###### Figure 2

Energy spectrum of the flux qubit

${\mathrm{NV}}^{-}$ spin ensemble hybrid system. (a) Transition frequency of an

${\mathrm{NV}}^{-}$ spin as a function of an in-plane magnetic field

${B}_{\mathrm{NV}}$. The dots represent the transition frequencies derived from the energy spectra of the flux qubit. Two curves are the results of the fitting to the Hamiltonian

${H}_{\mathrm{NV}}$ (see the main text). The parameters derived from the fitting are

$D=2.878\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{GHz}$ and

$E=4\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{MHz}$. (b) Energy spectrum of the flux qubit coupled to the

${\mathrm{NV}}^{-}$ spin ensemble under

${B}_{\mathrm{NV}}$ of 2.6 mT when the qubit splitting is tuned to

$\Delta =2.84\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{GHz}$. Here,

${P}_{\mathrm{sw}}$ is proportional to the population of the qubit excited state [

26]. In the series of experiments, the qubit ground (excite) state leads

${P}_{\mathrm{sw}}=0(0.45)$. (c) Energy spectrum of the flux qubit coupled to the

${\mathrm{NV}}^{-}$ spin ensemble when

${B}_{\mathrm{NV}}=2.6\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{mT}$ and

$\Delta =2.92\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{GHz}$. White curves represent transition frequencies of the hybrid system. The qubit is on resonance with the

${\mathrm{NV}}^{-}$ spin ensemble at point II, where we can perform an iswap operation based on a vacuum Rabi oscillation [

20]. Changing

${\Phi}_{\mathrm{qb}}$ away from 1.5

${\Phi}_{0}$ increases the detuning between them, resulting in the qubit being well decoupled from the spin ensemble at point I, where we perform qubit preparation, qubit detuning to store information in the memory, and qubit readout.

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