Toward high-fidelity quantum information processing and quantum simulation with spin qubits and phonons

TL;DR

This work develops a phonon-mediated spin-qubit platform using silicon-vacancy centers in diamond and shows that continuous dynamical decoupling (CDD), including a concatenated variant (CCDD), can protect qubits from low-frequency noise while preserving strong spin–phonon interactions. By deriving an effective dispersive spin–spin Hamiltonian and optimizing detunings and driving strengths, the authors demonstrate gate fidelities approaching or surpassing $10^{-4}$ for realistic parameters, and they provide a clear roadmap for scalability via spin–phonon superlattices and engineered spin models. The approach leverages dressed qubits to suppress dephasing, enables tunable XY/Ising/Heisenberg interactions, and addresses thermal Stark-shift dephasing, highlighting the practical potential of spins coupled to high-quality phononic lattices for quantum computation and simulation. Overall, the results indicate that spin–phonon interfaces in diamond can achieve high-fidelity operations competitive with other quantum platforms and scale toward moderate-to-large quantum devices. $\,$

Abstract

We analyze the implementation of high-fidelity, phonon-mediated gate operations and quantum simulation schemes for spin qubits associated with silicon vacancy centers in diamond. Specifically, we show how the application of continuous dynamical decoupling techniques can substantially boost the coherence of the qubit states while increasing at the same time the variety of effective spin models that can be implemented in this way. Based on realistic models and detailed numerical simulations, we demonstrate that this decoupling technique can suppress gate errors by more than two orders of magnitude and enable gate infidelities below $\sim 10^{-4}$ for experimentally relevant noise parameters. Therefore, when generalized to phononic lattices with arrays of implanted defect centers, this approach offers a realistic path toward moderate- and large-scale quantum devices with spins and phonons, at a level of control that is competitive with other leading quantum-technology platforms.

Figures (9)

• Figure 1: Schematic of the setup. Two SiV centers are coupled to the strain of a quantized vibrational mode of frequency $\omega_{\rm ph}$, which is localized in a phononic crystal structure made out of diamond. The lowest states $|0\rangle$ and $|1\rangle$ in the ground state manifold of the SiV center are split by a frequency $\omega_{10}\sim \omega_{\rm ph}$, which results in a near-resonant spin-phonon interaction with coupling strength $g$. As indicated in the inset at the bottom, this coupling can be enhanced by identifying a phonon mode with a strain field that is concentrated in a small region around the SiV centers. In addition, a strong microwave field is used for a continuous dynamical decoupling of the spin qubits from low frequency noise, while preserving a strong phonon-mediated interaction (see text for more details).
• Figure 2: Qubit parameters. Plots of (a) the qubit frequency splitting $\omega_{10}$, (b) the absolute values of the strain coupling matrix element $\eta_{L,x}$ and (c) the spin transition matrix element $\eta_{S,x}$ as a function of the rotation angle $\theta_B = \arctan(B_x/B_z)$ and different values of the static magnetic field, $|{\bf B}|$. In all plots, the respective quantities represent the average values obtained for a random distribution of static strain components $\Upsilon_{x,y}\in [-\Upsilon_{\rm max},\Upsilon_{\rm max}]$, and the shaded areas indicate their variation (one standard deviation). (d) For $\theta_B=1.2$ and randomly chosen $\Upsilon_{x,y}$ the value of $|{\bf B}|$ is adjusted to fix the qubit frequencies to $\omega_{10}/(2\pi)=3$ GHz. The plot shows the resulting distribution of matrix elements $\eta_{L,x}$ and $\eta_{S,x}$.
• Figure 3: Phonon-mediated spin-spin interactions. (a) Level scheme for two dressed qubits dispersively coupled to a cavity mode. (b) Sketch of the Rabi frequency $\Omega(t)$ during the implementation of a two-qubit gate operation. At the beginning (end) of the pulse the Rabi-frequency is ramped up (down) over a time $t_{\rm ramp}$, where $t_{\rm ramp}\ll t_{\rm g}$ in all the numerical examples.
• Figure 4: Preparation of a Bell state. (a) Plot of the residual error $\mathcal{E}$ versus the Rabi frequency $\Omega$, for the initial two-qubit state $|\tilde{\Psi}\rangle$. The dotted (solid) lines represent Eq. \ref{['Eq:Gate_error']} including (without) the contribution $\mathcal{E}_{\rm s-ph}^{\rm min}$ for $T_2^*=10 \mu$s (blue) and $3 \mu$s (red). The markers indicating the result of exact master equation simulations fall between the two lines, showing a good correspondence between analytic and numerical results. Each point is the result of 100 independent noise realisations, where the $\xi_i$ were randomly selected from the probability distribution $P(\xi)=(2\pi\sigma^2)^{-1/2}\exp{(-\xi^2/2\sigma^2)}$. Other relevant parameters are $Q=10^6$, $T=100$ mK, $g/(2\pi)\approx 0.75$ MHz and $\Delta_{\rm ph}/(2\pi)\approx 150$ MHz. (b) Plot of the minimal error $\mathcal{E}_\Psi^{\rm min}$ in Eq. (\ref{['Eq:Min_Gate_error']}) versus $Q$ and $T_2^*$. The two dashed lines indicate the boundary in this parameter space above which $\Omega_{\rm opt}/(2\pi)$ surpasses the values of $50$ MHz and $100$ MHz, respectively. This becomes relevant when there are additional experimental constraints on the maximal value of $\Omega$.
• Figure 5: High-fidelity two-qubit gate. (a) Plot of the error $\mathcal{E}$ versus the phonon temperature $T$. The blue dotted (solid) line represents $\mathcal{E}_{\Phi}$ including (without including) the contribution from $\mathcal{E}_{\rm s-ph}^{\rm min}$. The blue markers correspond to the results obtained from exact master equation simulations with an initial two-qubit state $|\tilde{\Phi}\rangle$, averaged over 50 random static-noise realizations. The red square (round) markers are the results from exact numerical simulations for the initial state $|\Phi\rangle$ ($|\Psi\rangle$), and using the CCDD method. (b) Sketch of the relevant frequency components of ${\bf B}_{x}(t)$ in the CCDD scheme. In addition to the central driving frequency at $\omega_{10}$, the phase modulation generates two weaker sidebands at $\omega_{10}\pm\Omega$. (c) Plot of the gate error $\mathcal{E}$ for the CCDD scheme as a function of $\Omega_\varepsilon$ and for an initial state $|\Phi\rangle$. Note that for this plot only the Hamiltonian evolution has been taken into account and for each value of $\Omega_\varepsilon$, $t_{\rm ramp}$ has been slightly adjusted to minimize the error. The dotted line is a guide to the eye. In (a), $\Omega_{\varepsilon}/\Omega=8\times10^{-3}$ and $t_{\rm ramp}=2.15\times 2\pi/\Delta_{\rm ph}$ were chosen based on the most favorable values identified in (c). The other relevant parameters are $T_2^*=10 \,\mu$s, $Q=10^6$, $g/(2\pi)=0.75$ MHz, $\Delta_{\rm ph}/(2\pi)\approx 150$ MHz and $\Omega/(2\pi)\approx 37$ MHz.