Roadmap towards Majorana qubits and nonabelian physics in quantum dot-based minimal Kitaev chains

Abstract

The possibility to engineer artificial Kitaev chains in arrays of quantum dots coupled via narrow superconducting regions has emerged as an attractive way to overcome the disorder issues that complicate the realization and detection of topological superconducting phases in other platforms. Although a true topological phase would require long chains, already a two-site chain realized in a double quantum dot can be tuned to points in parameter space where it hosts zero-energy states that seem identical to the Majorana bound states that characterize a topological phase. These states were named "poor man's Majorana bound states" (PMMs) because they lack formal topological protection. In this work, we propose a roadmap for next-generation experiments on PMMs. The roadmap starts with experiments to characterize a single pair of PMMs by measuring the Majorana quality, then moves on to initialization and readout of the parity of a PMM pair, which allows measuring quasiparticle poisoning times. The next step is to couple two PMM systems to form a qubit. We discuss measurements of the coherence time of such a qubit, as well as a test of Majorana fusion rules in the same setup. Finally, we propose and analyse three different types of braiding-like experiments which require more complex device geometries. Our conclusions are supported by calculations based on a realistic model with interacting and spinful quantum dots, as well as by simpler models to gain physical insight. Our calculations show that it is indeed possible to demonstrate nonabelian physics in minimal two-site Kitaev chains despite the lack of a true topological phase. But our findings also reveal that doing so requires some extra care, appropriately modified protocols and awareness of the details of this particular platform.

24 pages, 8 figures

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Cited by in corpus (53)

• A two-site Kitaev chain in a two-dimensional electron gas
• Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
• Mpemba effects in open nonequilibrium quantum systems
• Signatures of Majorana protection in a three-site Kitaev chain
• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Observation of edge and bulk states in a three-site Kitaev chain
• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• From perfect to imperfect poor man's Majoranas in minimal Kitaev chains
• Fermion-parity qubit in a proximitized double quantum dot
• Robustness of Majorana edge states of short-length Kitaev chains coupled with environment
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• Rabi and Ramsey oscillations of a Majorana qubit in a quantum dot-superconductor array
• Fate of poor man's Majoranas in the long Kitaev chain limit
• Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor
• Materials for Quantum Technologies: a Roadmap for Spin and Topology
• Majorana sweet spots in 3-site Kitaev chains
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• A flux-controlled two-site Kitaev chain
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• YSR Bond Qubit in a Double Quantum Dot with cQED Operation
• Superconducting Proximity Effect in Two-Dimensional Hole Gases
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
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• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Nonreciprocal Equilibrium Josephson Effect of Arbitrary Periodicity from Poor Man's Majorana Zero Modes
• Quantifying robustness and locality of Majorana bound states in interacting systems
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Fluctuation response of a minimal Kitaev chain in nonequilibrium states
• Quantum capacitance and parity switching of a quantum-dot-based Kitaev chain
• Optimal Majoranas in Mesoscopic Kitaev Chains
• Entanglement dynamics in minimal Kitaev chains