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arXiv:2303.04344 · Physical Review A

Proposal for a nonadiabatic geometric gate with an Andreev spin qubit

Mostafa Tanhayi Ahari, Yaroslav Tserkovnyak

Published Mar 1, 2024• 5 citations
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Abstract

We study a hybrid structure of a ferromagnetic insulator and a superconductor connected by a weak link, which accommodates Andreev bound states whose spin degeneracy is lifted due to the exchange interaction with the ferromagnet. The resultant spin-resolved energy levels realize a two-state quantum system, provided that a single electron is trapped in the bound state, i.e., an Andreev spin qubit. The qubit state can be manipulated by controlling the magnetization dynamics of the ferromagnet, which mediates the coupling between external fields and the qubit. In particular, our hybrid structure provides a simple platform to manipulate and control the spin qubit using spintronic techniques. By employing a modified Hahn spin echo protocol for the magnetization dynamics, we show that our Andreev spin qubit can realize a nonadiabatic geometric gate.

DOI
10.1103/physreva.109.032601

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We study a hybrid structure of a ferromagnetic insulator and a superconductor connected by a weak link, which accommodates Andreev bound states whose spin degeneracy is lifted due to the exchange interaction with the ferromagnet. The resultant spin-resolved energy levels realize a two-state quantum system, provided that a single electron is trapped in the bound state, i.e., an Andreev spin qubit. The qubit state can be manipulated by controlling the magnetization dynamics of the ferromagnet, which mediates the coupling between external fields and the qubit. In particular, our hybrid structure provides a simple platform to manipulate and control the spin qubit using spintronic techniques. By employing a modified Hahn spin echo protocol for the magnetization dynamics, we show that our Andreev spin qubit can realize a nonadiabatic geometric gate.
We show that Andreev spin qubits can be realized in a Josephson junction based on the helical edge states of a two-dimensional topological insulator (quantum spin Hall system) proximized by superconducting films, in the presence of magnetic doping. We demonstrate that the electric dipole transitions between the Andreev spin states induced by the magnetic doping can be harnessed to manipulate the Andreev spin qubit by microwave radiation pulses, without applying an external Zeeman field or invoking ancillary states. We numerically simulate the realization of NOT and Hadamard quantum logic gates, and discuss implementations in realistic setups.
We propose a variant of Andreev spin qubits (ASQs) defined in planar Josephson junctions based on spin-orbit coupled two-dimensional electron gases (2DEGs) in a weak out-of-plane magnetic field. The magnetic field induces a linear phase gradient across the junction, generating Josephson vortices that can host low-energy Andreev bound states (ABSs). We show that, in certain parameter regimes, the combined effect of the phase gradient and spin-orbit coupling stabilizes an odd-fermion parity ground state, where a single Josephson vortex binds a spinful low-energy degree of freedom that is energetically separated from the other ABSs. This low-energy degree of freedom can be exploited to define a special type of ASQ, which we dub the vortex spin qubit (VSQ). We show that single-qubit gates for VSQs can be performed via flux driving, while readout can be achieved by adapting standard circuit quantum electrodynamics (cQED) techniques developed for conventional ASQs. We further outline how an entangling two-qubit gate can be performed using an ac current drive. We argue that VSQs offer prospects for a substantial reduction in device complexity and hardware overhead compared to conventional ASQ implementations, while preserving key advantages such as supercurrent-based readout, single-qubit gates, and long-range two-qubit gates.
We show how superconductors can be used to couple, initialize, and read out spatially separated spin qubits. When two single-electron quantum dots are tunnel coupled to the same superconductor, the singlet component of the two-electron state partially leaks into the superconductor via crossed Andreev reflection. This induces a gate-controlled singlet-triplet splitting which, with an appropriate superconductor geometry, remains large for dot separations within the superconducting coherence length. Furthermore, we show that when two double-dot singlet-triplet qubits are tunnel coupled to a superconductor with finite charging energy, crossed Andreev reflection enables a strong two-qubit coupling over distances much larger than the coherence length.
In this work, we explore a hybrid qubit device where quantum information is encoded by quantum states of a transmon entangled with the spin of a trapped Andreev quasiparticle. We term such devices spinmons. We lift the spinmon Kramers degeneracy by introducing a Zeeman field and develop two routes for full qubit control via electrostatic gates and an AC flux drive, providing multiple directions for experimental implementations. Finally, we compute coherence times, verify the qubit robustness against flux, charge and gate voltage noise sources, and discuss the role of nuclear spin noise.
Solid-state spin qubits are promising candidates for the realization of a quantum computer due to their long coherence times and easy electrical manipulation. However, spin-spin interactions, which are needed for entangling gates, have only limited range as they generally rely on tunneling between neighboring quantum dots. This severely constrains scalability. Proposals to extend the interaction range generally focus on coherent electron transport between dots or on extending the coupling range. Here, we study a setup in which such an extension is obtained by using a superconductor as a quantum mediator. Because of its gap, the superconductor effectively acts as a long tunnel barrier. We analyze the impact of spin-orbit (SO) coupling, external magnetic fields, and the geometry of the superconductor. We show that while spin-nonconserving tunneling between the dots and the superconductor due to SO coupling does not affect the exchange interaction, strong SO scattering in the superconducting bulk is detrimental. Moreover, we find that the addition of an external magnetic field decreases the strength of the exchange interaction. Fortunately, the geometry of the superconducting link offers a lot of room to optimize the interaction range, with gains of over an order of magnitude from a two-dimensional (2D) film to a quasi-1D strip. We estimate that for superconductors with weak SO coupling (e.g., aluminum), exchange rates of up to 100 MHz over a micron-scale range can be achieved with this setup in the presence of magnetic fields of the order of 100 mT.
Mesoscopic Physics In superconductors, single particles cannot have energies smaller than the superconducting gap. Yet when two superconductors are separated by a thin nonsuperconducting bridge (the “weak link”), quasi-particles can occupy states that are inside the gap, the so-called Andreev bound states (ABSs). Janvier et al. fabricated such a structure out of superconducting aluminum and manipulated the occupation of a pair of ABSs. They observed oscillations in population between two of the energy levels, forming a type of qubit, which they dubbed the Andreev qubit. The results may lead to applications in quantum information processing. Science , this issue p. [1199][1] [1]: /lookup/doi/10.1126/science.aab2179