###### Figure 1

Description of the hybrid quantum circuit demonstrated in this work. (a),(b) Three-dimensional sketch of the device and corresponding electrical scheme. The ensemble

$N\mathrm{\text{\u2212}}V$ of electronic spins (magenta) consists of

${10}^{11}$ NV centers in a diamond crystal glued on the chip surface. The transmon qubit

$Q$ (in red) is capacitively coupled to a resonator

$R$ (in blue) made nonlinear with a Josephson junction and used to readout its state. The bus

$B$ (in yellow) is electrostatically coupled to

$Q$ and magnetically coupled to

$N\mathrm{\text{\u2212}}V$. Bus

$B$ contains a SQUID that makes its frequency

${\omega}_{B}(\Phi )$ tunable by applying in its loop a flux

$\Phi $ via a fast on-chip current line

$F$ (in green). A magnetic field

${B}_{\mathrm{NV}}$ is applied parallel to the [1,1,1] crystallographic axis. (c), (lower left inset) Energy level structure of NV centers. Transitions between

${m}_{S}=0$ and

${m}_{S}=\pm 1$ at frequency

${\omega}_{\pm}$ are further split in three resonance lines due to the hyperfine interaction with the

${}^{14}\mathrm{N}$ nuclear spin [

20]. (main panel) Two-dimensional plot of the transmission

$|{S}_{21}|(\omega ,\Phi )$ through

$B$ in dB units, with

$\Phi $ expressed in units of the superconducting flux quantum

${\Phi}_{0}=h/2e$, for a field

${B}_{\mathrm{NV}}=1.4\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{mT}$ applied to the spins. Color scale goes from

$-55\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{dB}$ (background, green) to

$-30\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{dB}$ (magenta). Four vacuum Rabi splittings are observed whenever

${\omega}_{B}$ matches one NV center resonance frequency. The four transition frequencies

${\omega}_{\pm \mathrm{I},\mathrm{III}}$ correspond to the two distinct families

$\mathrm{I}$ and

$\mathrm{III}$ of NV centers, aligned along the [1,1,1] crystal direction parallel to

${B}_{\mathrm{NV}}$ or along one of the three other possible

$\u27e81,1,1\u27e9$ axes, respectively (see upper right inset). (main panel, bottom right) Qubit excited state probability

${P}_{e}$ as a function of the frequency of the exciting microwave and

$\Phi $. Color scale goes from 0.1 (background, purple) to 0.3 (yellow). When

${\omega}_{B}$ matches the qubit frequency

${\omega}_{Q}=2.607\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{GHz}$, the qubit spectrum shows an anticrossing demonstrating its coupling to

$B$ with constant

${g}_{Q}/2\pi =7.2\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{MHz}$.

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