Solid-Neon Microparticles in Quantum Devices

• Solid-Neon microparticles are diamagnetic, face-centered-cubic crystalline spheres that act as electron carriers, enabling robust tunable eNe qubit arrays.
• They are fabricated via a mist-agglomeration process near the neon triple point, yielding nearly perfect spheres with controlled size distribution and high sphericity.
• Magnetic levitation and tunable electron trapping minimize substrate-induced noise while providing GHz-range transition frequencies and scalable integration with superconducting resonators.

Solid-neon microparticles are diamagnetic, face-centered-cubic crystalline spheres utilized as electron carriers in advanced quantum computing architectures. Their integration in the electron-on-neon (eNe) qubit platform leverages magnetic levitation to suspend these particles above superconducting processor chips, eliminating adverse substrate effects, and enabling robust, scalable, and reproducible electron qubit arrays (Inui et al., 29 Nov 2025). This system achieves GHz-range qubit transition frequencies, tunable anharmonicity up to ∼0.8 GHz, and tightly controlled electron-resonator coupling, addressing the longstanding challenges of irreproducible device performance and charge noise in surface-bound implementations.

1. Fabrication, Geometry, and Material Properties

The solid-neon (SNe) microparticles are synthesized via a mist-agglomeration technique conducted near the neon triple point (24.6 K, 0.43 bar). A cryogenic chamber maintained at ≈25 K is filled with liquid neon. Rapid pump-down in the presence of active magnetic traps produces nanodroplet mists, which agglomerate in high-field regions governed by the trap volume $V_\text{trap}$ (several hundred μm³). Subsequent forced evaporation yields cooling down to the triple point, where droplets solidify into nearly perfect spheres. The final diameter $R_s$ (0.5–5 μm) is reduced by less than 5% relative to initial droplet size, determined indirectly by resonance-frequency shifts in the microwave resonator rather than direct imaging.

Key material parameters include:

• Mass density $\rho = 1.44$ g/cm³
• Magnetic susceptibility $\chi = -6.25\times10^{-6}$ (diamagnetic)
• Sphericity inferred from isotropic surface tension and consistent resonator shifts
• No substrate-induced roughness due to levitation

Size distribution is controlled by aggregation time and trap volume; direct SEM imaging has not been reported.

Radius $R_s$ (μm)	Mass Density $\rho$ (g/cm³)	Mass $m$ (kg)
0.5	1.44	$\approx2.3\times10^{-15}$
1.0	1.44	$\approx1.8\times10^{-14}$
3.0	1.44	$\approx1.6\times10^{-13}$

2. Magnetically-Levitated Trap Architecture

Diamagnetic levitation is central to the platform. Solid-neon microparticles are suspended above the processor using the combined fields from a superconducting loop (REBCO or MgB₂; inner radius $R_0$ = 10–50 μm, width $W$ = 10–20 μm, thickness $\delta$ ≈5 μm) and a uniform background field $B_0$ (–0.02 to –0.3 T). The field-squared component of the magnetic potential energy,

$E(z) = \rho g z + \frac{|\chi|}{2\mu_0} B^2(z),$

determines the equilibrium (levitation) height $z_L$, where

$$\left.\frac{\partial B^2}{\partial z}\right|_{z=z_L} = -\mu_0 g \rho/|\chi| \approx -28.4 \text{ T}^2/\text{cm}.$$

Finite-element and Biot–Savart simulations yield $z_L$ in the 5–30 μm range for the specified loop and field parameters.

The magnetic potential is approximately quadratic near $z_L$:

$U_m(z) \simeq \frac{1}{2} m \omega_m^2 (z-z_L)^2,$

where the trap stiffness $k_m$ and mechanical frequencies $\omega_m/2\pi \sim 1$–10 kHz (for $R_s = 1$–3 μm) produce thermal amplitudes $x_\text{th} < 10$ nm at $T\approx100$ mK, with quality factors $Q_m \gg 10^3$ in ultrahigh vacuum. Active feedback can suppress residual motion to sub-nanometer scales.

Diamagnetic levitation circumvents Earnshaw’s theorem, as confinement arises from field-squared energies rather than static charge distributions.

3. Electron Trapping and Integration with Qubit Arrays

Electrons are bound vertically to the dielectric SNe sphere by the image-charge potential,

$$U_\perp(z) = -\frac{(\epsilon-\epsilon_0)}{4(\epsilon+\epsilon_0)} \frac{e^2}{4\pi\epsilon_0 z},$$

where $\epsilon = 1.24\epsilon_0$. The resulting vertical ground-state energy is approximately –15.8 meV, with the first excited state at +12.7 meV ($f_\perp \approx 3.1$ THz), securing the electron in the vertical ground state under operational conditions.

Lateral confinement is established via a positive DC bias $V_b$ applied to resonator center pins, forming an electrostatic potential $U_\parallel(\theta)$ over the spherical SNe surface. The lateral Hamiltonian (neglecting spin) is

$$H_\parallel = -\frac{\hbar^2}{2m_e R_s^2}\nabla^2_{\theta\phi} + \frac{eB_0}{2m_e}L_z + \frac{e^2 B_0^2 R_s^2}{8m_e}\sin^2\theta + U_\parallel(\theta).$$

Eigenstates $|\psi_{nm}\rangle$ are characterized by quantum numbers $n$ (polar) and $m$ (azimuthal). The qubit is encoded between $|g\rangle \equiv |\psi_{00}\rangle$ and $|e\rangle \equiv |\psi_{01}\rangle$, with transition frequency

$f_q = (E_{01} - E_{00})/h,$

tunable over 1–10 GHz by adjusting $V_b \sim 0.05$–0.3 V and ring height $H \sim 0.6$–1.0 μm. The system exhibits an anharmonicity

$\alpha = (E_{02} - 2E_{01} + E_{00})/h,$

that can reach up to ~0.8 GHz as the lateral potential profile transitions between single-minimum and ring-shaped minima.

Electron coupling to the superconducting microwave resonator is mediated by the electric response,

$H_\text{int} = -\vec{d}\cdot\vec{E}$

with dipole matrix elements $$d_m = -e R_s \sqrt{\frac{4\pi}{3}}Y_{1m}(\theta,\phi)$$ interacting with resonator zero-point fields. Typical coupling strengths $g/2\pi \gtrsim 5$ MHz (standard impedance $Z_\text{diff} \sim 100\ \Omega$, $\omega_r/2\pi = 5$ GHz), rising above 20 MHz for $Z_\text{diff} \sim 2$ k$\Omega$ resonators.

4. Tunability and Scalability in Qubit Networks

Tuning the resonator bias $V_b$ modulates $f_q$ at rates $\partial f_q/\partial V_b \sim 10$–20 GHz/V, with GHz-range adjustment over $V_b$ swings of 0.1–0.3 V. Anharmonicity $\alpha$ is similarly tunable from near zero (weak confinement) to 0.8 GHz (strong confinement), controlled by $V_b$ and $H$.

Multiplexed arrays are achievable via patterned HTS loops and CPW resonators on-chip, providing SNe sites separated by $O(10$–$100)$ μm. Individual $f_q$ tuning via local bias voltages circumvents frequency crowding. Qubit readout and interconnect are conducted via shared $\lambda/2$ or $\lambda/4$ resonators; dispersive two-qubit couplings $g_{ee} \approx g_1g_2/\Delta \sim 2$–6 MHz support scalable quantum register architectures.

Qubit Parameter	Range	Tunability
$f_q/h$ (GHz)	1–10	via $V_b$, $H$
$\alpha/h$ (MHz)	0–800	via $V_b$, $H$
$g/2\pi$ (MHz)	5–30	via $Z_\text{diff}$

5. Noise Suppression: Mechanical and Charge Stability

Mechanical noise in levitated SNe qubits is negligible due to low thermal amplitudes ($x_\text{th} < 10$ nm), high vacuum, and quality factors $Q_m \gg 10^3$. Passive stability is at the nanometer scale, and active feedback can reduce residual motional noise below 1 nm.

Charge noise benefits substantially from the elimination of substrate-induced trapping centers and the evasion of direct substrate contact. Projected charge noise spectral density is $S_q(f) \leq 10^{-6}e/\sqrt{\text{Hz}}$ at 1 Hz—an order of magnitude lower than substrate-based platforms. Experimental motional $T_2$ coherence times in solid-neon films reach $\sim$0.1 ms, and the levitated architecture is projected to boost $T_2$ by more than tenfold. Spin $T_2$ (isotopically purified) may reach $\leq$81 s.

6. Context and Implications in Quantum Computing Architectures

Solid-neon microparticles as diamagnetically levitated electron carriers constitute a significant advance in the eNe qubit platform by reconciling the vacuum isolation of trapped ions with circuit-based scalability. The elimination of substrate roughness and charge noise, robust GHz-range tunability, and engineered interconnect architectures collectively enhance reproducibility and scalability for quantum computing applications. This suggests further research directions in noise suppression, levitated architectures without direct material contact, and hybrid quantum systems that integrate high-impedance resonator arrays (Inui et al., 29 Nov 2025).