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arXiv:2205.01410 · Physical Review Letters

SWAP Gate between a Majorana Qubit and a Parity-Protected Superconducting Qubit

Luca Chirolli, Norman Y. Yao, Joel E. Moore

Published Oct 20, 2022• 9 citations
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Abstract

High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this Letter, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a π-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the implementation of a SWAP gate, allowing for the transduction of quantum information between the topological and conventional qubit. This architecture combines fast gates, which can be realized with the superconducting qubit, with a topologically protected Majorana memory.

DOI
10.1103/physrevlett.129.177701

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High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this Letter, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a π-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the implementation of a SWAP gate, allowing for the transduction of quantum information between the topological and conventional qubit. This architecture combines fast gates, which can be realized with the superconducting qubit, with a topologically protected Majorana memory.
Hybrid semiconductor-superconductor qubits have recently emerged as a promising alternative to traditional platforms, combining material advantages with device-level tunability. A defining feature is their gate-tunable Josephson coupling, enabling superconducting qubit architectures with full electric-field control and offering a path toward scalable, low-crosstalk quantum processors. This approach seeks to merge benefits of superconducting and semiconductor qubits, for instance by encoding quantum information in the spin of a quasiparticle occupying an Andreev bound state, thus combining long coherence times with fast, flexible control. Progress has accelerated through bottom-up engineering of Andreev states in coupled quantum dot arrays, leading to architectures such as minimal Kitaev chains hosting Majorana zero modes. In parallel, Hamiltonian-protected designs aim to enhance resilience against local noise and decoherence by exploiting superconducting phase dynamics and discrete charge or flux degrees of freedom. This article reviews recent theoretical and experimental advances in hybrid qubits, providing an overview of physical mechanisms, device implementations, and emerging architectures, with emphasis on their potential for (topologically) protected quantum information processing. While many designs remain at proof-of-concept stage, rapid progress suggests practical demonstrations may soon be achievable.
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.
Quantum memory remains a critical bottleneck in the development of practical quantum computing and quantum communication. Current approaches to quantum memory, primarily based on superconducting or trapped ion technologies, struggle to maintain qubit coherence for extended periods and face significant challenges in scaling to large numbers of qubits. This research proposes a novel approach utilizing topological qubits, specifically Majorana fermions, to realize a dynamically reconfigurable quantum memory. The core concept involves harnessing the robust topological protection inherent in Majorana qubits to drastically reduce decoherence. By applying external magnetic fields, we can manipulate and control the entanglement state of these qubits, enabling rapid data access, retrieval, and erasure. This architecture represents a fundamental shift in quantum memory design, potentially circumventing the limitations of existing technologies and paving the way for scalable and long-lived quantum information storage. The proposed system utilizes a carefully engineered topological substrate to ensure high fidelity operations and minimal sensitivity to environmental noise. This paper details the theoretical framework, the proposed architecture, and explores the key considerations for implementing this dynamically reconfigurable quantum memory.
Parity-protected superconducting qubits offer intrinsically long coherence, but many current implementations require magnetic-flux biasing, which introduces flux noise, control overhead, and limited scalability. Here we propose a parity-protected qubit based on a gate-tunable superconductor-altermagnet-superconductor Josephson junction. Altermagnets are compensated magnets with momentum-dependent spin splitting and zero net magnetization, providing spin-dependent functionality without external magnetic fields. In the proposed junction, the two spin sectors acquire opposite phase shifts, generating two Josephson channels whose interference is controlled electrically by the chemical potential. At the tuned 000-πππ transition, the first Josephson harmonic is strongly suppressed while the second harmonic dominates, yielding a double-well potential with two nearly degenerate states of opposite Cooper-pair parity. For realistic gatemon-compatible parameters, we estimate coherence times of up to tens of milliseconds while maintaining fully gate-controlled qubit operations. These results establish altermagnetic Josephson junctions as a promising route toward protected superconducting qubits with local, scalable, and all-electrical control.
We propose and analyze a physical system capable of performing topological quantum computation with Majorana zero modes (MZMs) in a one-dimensional topological superconductor (1DTS). One of the leading methods to realize quantum gates in a 1DTS is to use T junctions, which allows one to maneuver MZMs in such a manner as to achieve braiding. In this paper, we propose a scheme for implementing quantum logical gates in a purely one-dimensional geometry without T junctions, instead replacing it with an auxiliary qubit. This has the additional benefit of introducing a non-Clifford gate, corresponding to one- and two-logical-qubit ZZZ rotations. We first design a topologically protected logical ZZZ gate based entirely on local interactions within the 1DTS. Using an auxiliary qubit coupled to the topological superconductors, we extend the ZZZ gate to non-Clifford single- and multiqubit arbitrary rotations with partial topological protection. Finally, to perform universal quantum computing, we introduce a scheme for performing arbitrary unitary rotations, albeit without topological protection. We develop a formalism based on unitary braids which creates transitions between different topological phases of the 1DTS system. The unitary formalism can be simply converted to an equivalent adiabatic scheme, which we numerically simulate, and we show that high-fidelity operations should be possible with reasonable parameters.