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Quantum information processing with majorana bound states in superconducting circuits

Constantin Schrade

Published Dec 6, 2023• 0 citations
OpenAlex

Abstract

In a weak link of two s-wave superconductors (SCs) coupled via a time-reversal-invariant (TRI) topological superconducting (TSC) island, a Josephson current can flow due to Cooper pairs tunneling in and out of spatially separated Majorana Kramers pairs (MKPs), which are doublets of Majorana bound states (MBSs). The sign of the resulting Josephson current is fixed by the joint parity of the four Majorana bound states that make up the MKPs on the TSC island. This parity-controlled Josephson effect can be used as a read-out mechanism for the joint parity in Majorana-based quantum computing. For a TSC island with four terminals, the SC leads can address a Majorana superconducting qubit (MSQ) formed by the charge ground states of the TSC island's terminals. Cooper pair splitting enables single-qubit operations, qubit read-out, as well as two-qubit entangling gates. Hence, TSC islands between SC leads may provide an alternative approach to superconducting quantum computation.

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In a weak link of two s-wave superconductors (SCs) coupled via a time-reversal-invariant (TRI) topological superconducting (TSC) island, a Josephson current can flow due to Cooper pairs tunneling in and out of spatially separated Majorana Kramers pairs (MKPs), which are doublets of Majorana bound states (MBSs). The sign of the resulting Josephson current is fixed by the joint parity of the four Majorana bound states that make up the MKPs on the TSC island. This parity-controlled Josephson effect can be used as a read-out mechanism for the joint parity in Majorana-based quantum computing. For a TSC island with four terminals, the SC leads can address a Majorana superconducting qubit (MSQ) formed by the charge ground states of the TSC island's terminals. Cooper pair splitting enables single-qubit operations, qubit read-out, as well as two-qubit entangling gates. Hence, TSC islands between SC leads may provide an alternative approach to superconducting quantum computation.
We propose a universal gate set acting on a qubit formed by the degenerate ground states of a Coulomb-blockaded time-reversal invariant topological superconductor island with spatially separated Majorana Kramers pairs: the "Majorana Kramers qubit." All gate operations are implemented by coupling the Majorana Kramers pairs to conventional superconducting leads. Interestingly, in such an all-superconducting device, the energy gap of the leads provides another layer of protection from quasiparticle poisoning independent of the island charging energy. Moreover, the absence of strong magnetic fields-which typically reduce the superconducting gap size of the island-suggests a unique robustness of our qubit to quasiparticle poisoning due to thermal excitations. Consequently, the Majorana Kramers qubit should benefit from prolonged coherence times and may provide an alternative route to a Majorana-based quantum computer.
We propose a platform for universal quantum computation that uses conventional s-wave superconducting leads to address a topological qubit stored in spatially separated Majorana bound states in a multiterminal topological superconductor island. Both the manipulation and readout of this "Majorana superconducting qubit" are realized by tunnel couplings between Majorana bound states and the superconducting leads. The ability of turning on and off tunnel couplings on demand by local gates enables individual qubit addressability while avoiding cross-talk errors. By combining the scalability of superconducting qubit and the robustness of topological qubits, the Majorana superconducting qubit may provide a promising and realistic route towards quantum computation.
A practical quantum computer demands a physical quantum bit (qubit) that is scalable, has a well-defined initial state, and brings together coherence with reliable control and read-out. A compelling idea is to put together a locally protected Majorana qubit with a superconducting qubit. The superconducting qubit is used to read out the Majorana states while the Majorana qubit may act as a quantum memory. This thesis presents a series of studies on quantum transport in semiconducting nanowires coupled to superconductors to investigate various platforms for realizing Majorana. These studies are followed by microwave measurements on superconducting circuits compatible with semiconducting-superconducting heterostructures. We first evaluate the potential of Ge/Si core/shell nanowires by achieving induced superconductivity as well as estimating spin-orbit coupling. Next we explore the transport mediated by Andreev bound states formed in InSb nanowire quantum. A subgap negative differential conductance is investigated together with the coalescing Andreev resonances at zero bias relevant for the correct interpretation of Majorana experiments done on the same structures. We conclude our studies of semiconducting nanowires by exploring tunnel junctions in Sn-InSb nanowires that are prepared by in-situ shadowing using nearby nanowires and flakes. Tin shells are found to induce a hard superconducting gap persisting up to high magnetic fields. We observe the two-electron charging effect from a small superconducting island of Sn-InSb. This effect is attributed to charge parity stability, which makes this nanowire system an intriguing candidate for superconducting and topological quantum circuits. These Sn-InSb junctions are then used as the nonlinear element in a transmon qubit design where we observe a dispersive coupling between this nanowire Josephson junction and a superconducting resonator. We also present our progress towards building a magnetic field resilient superconducting circuit that allows integration with semiconducting and topological structures. In the last chapter, InSb semiconducting nanowires are utilized as shadow masks prior to superconductor deposition on an InAs quantum well. We study Josephson current properties in Josephson junctions made from these nanowire shadows. Our results point to highly transparent junctions that can be developed further for hybrid superconductor-semiconductor qubit systems.
We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the charge-stability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multilevel spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a non-Markovian environment. In particular, we study a gate-controlled protocol where conversion between Coulomb-blockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection.
In this paper, we study a set-up in which quantum dot is tunnel-coupled to Majorana-Kramers pair(MKP) which are the edge modes of time reversal invariant topological superconductor (TRITOPS), which is an experimental realization of time reversal invariant Kitaev chain model. Our motivation is to study the effect of Majorana-Kramers pair on Kondo fixed point and conversely the effect of Kondo interaction on Majorana-Kramers pair. This way we can capture the signatures of Majorana fermions on Kondo effect in quantum dots which can be probed feasibly in experiments. Employing the renormalization group method, we report the first study of the signatures of Majorana-Kramers pair in the dynamical spin susceptibility of the quantum dot electrons. We not only calculate the flow equations for coupling constants but also study the renormalization of observables and especially calculate dynamical spin susceptibility. We propose that since these dynamical quantities have signatures of Majorana-Kramers pair, so they provide an unambiguous experimental probe for detection of Majorana fermions in TRITOPS.
Minimal Kitaev chains composed of two semiconducting quantum dots coupled via a superconductor have emerged as a promising platform to realize and study Majorana bound states (MBSs), which appear for fine-tuned configurations. We propose a hybrid qubit based on a Josephson junction between two such double quantum dots (DQDs) embedded in a superconducting qubit geometry. The qubit makes use of the $4\ensuremath{\pi}$-Josephson effect in the Kitaev junction to create a subspace based on the even/odd fermionic parities of the two DQD arrays hosting MBSs. Deep in the transmon regime, we demonstrate that by performing circuit QED spectroscopy on such a hybrid Kitaev-transmon ``Kitmon'' qubit, one could observe distinct MBS features in perfect agreement with precise analytical predictions in terms of DQD parameters only. This agreement allows us to extract the Majorana polarization in the junction from the microwave response.