Majorana box qubits from the dispersive to the resonant regime
• Optimal Majoranas in Mesoscopic Kitaev Chains
• Fluctuation response of a minimal Kitaev chain in nonequilibrium states
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Poor-man's Majorana edge mode enabled by specular Andreev reflection