Superconducting Spin-Singlet QuBit in a Triangulene Spin Chain

TL;DR

The paper addresses decoherence challenges in spin-based qubits by proposing a spin-singlet qubit realized on triangulene spin chains grown on a superconducting substrate, leveraging the valence-bond solid phase of a spin-$1$ chain. Using numerical renormalization group, the authors identify a protected two-state singlet manifold $|S angle,|S' angle$ that forms an avoided crossing and is well separated from parity-opposite doublets; they map the system to a unified two-impurity model and validate a two-level description with time-dependent NRG. To enable practical operation, they design a mesoscopic triple-quantum-dot device that emulates the triangulene spectrum and supports gate-driven driving and readout, with an effective two-level model confirmed by simulations. The work demonstrates a potentially robust, electrically controllable qubit platform compatible with existing quantum-dot and circuit-QED technologies, and discusses strategies to mitigate quasi-particle poisoning and noise.

Abstract

Chains of triangular nanographene (triangulene), recently identified as realizing the valence-bond solid phase of a spin-1 chain, offer a promising platform for quantum information processing. We propose a spin-singlet qubit based on these chains grown on a superconducting substrate. Using the numerical renormalization group (NRG), we identify a manifold consisting of the two lowest-lying, spin-singlet states isolated from doublet states of opposite fermion parity, which undergo an avoided crossing. A qubit utilizing these states is thus protected from random Zeeman and/or spin-orbit coupling. Despite the unavoidable effect of quasiparticle poisoning on qubit performance, the isolation of the singlet states offers additional protection. In addition, we introduce a mesoscopic device architecture, based on a triple quantum dot coupled to a superconducting junction, that quantum simulates the spin chain and enables control and readout of the qubit. An effective two-level description of the device is validated using time-dependent NRG.

Figures (9)

• Figure 1: (a) Sketch of an open triangulene spin chain (TSC, see e.g. Ref. mishra2021). For sufficiently long chains, it hosts two spin-$\tfrac{1}{2}$ states that are exponentially localized near the edges. (b) Illustration of the TSC on a superconductor. The edge states couple to the superconductor via Kondo exchange interaction. Since the latter is weaker than the antiferromagnetic exchange between the inner spin-$1$ triangulenes, the central region remains decoupled in a valence bond solid (VBS) phase.
• Figure 2: Low-lying spectrum for $J_{12}=\Delta=0.025D$ and $J_2=20\Delta$: (a) Low-energy spectrum for the effective two Kondo-impurity model describing a triangulene spin chain (TSC) on a superconductor (cf. Fig. \ref{['fig:Fig2']}). (b) Low-energy spectrum of the mesoscopic device that "quantum simulates" the TSC on a Superconductor (cf. Fig. \ref{['fig:fig3']}) (c) Blow-up of the avoided crossing of spin-singlet states for the TSC. The minimum gap between the spin singlets is controlled by the scattering potentials $V_1$ and $V_2$ (d) Blow up of the avoided crossing for the device, in which minimum gap can be controlled by the junction tunneling amplitude or phase bias.
• Figure 3: Sketch of the mesoscopic device that emulates the TSC-superconductor system using a triple quantum dot system with the outer dots coupled to a junction of two superconducting wires. Seven gates, $G_1$, $G_2$, $E_1$, $E_2$, $E_3$, $V_{13}$ and $V_{32}$ define the dots and control the system parameters, including the Kondo couplings, $J_1$ and $J_2$, and the (AFM) super-exchange coupling $J_{12}$. The tunneling amplitude $t_{12}$ or the phase bias across the junction determines the size of the minimum gap at the avoided crossing of the two lowest-energy spin-singlets.
• Figure 4: Panels (a) and (b): Blue and Red lines are the overlaps between the time-evolved qubit state and the two initial singlet states computed using time-dependent NRG. The black dashed lines correspond to the overlap derived from the effective two-level model in Eq. \ref{['eq:tls']}. The figures below are the corresponding quench profiles. (c) Overlap under a continuous driving calculated from the two-level effective model from Eq. \ref{['eq:tls']}.
• Figure 5: Results obtained using the zero-bandwidth approximation (ZBA): (a) Phase diagram of the two impurity model for $J_{12}=\Delta$ and $t_{12}=0$ as a function of the individual Kondo exchange couplings with the substrate, $J_1$ and $J_2$. (b) and (c) Evolution of the energy of the four lowest-lying states along the dashed and dotted lines in panel (a), respectively. (d) Comparison between no hopping (dashed lines) and a small hopping term (solid line) in the vicinity of the $S_0\rightarrow S_2$ transition in panel (a).