Decoherence-protected entangling gates in a silicon carbide quantum node

Abstract

Solid-state color centers are promising candidates for nodes in quantum network architectures. However, realizing scalable and fully functional quantum nodes, comprising both processor and memory qubits with high-fidelity universal gate operations, remains a central challenge in this field. Here, we demonstrate a fully functional quantum node in silicon carbide, where electron spins act as quantum processors and nuclear spins serve as quantum memory. Specifically, we design a pulse sequence that combines dynamical decoupling with hyperfine interactions to realize decoherence-protected universal gate operations between the processor and memory qubits. Leveraging this gate, we deterministically prepare entangled states within the quantum node, achieving a fidelity of 90%, which exceeds the fault-tolerance threshold of certain quantum network architectures. These results open a pathway toward scalable and fully functional quantum nodes based on silicon carbide.

Figures (4)

• Figure 1: Energy levels of a PL6 center strongly coupled with a $^{29}$Si nuclear spin in a silicon carbide quantum node. (a) Schematic illustration of nuclear spin-memory qubit surrounding a PL6 defect-processor qubit. MW: microwave; RF: radiofrequency pulses. (b) Simplified energy-level diagram of the hybrid electron–nuclear spin register. MW1 and MW2 drive nuclear spin-conserving electron spin transitions, while the RF pulse drives an electron spin-conserving nuclear spin transition. (c) and (d) Optically detected magnetic resonance (ODMR) spectra recorded at zero magnetic field ($B = 0$ Gs) and under a small external field ($B = 4.2$ Gs) aligned with the PL6 symmetry axis. The splitting of 12.4 MHz shown in the figure represents the hyperfine coupling constant of the nuclear spin. Blue dots indicate raw data; orange lines are Lorentzian fits.
• Figure 2: Coherent Control of Nuclear Spins and Quantum State Tomography of Hybrid Entangled States. (a) The ODMR spectra recorded at a 330 Gs magnetic field applied along the direction of the PL6 defect. The solid-line circle highlights the disappearance of the right branch of the hyperfine-split resonance. (b) The ODNMR spectrum. A peak at around 12.145 MHz is observed, indicating a $\rm{Si_{IIa}}$ nuclear spin coupled with a single PL6. (c) Nuclear Rabi oscillations. (d) The Nuclear Ramsey fringes are fitted with a double cosine exponential decay function. Blue dots represent raw data, and orange lines indicate the Lorentzian fits. (e) and (f) The real and imaginary parts of the entangled-state density matrix reconstructed via maximum likelihood estimation are shown. The total preparation time is 14.7 $\mu$s, and the resulting fidelity is only $70 \pm 3\%$.
• Figure 3: Implementing decoherence-protected quantum gates for electron-nuclear spin registers using DDRF. (a) Schematic of the DDRF gate pulse sequence. Microwave (MW) pulses for the electron spin (gray) are interleaved with radiofrequency (RF) pulses (blue and orange, denoting odd and even RF numbers, respectively), enabling selective control of a single nuclear spin. The parameters $\tau$ and $\phi_\tau = A_{zz}\tau$ represent the RF pulse duration and the applied phase correction, respectively. (b) Rotation of the nuclear spin under the pulse sequence in (a). The initial nuclear spin state (coincide with the z-axis) undergoes either a complete $\pi$ rotation (blue arrow) or remains unchanged (orange arrow) depending on whether the electron spin is initially in state $|-1\rangle$ or $|0\rangle$, respectively. Circles 1 and 2 correspond to the applied conditional and unconditional pulses illustrated in (a). (c)-(d) Unconditional nuclear gate calibrations when the electron spin is initialized in either the $\left| 0 \right\rangle$ (c) or $\left| -1 \right\rangle$ (d) state, the nuclear spin undergoes identical rotations. (e)-(f) Conditional nuclear gate calibration. When the electron spin is initialized in the $\left| 0 \right\rangle$ state, the nuclear spin exhibits no rotation around the z-axis (e). However, when the electron spin is initialized in the $\left| -1 \right\rangle$ state, the nuclear spin undergoes a controlled rotation around the effective $x$-axis, with the rotation angle increasing as the number of pulses $N$ increases (f).
• Figure 4: The performance of DDRF decoherence-protected gates. (a) The measurement of electron spin coherence is conducted using dynamical decoupling sequences with varying numbers of $\pi$ pulses $N$. (b) The entangled state preparation sequence and the sequence to validate the effectiveness of the decoherence-protected gate. (c) The reconstructed absolute density matrices ($| \rho |$) after applying the DDRF decoherence-protected gate. The quantum state tomography results for gate numbers $N = 4, 12, 16$ are displayed from left to right, demonstrating a significant enhancement in fidelity. (d) The fidelity and the magnitude of the off-diagonal element ($\rho_{14}$) of the Bell state as a function of the number of decoupling pulses $N$.