Artificial Kitaev chains have emerged as a promising platform for realizing topological quantum computing. Once the chains are formed and the Majorana zero modes are braided/fused, reading out the parity of the chains is essential for further verifying the non-Abelian property of the Majorana zero modes. Here we demonstrate the feasibility of using a superconducting transmon qubit, which incorporates an end of a four-site quantum dot-superconductor chain based on a Ge/Si nanowire, to directly detect the singlet/doublet state, and thus the parity of the entire chain. We also demonstrate that for multiple-dot chains there are two types of 0-π transitions between different charging states: the parity-flip 0-π transition and the parity-preserved 0-π transition. Furthermore, we show that the inter-dot coupling, hence the strengths of cross Andreev reflection and elastic cotunneling of electrons, can be adjusted by local electrostatic gating in chains fabricated on Ge/Si core-shell nanowires. Our exploration would be helpful for the ultimate realization of topological quantum computing based on artificial Kitaev chains.
Artificial Kitaev chains have emerged as a promising platform for realizing topological quantum computing. Once the chains are formed and the Majorana zero modes are braided/fused, reading out the parity of the chains is essential for further verifying the non-Abelian property of the Majorana zero modes. Here we demonstrate the feasibility of using a superconducting transmon qubit, which incorporates an end of a four-site quantum dot-superconductor chain based on a Ge/Si nanowire, to directly detect the singlet/doublet state, and thus the parity of the entire chain. We also demonstrate that for multiple-dot chains there are two types of 0-π transitions between different charging states: the parity-flip 0-π transition and the parity-preserved 0-π transition. Furthermore, we show that the inter-dot coupling, hence the strengths of cross Andreev reflection and elastic cotunneling of electrons, can be adjusted by local electrostatic gating in chains fabricated on Ge/Si core-shell nanowires. Our exploration would be helpful for the ultimate realization of topological quantum computing based on artificial Kitaev chains.
Artificial Kitaev chains (AKCs), formed of quantum dot--superconductor linear arrays, provide a promising platform for hosting Majorana bound states (MBSs) and implementing topological quantum computing. The main challenges along this research direction include the tuning of AKCs for hosting MBSs and the readout of the parity of the chains. In this work, we present a step-by-step procedure for tuning a three-site AKC to its sweet spots based on the spectra of a transmon circuit which is integrated with the chain for the purpose of reading out the parity of the chain. The signatures of the transmon's plasma modes in each step, in particular those related to the appearance of MBSs in the chain, will be given. We find that the sweet spots in a three-site AKC can be classified into three types based on the relative strengths of the elastic cotunneling (ECT) and crossed Andreev reflection (CAR): ECT-dominated sweet spots, genuine sweet spots, and CAR-dominated sweet spots. We show that the ECT-dominated and CAR-dominated sweet spots can be more conveniently accessed and utilized in transmon-based measurements.
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.
Artificial Kitaev chains (AKCs), formed of quantum dot-superconductor linear arrays, provide a promising platform for hosting Majorana bound states (MBSs) and implementing topological quantum computing. The main challenges along this research direction would include the tuning up of AKCs for hosting MBSs and the readout of the parity of the chains. In this work, we present a step-by-step procedure for tuning up a three-site AKC to its sweet spots based on the spectra of a transmon circuit which is integrated with the chain for the purpose of reading out the parity of the chain. The signatures of the transmon's plasma modes in each step, particular those related to the appearance of MBSs in the chain, will be given. We find that the sweet spots in a three-site AKC can be classified into three types based on the relative strengths of elastic cotunneling (ECT) and crossed Andreev reflection (CAR): ECT-dominated sweet spots, genuine sweet spots and CAR-dominated sweet spots. We show that the ECT-dominated and CAR-dominated sweet spots can be more conveniently accessed and utilized in transmon-based measurements.
The possibility of engineering 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, a two-site chain realized in a double quantum dot can already 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 have been named “poor man’s Majorana bound states” (PMMs) because they lack formal topological protection. In this work, we propose a pathway for next-generation experiments on PMMs. The pathway starts with experiments to characterize a single pair of PMMs by measuring the Majorana quality and then moves on to initialization and readout of the parity of a PMM pair, which allows the measurement of 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 analyze three different types of braidinglike experiments that 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 non-Abelian physics in minimal two-site Kitaev chains despite the lack of a true topological phase. However, our findings also reveal that doing so requires some extra care, appropriately modified protocols, and awareness of the details of this particular platform. Published by the American Physical Society 2024
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.
Topological quantum computation based on anyons is a promising approach to achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev chain are an example of non-Abelian anyons where braiding operations can be used to perform quantum gates. Here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the Majorana zero modes of a Kitaev chain. The quantum simulation is performed by mapping the Kitaev chain to its equivalent spin version and realizing the ground states in a superconducting quantum processor. The teleportation transfers the quantum state encoded in the spin-mapped version of the Majorana zero mode states between two Kitaev chains. The teleportation circuit is realized using only braiding operations and can be achieved despite being restricted to Clifford gates for the Ising anyons. The Majorana encoding is a quantum error detecting code for phase-flip errors, which is used to improve the average fidelity of the teleportation for six distinct states from 70.76±0.35% to 84.60±0.11%, well beyond the classical bound in either case.