Skyrmionic qubits stabilized by Dzyaloshinskii-Moriya interaction as platforms for qubits and quantum gates

TL;DR

This work proposes skyrmionic qubits stabilized by Dzyaloshinskii-Moriya interaction in a 2D spin lattice and analyzes their viability for quantum gates. Using exact diagonalization on a 19-spin triangular lattice, the authors compare quantum skyrmions under periodic boundaries with classical-like, topologically protected skyrmions under open boundaries, demonstrating Pauli X, Y, Z and Hadamard gates in both regimes. They show that DMI sustains skyrmion textures but also drives decoherence and reduced gate fidelity, with topological protection appearing only in the open-boundary classical-like regime. By combining static phase diagrams, dynamic gate simulations, and Lindblad Decoherence modeling, they provide a framework for engineering skyrmion-based qubits and discuss measurement strategies and two-qubit gates via antiferromagnetic skyrmions. The results highlight a dual role for DMI: it enables skyrmion formation while simultaneously inducing decoherence during manipulation, guiding material design toward optimized DMI strengths and boundary conditions for quantum information applications.

Abstract

Quantum computation departs from the classical paradigm of deterministic, bit-based processing by exploiting inherently quantum phenomena such as superposition and entanglement. We propose a framework for qubit realization based on skyrmionic states stabilized by the Dzyaloshinskii-Moriya interaction (DMI) in two-dimensional spin lattices. The model incorporates competing exchange interactions, perpendicular magnetic anisotropy, and Zeeman coupling, solved via exact diagonalization under periodic (PBC) and open boundary conditions (OBC). A quantum skyrmionic phase emerges for PBC within a parameter space defined by DMI, exchange, field, and anisotropy, while OBC favor classical-like, topologically protected skyrmions. Quantum logic gates (Pauli X, Y, Z, Hadamard) are implemented on both skyrmion types. Energy density and entanglement entropy analyses reveal that quantum skyrmions suffer from DMI-driven decoherence and reduced gate fidelity, whereas classical-like skyrmions maintain stability. Exact simulations of qubit dynamics, including drive effects and Lindblad decoherence, demonstrate tunable anharmonic energy levels and coherent Bloch-sphere manipulation, making these skyrmionic states promising candidates for qubit implementation. Overall, the Dzyaloshinskii-Moriya interaction plays a dual role-stabilizing skyrmionic qubits while simultaneously inducing decoherence during gate operations.

Figures (28)

• Figure 1: Triangular spin grid with 19 spins. The arrows in the bondings define the bonding direction, assigning the same phase to the DMI vector $\vec{D}$ represented by the red arrows. Putting $\vec{D} \perp \vec{r}_{ij}$ will lead to Néel type skyrmions.
• Figure 2: Quantum phase diagrams in the two variables space of magnetic field ($B$) and direct exchange ($J$), in units of DMI ($D=1$) illustrating the: (a) Scalar chirality, (b) Average on-site polarization, (c) Entanglement entropy density, (d) Line analysis corresponding to $J=0.5$ and variable $B$ corresponding to the black line in each quantum phase diagrams. The quantum skyrmionic state (SK) corresponds to $\left<Q \right> \sim 0.5$, the helical states (HS) to $\left<Q \right> < 0.5$ and the fully polarized states to $\left<Q \right> =0$. The $\left<S_z \right>$ values are in units of $\hbar/2$.
• Figure 3: (a) On-site average spin polarization corresponding to helical (HS), quantum skyrmionic (SK), and fully polarized (FP) spin states. (b) The FFT of the quantum spin-spin correlation functions and (c) the elastic magnetic neutron scattering cross section $d\sigma/d\Omega$ at momentum transfer vector $\bm{q}$ corresponding to H, SK and FP states. Note that for (b) and (c) the images correspond to the 2D $1^{\rm st}$ Brillouin zone defined by $q_x/\pi=[-1,+1]$ and $q_y/\pi=[-1,+1]$.
• Figure 4: Bloch sphere representation for a 2-level state qubit, illustrating the main states $\ket{0}=$ ground state, $\ket{1}=$ excited state.
• Figure 5: Simulated time dynamics trajectory on the Bloch sphere, corresponding to (a) Pauli-$X$(b) Pauli-$Y$(c) Pauli-$Z$ (phase-shift) and (d, e) Hadamard gates. Each trajectory is constructed by applying the corresponding field drive term [see Eq. \ref{['eq:drive']}], and propagating the Schrödinger equation solution $\ket{\psi(t)}$ over 300 points grid of the time window corresponding to the Rabi period.