Fusion protocol for Majorana modes in coupled quantum dots

Abstract

In a recent breakthrough experiment [Nature (London) 614, 445 (2023)], signatures of Majorana zero modes have been observed in tunnel spectroscopy for a minimal Kitaev chain constructed from coupled quantum dots. However, as Ising anyons, Majoranas' most fundamental property of non-Abelian statistics is yet to be detected. Moreover, the minimal Kitaev chain is qualitatively different from topological superconductors in that it supports Majoranas only at a sweet spot. Therefore, it is not obvious whether non-Abelian characteristics such as braiding and fusion can be demonstrated in this platform with a reasonable level of robustness. In this work, we theoretically propose a protocol for detecting the Majorana fusion rules in an artificial Kitaev chain consisting of four quantum dots. In contrast with the previous proposals for semiconductor-superconductor hybrid nanowire platforms, here we do not rely on mesoscopic superconducting islands, which are difficult to implement in quantum dot chains. To show the robustness of the fusion protocol, we discuss the effects of three types of realistic imperfections on the fusion outcomes, e.g., diabatic errors, dephasing errors, and calibration errors. We also propose a fermion parity readout scheme using quantum capacitance. Our work will shed light on future experiments on detecting the non-Abelian properties of Majorana modes in a quantum dot chain.

8+5 pages, 4+3 figures

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Scaling of Majorana Zero-Bias Conductance Peaks
• Realization of a minimal Kitaev chain in coupled quantum dots
• InAs-Al Hybrid Devices Passing the Topological Gap Protocol
• Parity qubits and poor man's Majorana bound states in double quantum dots
• Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires
• Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor-superconductor nanowires
• Plateau regions for zero-bias peaks within 5% of the quantized conductance value $2e^2/h$
• Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas
• Dephasing and leakage dynamics of noisy Majorana-based qubits: Topological versus Andreev
• Small-signal equivalent circuit for double quantum dots at low-frequencies
• Fusion rules in a Majorana single-charge transistor
• Creating and detecting poor man's Majorana bound states in interacting quantum dots

Cited by in corpus (33)

• 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
• Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
• Probing Majorana localization in minimal Kitaev chains through a quantum dot
• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Observation of edge and bulk states in a three-site Kitaev chain
• Robustness of Majorana edge states of short-length Kitaev chains coupled with environment
• Fate of poor man's Majoranas in the long Kitaev chain limit
• 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
• Majorana modes in quantum dots coupled via a floating superconducting island
• Majorana sweet spots in 3-site Kitaev chains
• Machine-learned tuning of artificial Kitaev chains from tunneling-spectroscopy measurements
• Coupling of quantum-dot states via elastic-cotunneling and crossed Andreev reflection in a minimal Kitaev chain
• Scaling up a sign-ordered Kitaev chain without magnetic flux control
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• A flux-controlled two-site Kitaev chain
• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Probing the non-Abelian fusion of a pair of Majorana zero modes
• Transport of Majorana Bound State in the presence of telegraph noise
• Flux-Tunable Hybridization in a Double Quantum Dot Interferometer
• Majorana bound state parity exchanges in planar Josephson junctions
• Majorana braiding simulations with projective measurements
• Transport and fusion of Majorana zero modes in the presence of nonadiabatic transitions
• Transport-based fusion that distinguishes between Majorana and Andreev bound states
• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• Signatures of quantum phases in a dissipative system
• Fluctuation response of a minimal Kitaev chain in nonequilibrium states
• Quantum capacitance and parity switching of a quantum-dot-based Kitaev chain
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States
• Parity readout in Majorana box qubits from the dispersive to the resonant regime