Qubits based on merons in magnetic nanodisks

The study investigates whether nanoscale magnetic merons in nanodisks can function as qubits, with the meron core spin polarity (up or down) encoding the computational basis states |0> and |1>. The context is the broader search for solid-state, topologically robust qubits leveraging magnetic textures. The authors aim to (i) establish the smallest stable meron size in realistic ferromagnetic nanodisks, and (ii) demonstrate that universal quantum computation can be realized using control of the meron core spin via magnetic fields and spin-polarized currents. The importance lies in potentially exploiting topological spin textures for quantum information processing with fast gate operations and intrinsic robustness associated with topology.

The work builds on extensive literature on magnetic vortices, merons, and skyrmions, including stabilization in chiral magnets and manipulation in nanodisks. Prior studies demonstrated vortex core switching using magnetic fields, rotating fields, and spin-polarized currents, as well as imaging techniques for vortex and meron-like textures. Recent proposals have considered skyrmion-based qubits and logic. This paper extends these ideas to meron core-spin qubits in nanodisks and outlines universal gate constructions leveraging established control modalities.

Static meron configurations in circular nanodisks are computed using the GPU-accelerated micromagnetic simulator MuMax3. The energy density includes ferromagnetic exchange (A_ex), easy-plane anisotropy (K < 0), Zeeman coupling to applied field B, dipole-dipole interaction (DDI), and bulk Dzyaloshinskii–Moriya interaction (D) that stabilizes Bloch-type merons. Simulations use a square lattice with circular boundary, lattice constant (mesh) 0.4 nm × 0.4 nm, 1 nm thickness, open boundaries. Default parameters: A_ex = 0.32 pJ m^-1, M_s = 152 kA m^-1, D = 0.5 mJ m^-2, K = −0.5 MJ m^-3. Spin dynamics at zero and finite temperatures are simulated with OOMMF by solving the Landau–Lifshitz–Gilbert equation with damping α (default 0.3), including stochastic thermal fields for finite T. Finite-temperature simulations use time step 2×10^-15 s; zero-temperature time step is adaptive. Stability of merons with radius containing n spins is tested by embedding radius-n merons into (2n−1)×(2n−1) lattices for n = 3–10, including exchange, DMI, DDI, and easy-plane anisotropy. Gate operations are modeled by effective qubit Hamiltonians: single-qubit H = α_x σ_x + α_z σ_z with time-controlled α_x, α_z via applied fields or currents; two-qubit Ising coupling H_Ising = J_exchange σ_z^(1) σ_z^(2) between vertically stacked nanodisks separated by a spacer with interlayer exchange A_inter. Unitary evolutions U_z(θ) = exp[−i(θ/2)σ_z] and U_x(θ) = exp[−i(θ/2)σ_x] are realized by pulsing α_z(t) and α_x(t), respectively; the Ising gate U_zz(θ) = exp[−i(θ/2) σ_z^(1) σ_z^(2)] is realized by pulsing J_exchange(t). Gate compositions for π/4 phase, Hadamard, CZ, and CNOT follow standard constructions from these primitives. Energetics (Zeeman splitting, interlayer exchange energy differences) are computed to estimate gate operation times.

- Stable nanoscale merons: Simulations show a meron can be stabilized in a ferromagnetic nanodisk when its radius contains n ≥ 7 spins; the minimum estimated physical size is on the order of ~3 nm. - Energetics vs size: Total energy rises with meron size, dominated by exchange energy; DMI energy decreases with increasing size; easy-plane anisotropy and DDI energies increase with size; normalized out-of-plane magnetization decreases with size (more vortex-like texture). - Pauli-Z (σ_z) via perpendicular field: Under B_z, the energy splitting between p = +1 (|0>) and p = −1 (|1>) is ~1×10^-22 J at B_z = 100 mT, implying an operation time on the order of ~1 ps from the chosen pulse relation. - Pauli-X (σ_x) via in-plane field/current: An in-plane magnetic field pulse H_x = 400 mT applied for 60 ps flips the meron core polarity; the overall switching completes in ~200 ps (with relaxation observed up to 1000 ps). Time traces of m_x, m_y, m_z and snapshots show the spin-rotation pathway. - Two-qubit Ising coupling in a bilayer: For vertically stacked merons (n = 7) with interlayer exchange A_inter = 0.005 pJ m^-1, the total energy difference between identical and opposite polarities is ~3.6×10^-22 J, yielding an estimated gate time ~0.23 ps for the targeted Ising phase. - Universal quantum gates: Arbitrary phase-shift, Hadamard, and CNOT gates are explicitly constructed from U_z, U_x, and U_zz pulse sequences; CZ is built from z-rotations and Ising coupling; CNOT from CZ sandwiched by Hadamards. - Thermal stability: At T ≤ 1 K, the meron core spin and topological charge Q ≈ 0.5 remain stable; at T ≈ 3 K, core flips occur and Q changes; at T ≈ 5 K, the meron texture is destroyed. Operation thus requires cooling below ~3 K. - Relaxation/coherence considerations: In an infinite sample, skyrmion-number conservation gives topological protection (infinite relaxation time); in finite nanoscale disks (~100 nm or smaller), topological protection is reduced, allowing controlled core switching by fields or currents.

The results demonstrate that the core spin polarity of a nanoscale meron can encode a qubit with controllable single- and two-qubit operations using experimentally accessible stimuli (perpendicular and in-plane magnetic fields, spin-polarized currents, and interlayer exchange coupling). Stabilization down to merons containing about seven spins shows feasibility at nanometer scales, addressing the key question of whether sufficiently small and controllable meron textures can exist for quantum computation. Estimated gate times in the sub-ps to hundreds of ps range indicate potentially fast operations. However, thermal analysis reveals that robust meron-based qubit operation requires cryogenic temperatures below ~3 K to prevent spontaneous polarity flips and texture degradation. The topological nature of the meron suggests inherent robustness, though finite-size effects reduce perfect topological protection, balancing controllability and stability. Overall, the work supports meron-based qubits as a path toward topological spin-texture quantum information processing with universal gate sets and practical control mechanisms.

The study proposes and analyzes meron core-spin qubits in magnetic nanodisks, demonstrating through micromagnetic simulations and effective Hamiltonian modeling that: (i) nanoscale merons (down to ~7-spin radius) can be stabilized; (ii) universal quantum computation is achievable by composing single-qubit rotations (via magnetic fields or currents) with an interlayer Ising coupling; and (iii) gate operation times can be in the ps to sub-ns regime. Thermal stability considerations indicate operation below ~3 K. These findings open a route to quantum computation based on topological spin textures. Future work should focus on experimental realization of merons at the smallest possible scales, engineering materials and device geometries to enhance thermal stability and coherence, precise measurement of decoherence and relaxation times, scalable architectures for meron arrays, and optimized control schemes (e.g., low-power spin-torque or microwave protocols) for high-fidelity gate operations.

- Thermal requirement: Stable operation requires temperatures below ~3 K; above this, core flips and texture destruction occur, limiting practicality. - Finite-size topological protection: In small nanodisks, topological protection is weakened, enabling desired switching but also potentially increasing susceptibility to noise and decoherence. - Coherence/relaxation not fully quantified: While energy barriers and qualitative relaxation behavior are discussed, detailed decoherence mechanisms and T1/T2 times are not measured. - Fabrication constraints: The predicted minimum meron size (~3 nm) and precise interlayer coupling control may be challenging experimentally; the work is primarily simulation-based. - Control energetics: Gate estimates rely on specific field strengths (e.g., H_x = 400 mT) and exchange parameters; power dissipation, cross-talk, and variability are not analyzed.