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0 introduction
Hybrid quantum device involving superconducting quantum circuits and nitrogen-vacancy
(NV) centers, has emerged as one of the most promising candidates for present-day realization of
quantum information protocols [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. This hybrid system combines
the two different components and takes the best of both worlds: On one hand, the solid-state
superconducting circuits have the merits of flexibility, tunability, and scaling on-chip with
nanofabrication techniques [13, 14, 15]. In addition, the elements in superconducting circuits
are strongly coupled to electromagnetic fields, which renders it for robust control, storage, and
readout [16, 17, 18]; On the other hand, the NV center exhibits excellent properties such as fast
microwave manipulation [19], optical preparation and detection [20], and long coherence time
even at room temperature [21]. Moreover, it does not require challenging trapping techniques,
and can be initialized, manipulated, measured, and readout with high fidelity even under
ambient conditions [22, 23, 24]. Therefore, most recently this type of composite system has
attracted great interest in the field of quantum information and computation.
An ensemble of NV centers represents a collection of electronic spins, which can couple to
superconducting quantum circuits through magnetic interactions. In the low excitation limit,
the electronic spin ensemble behaves as a harmonic oscillator, and can reach a regime of strong
coupling with the circuits, benefiting from the enhancement by a factor
√
N of the individual
coupling strength [25, 26]. Experimentally, strong coupling of an ensemble of NV centers to a
superconducting resonator [27, 28] and a superconducting flux qubit [29] have been achieved.
Since the NV center has significant electronic spin lifetime, the NVE has been explored as solid-
state quantum memory to store the states of superconducting qubits [30, 31, 32], or microwave
photons [33]. In another aspect, in order to perform scalable quantum computation, a key step
is to construct a NVE-based quantum network. Based on this point, several schemes have been
proposed to implement quantum state transfer [34], and generate entangled states [35, 36] of
two distant electronic spin ensembles.
Recently, S. Zippilli and coauthors have proposed an interesting scheme to realize entan-
glement replication in a pair of independent chains of linearly coupled quantum systems [37].
In that scheme, the constituents in each array consist of a resonator and a two-level system.
They have shown that, when the arrays are locally driven by a two-mode entangled field, in
the steady state the entanglement of the driving field is reproduced in a series of inter-array
entangled pairs. Motivated by that work, we generalize it to hybrid superconducting quantum
circuits consisting of two independent linearly coupled superconducting transmission line res-
onator arrays, locally driven by a common two-mode squeezed microwave field. Different from
the previous work, here we consider the case in which each resonator is magnetically coupled to
a separate NVE, which will lead to a remarkably fast convergence speed, benefiting from the
collective enhancement of the interactions. We show that at steady state a series of inter-array
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