PRL 107, 220501 (2011)

PHYSICAL REVIEW LETTERS

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Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble
Y. Kubo,1 C. Grezes,1 A. Dewes,1 T. Umeda,2 J. Isoya,2 H. Sumiya,3 N. Morishita,4 H. Abe,4 S. Onoda,4 T. Ohshima,4
V. Jacques,5 A. Dréau,5 J.-F. Roch,5 I. Diniz,6 A. Auffeves,6 D. Vion,1 D. Esteve,1 and P. Bertet1
1

Quantronics group, SPEC (CNRS URA 2464), IRAMIS, DSM, CEA-Saclay, 91191 Gif-sur-Yvette, France
2
Research Center for Knowledge Communities, University of Tsukuba, Tsukuba 305-8550, Japan
3
Sumitomo Electric Industries Ltd., Itami 664-001, Japan
4
Japan Atomic Energy Agency, Takasaki 370-1292, Japan
5
LPQM (CNRS UMR 8537), ENS de Cachan, 94235 Cachan, France
6
Institut Néel, CNRS, BP 166, 38042 Grenoble, France(Received 19 October 2011; published 21 November 2011)
We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit
and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin
ensemble consisting of nitrogen-vacancy centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare a superposition of the qubit
states that we store into collective excitations of the spin ensemble and retrieve back into the qubit later on.
These results constitute a proof of concept of spin-ensemble based quantum memory for superconducting
qubits.
DOI: 10.1103/PhysRevLett.107.220501

PACS numbers: 03.67.Lx, 42.50.Ct, 42.50.Pq, 85.25.Cp

Present-day implementations of quantum information
processing rely on two widely different types of quantum
bits (qubits). On the one hand, microscopic systems such asatoms or spins are naturally well decoupled from theirenvironment and as such can reach extremely long coherence times [1,2]; on the other hand, more macroscopic
objects such as superconducting circuits are strongly
coupled to electromagnetic fields, making them easy toentangle [3,4] although with shorter coherence times [5,6].
It thus seems appealing to combine the two types ofsystems in hybrid structures that could possibly take thebest of both worlds.
But if superconducting qubits have been successfully
coupled to electromagnetic [7] as well as mechanical[8] resonators, coupling them to microscopic systems in
a controlled way has up to now remained an elusive
perspective—even though qubits sometimes turn out tobe coupled to unknown and uncontrolled microscopic degrees of freedom with relatively short coherence times [9].
Whereas the coupling constant g of one individual microscopic system to a superconducting circuit is usually too
weak for quantum information applications, pensemblesof
ﬃﬃﬃﬃ
N such systems are coupled with a constant g N enhanced
by collective effects. This makes possible to reach a regimeof strong coupling between one collective variable ofthe ensemble and the circuit. This collective variable,
which behaves in the low excitation limit as a harmonic
oscillator, has been proposed [10–13] as a quantum
memory for storing the state of superconducting qubits.
Experimentally, the strong coupling between an ensembleof electronic spins and a superconducting resonator has
been demonstrated spectroscopically [14–16], and the storage of a microwave field into collective excitations of a
0031-9007=11=107(22)=220501(5)spin ensemble has been observed very recently [17,18].
These experiments were however carried out in a classicalregime since the resonator and spin ensemble behaved as
two coupled harmonic oscillators driven by large microwave fields. In the perspective of building a quantum
memory, it is instead necessary to perform experiments
at the level of a single quantum of excitation. For that
purpose, we integrate on the same chip three different
quantum systems: an ensemble of electronic spins, a superconducting qubit, and a resonator acting as a quantum bus
between the qubit and the spins. A sketch of the experimentis shown in Fig. 1.
The spin ensemble N-V consists of 1011 negatively
charged nitrogen vacancy (NV) color centers [19] in adiamond crystal. These centers have an electronic spin
S ¼ 1, with electron spin resonance (ESR) transition frequencies ! =2 ’ 2:88 GHz between energy levelsmS ¼ 0 and mS ¼ 1 in zero magnetic field [seeFig. 1(c)]. The electronic spin of the NV center is further
coupled by hyperfine (HF) interaction to the spin-one 14 N
nucleus, which splits ! into three peaks separated by
2.2 MHz [20,21]. In our experiment, the diamond crystal
is glued on top of the chip, and the degeneracy between
states mS ¼ 1 is lifted with a BNV ¼ 1:4 mT magnetic
field applied parallel to the chip and along the [1, 1, 1]
crystalline axis. The NV frequencies being sensitive only tothe projection of BNV along the NV axis, two groups of NVs
thus experience different Zeeman effects: those along[1,1,1] (denoted I) and those along either of the three otherh1; 1; 1i axes (denoted III as they are 3 times more numerous). This results in four different ESR frequencies !I;III .
The qubit Q is a Cooper-pair box of the transmon type[5,22] with transition frequency !Q between its ground220501-1

Ó 2011 American Physical Society

ac 2.95

B

Q

BN-V

F

N-V

2.90

R

B N-V

b

Q drive

B drive|S21|

Q readout
Pe

gR
R

gQ
Q

III

ω+I
Frequency, ω/2π (GHz)B

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PHYSICAL REVIEW LETTERS

PRL 107, 220501 (2011)

ω+III
ω-III

2.85
ms= ±1

ω-I

+1
-1

2.62

N-V

B

I

2.88GHz

g

ω-

ω+
ωQ

ms=0
F

Φ

2.57
0.30

Flux

0.35
Flux, Φ/Φ0

0.42

FIG. 1 (color online). Description of the hybrid quantum circuit demonstrated in this work. (a),(b) Three-dimensional sketch of thedevice and corresponding electrical scheme. The ensemble N-V of electronic spins (magenta) consists of 1011 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 witha Josephson junction and used to readout its state. The bus B (in yellow) is electrostatically coupled to Q and magnetically coupled to
N-V. Bus B contains a SQUID that makes its frequency !B ðÞ tunable by applying in its loop a flux  via a fast on-chip current line F(in green). A magnetic field BNV is applied parallel to the [1,1,1] crystallographic axis. (c), (lower left inset) Energy level structure of
NV centers. Transitions between mS ¼ 0 and mS ¼ 1 at frequency ! are further split in three resonance lines due to the hyperfine
interaction with the 14 N nuclear spin [20]. (main panel) Two-dimensional plot of the transmission jS21 jð!; Þ through B in dB units,with  expressed in units of the superconducting flux quantum 0 ¼ h=2e, for a field BNV ¼ 1:4 mT applied to the spins. Color scalegoes from 55 dB (background, green) to 30 dB (magenta). Four vacuum Rabi splittings are observed whenever !B matches one
NV center resonance frequency. The four transition frequencies !I;III correspond to the two distinct families I and III of NV centers,aligned along the [1,1,1] crystal direction parallel to BNV or along one of the three other possible h1; 1; 1i axes, respectively (see upper
right inset). (main panel, bottom right) Qubit excited state probability Pe as a function of the frequency of the exciting microwave and. Color scale goes from 0.1 (background, purple) to 0.3 (yellow). When !B matches the qubit frequency !Q ¼ 2:607 GHz, the qubit
spectrum shows an anticrossing demonstrating its coupling to B with constant gQ =2 ¼ 7:2 MHz.

state jgi and excited state jei. It is coupled to a nonlinear
resonator R which is used to readout its state, as in related
circuit quantum electrodynamics experiments [23]. Singlequbit rotations are realized by applying microwave pulses
at !Q through R. Qubit state readout is performed bymeasuring the phase of a microwave pulse reflected on
R, which depends on the qubit state; the probability Pe tofind the qubit in jei is then determined by repeating 104
times the same experimental sequence.
The quantum bus B, a superconducting resonator withquality factor 104 , is electrostatically coupled to thequbit and magnetically coupled to the spin ensemble. In
order to bridge the difference in frequency between Q and
N-V, the bus frequency !B can be tuned on a nanosecond
time scale [24] by applying current pulses through an onchip flux line F, inducing a magnetic flux  through a
SQUID embedded in B [21,25].
We first characterize our hybrid circuit by spectroscopic
measurements. The NV frequencies and coupling
constants are obtained by measuring the microwave

transmission jS21 ð!Þj through the bus, while scanning its
frequency !B ðÞ across the NV resonances. Vacuum Rabi
splittings are observed when !B matches the ESR frequencies at !þI =2 ¼ 2:91 GHz, !I =2 ¼ 2:84 GHz,!þIII =2 ¼ 2:89 GHz, and !III =2 ¼ 2:865 GHz (seeFig. 1). From the data we extract the coupling constantsgI =2 ¼ 2:9 MHz and gIII =2 ¼ 3:8 MHz, the difference between the two values resulting essentially from thelarger number of NV centers in group III. Qubit spectroscopy is performed by scanning the frequency of a microwave pulse applied through R, and by measuring Pe , whichyields !Q =2 ¼ 2:607 GHz. This spectroscopy, measured
while scanning !B across !Q , shows an anticrossing[see Fig. 1(c)] that yields the coupling constant gQ =2 ¼
7:2 MHz between Q and B.
Throughout the experiments reported in the following,
the spins and qubit frequencies are kept fixed, and only !Bis varied in order to transfer coherently quantum information between Q and N-V. For this purpose, a key operationis the qubit-bus SWAP gate that transfers an arbitrary qubit

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PHYSICAL REVIEW LETTERS

PRL 107, 220501 (2011)

state jgi þ jei into the corresponding photonic statej0iB þ j1iB of the bus, leaving the qubit in jgi. This
SWAP gate could be performed by tuning !B in resonancewith !Q for a duration =2gQ [26]. Here we prefer instead
to adiabatically sweep !B across !Q as this sequence ismore immune to flux noise in the SQUID loop of B [21].
This adiabatic SWAP (aSWAP) achieves the same quantum
operation as the resonant SWAP except for an irrelevant
dynamical phase. The experiments then proceed by combining single-qubit rotations, aSWAP gates, and flux pulses
placing B and N-V in and out of resonance for properlychosen interaction times .
We apply such a sequence with the qubit initially prepared in jei (see Fig. 2). A first aSWAP converts jei into thebus Fock state j1iB ; B is brought in or near resonance withthe spin ensemble for a duration ; the resulting B state isthen transferred back into the qubit, which is finally readout. Figure 2(b) shows the resulting curves Pe ðÞ when thebus is brought in resonance either with !III or !I . An
oscillation in Pe is observed, revealing a storage in the spin
ensemble of the single quantum of excitation initially inthe qubit at s;III ¼ 65 ns or s;I ¼ 97 ns, and a retrieval
back into the qubit at r;III ¼ 116 ns or r;I ¼ 146 ns. The
fidelity of this storage-retrieval process, defined as
a

N-V

π

τ

ωB(Φ)

R

Q
aSWAP

B

0.05

b

0.34

ω+III

ω-I

0.4

τs,I
0.2
0

ω-III

τr,I
200

c
0.32

ω+I

τr,IIIPe

0.2

τs,III

0.20

Φ/Φ0

0.4

Pe

ω-III

0.38

ω-I
400

600

Interaction time,τ (ns)200400Interaction time,τ (ns)600

FIG. 2 (color online). Storage and retrieval of a single quantum of excitation from the qubit to the spin ensemble. (a),Experimental sequence showing the microwave pulses used for
exciting the qubit in jei ( pulse) and for reading it out (R pulse),
as well as transition frequencies of the quantum bus (B), qubit(Q), and spins (N-V). (b), Experimental (red dots) and theoretical (black line—see text) probability Pe ðÞ for !B tuned to !III(top) or !I (bottom), showing the storage and retrieval times sand r . (c), Two-dimensional plot of Pe versus interaction time and flux pulse height , showing resonance with the four spingroups. Chevron-like patterns are observed, showing a faster
oscillation with reduced amplitude when !B is detuned from thespin resonance, as expected. Note that the difference between the! and !þ patterns in the same NV group is simply caused by
the nonlinear dependence of !B on  [25].

week ending
25 NOVEMBER 2011Pe ðr Þ=Pe ð0Þ, is 0.14 for group III and 0.07 for group I.
These relatively low values are not due to a short spindephasing time, but rather to an interference effect causedby the HF structure of NV centers, as evidenced by thenonexponential damping observed in Pe ðÞ. These measurements are accurately reproduced by a full calculationof the spin-resonator dynamics [18,21,27,28] taking into
account this HF structure, with the linewidth of each HF
peak as the only adjustable parameter. A linewidth of
1.6 MHz is in this way determined for the spins in group
I [21], and of 2.4 MHz for group III. This larger value is due
to a residual misalignment of BNV from the [1,1,1] crystalline axis causing each of the three h1; 1; 1i NV orientations noncollinear with the field to experience slightly
different Zeeman shifts. We finally note that in both curves
shown in Fig. 2(b) Pe ðÞ tends towards 0.08 at long times,
as is also found with the qubit initially in jgi. This provesthat the collective spin variable coupled to B is, as requested for experiments in the quantum regime, in its
ground state j0iI;III with a large probability 0:92 at
equilibrium, which corresponds to a temperature of50 mK. Varying both !B and  with the same pulse
sequence, we observe similar storage-retrieval cycles at
all four spin frequencies [see Fig. 2(c)].
In addition to storing a single excitation from the qubit,
one has to test if a coherent superposition of states can betransferred to the spin ensemble and retrieved. For that, we
now perform the aSWAP and bring !B in resonance withpﬃﬃﬃ
!I after having prepared the qubit in ðjgi þ jeiÞ= 2
instead of jei, and we reconstruct the Bloch vector of thequbit by quantum state tomography at the end of thesequence (see Fig. 3). More precisely, we measure hX i,
hY i and hZ i by using =2 rotations around Y, X, or no
rotation at all (I) prior to qubit readout. After substracting atrivial rotation around Z occurring at frequency (!I !Q ), we reconstruct the trajectory of this Bloch vector as afunction of the interaction time . It is plotted in Fig. 3,
together with the off-diagonal element ge of the final qubit
density matrix, which quantifies its coherence. We find thatno coherence is left in the qubit at the end of the sequencefor  ¼ s;I , as expected for a full storage of the initial state
into the ensemble. Then, coherence is retrieved at  ¼ r;I ,although with an amplitude 5 times smaller than its valueat  ¼ 0 (i.e., without interaction with the spins). Note the phase shift occurring after each storage-retrieval cycle,
characteristic of 2 rotations in the two-level space
fj1B ; 0I i; j0B ; 1I ig. The combination of the results ofFigs. 2 and 3 demonstrates that superpositions of thetwo qubit states can be stored and retrieved in a spin
ensemble—although with limited fidelity—and thus represents a proof-of-concept of a spin-based quantum memory for superconducting qubits.
To evaluate the time during which quantum coherence
can be stored in the ensemble, we perform a Ramsey-likeexperiment on the spin ensemble at the single-photon level220501-3

N-V

X(π/2)aτ

I, X,Y

N-V

R

Q

τs,I
τr,I

0.2

0.4

0.2

180

-0.2

0

arg(ρge)

0.0

Excited state probability, Pe

c

b

δω
τ

τπ/2

R

-<σy>

0.2 0

-180
100
200
300
400
Interaction time τ (ns)FIG. 3 (color online). Storage and retrieval of a coherent
superposition of states from the qubit to the spin ensemble.
(a) Experimental pulse sequence:pﬃﬃﬃ the qubit is prepared by a
=2 pulse in state ðjgi þ jeiÞ= 2, which is transferred to B by an
aSWAP. Bus B is then immediately tuned to !I =2 ¼
2:84 GHz for an interaction time . The quantum state of B isthen transferred back to the qubit by a second aSWAP. Quantum
state tomography is finally performed to determine the qubit
state by applying either I, X, or Y operation to the qubit. (b),Trajectory of the qubit Bloch vector on the Bloch sphere (bottom
inset), and its projection on the equatorial plane. (c), Modulus
and phase of the off-diagonal element ge of the qubit density
matrix as a function of interaction time .

(see Fig. 4): we initially prepare the qubit in jei, transfer its
state to B, then tune !B to !I for a duration =2 ¼
s;I =2, after which !B is suddenly detuned by !=2 ¼
38 MHz for a time . At this point, the joint bus-spin
ensemble statepﬃﬃﬃ is an entangled state ðj1B ; 0I i þ
ei’ j0B ; 1I iÞ= 2 with a phase ’ ¼ !. Bus B is thenput back in resonance with the spins for a second interaction of duration =2 that converts the phase ’ into population of j1B ; 0I i. This population is finally transferred tothe qubit, and readout. Oscillations at frequency ! areobserved in Pe ðÞ as seen in Fig. 4, confirming that theresonator and the spins are entangled after the first halfswap pulse. These oscillations are modulated by a beating
pattern, with an overall damping of the oscillations envelope in 200 ns. Quite remarkably, this beating observedin the qubit excited state probability is directly caused by
the HF structure of NV centers, as proved by the Fouriertransform of Pe ðÞ which shows the three HF lines. The fullcalculation of the system dynamics quantitatively captures
both the beatings and the oscillations damping, which isthus completely explained by the 1.6 MHz inhomogeneous
linewidth of each HF line taken into account in thetheory.

aSWAP

0.4

0.3

30 35 40 45
Frequency (MHz)

0.2
0

200

400

600

Delay time, τ (ns)

X
0

B

b 0.5

2|ρge|

0.4

<σx>

τπ/2

Q
aSWAP

B

-0.4
-0.2

π

FFT amp (a.u.)aweek ending
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PHYSICAL REVIEW LETTERS

PRL 107, 220501 (2011)

FIG. 4 (color online). Ramsey-like experiment on the spin
ensemble at the single-photon level. (a), Experimental pulse
sequence: the qubit is prepared in its excited state jei by a pulse; the state je; 0B i is then adiabatically transferred to jg; 1B i
by an aSWAP. A fast flux pulse subsequently brings !B onto !I ,and then lets B and the spins from group I interact for half aswap time =2 ¼ s;I =2, generating an entangled state of thetwo systems. B is then detuned from the spins by !=2 ¼
38 MHz during a time , and a second half-swap is performed.
The quantum state of B is then transferred back to the qubit,
which is finally readout. (b), Measured (red circles) and calculated (black line—see text) probability Pe ðÞ, as well as theFourier transform of the experimental data (inset) revealing theNV centers HF structure.

The previous results suggest that the storage of quantum
information in the NV centers ensemble is at present
limited both by its HF structure and by the inhomogeneous
broadening of its resonance. This broadening is attributed
to dipolar interactions between the NV centers and residual
paramagnetic impurities (likely neutral nitrogen atoms) inthe diamond crystal. Crystals having a nearly complete
conversion of the nitrogen into NV centers should thus
greatly improve the present performance of our device.
Note that the hyperfine coupling to the nuclear spin of14
N could be turned into a useful resource if quantum
information was transferred from the electron spin to the
nuclear spin degree of freedom, which has much narrower
linewidth. Finally, refocusing techniques borrowed fromquantum memories in the optical domain [29] should also
lead to increase in the storage time by 2 orders ofmagnitude.
In conclusion our experiments bring a proof of conceptof a spin-based quantum memory for superconducting
qubits. In a longer-term perspective, they open the way tothe implementation of genuine quantum lab on chips,
where superconducting qubits would coherently interact
with electron and nuclear spins as well as optical photons.
We acknowledge useful discussions with K. Moelmer, F.
Jelezko, J. Wrachtrup, D. Twitchen, and within the
Quantronics group, and technical support from P. Sénat,

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PHYSICAL REVIEW LETTERS

P.-F. Orfila, T. David, J.-C. Tack, P. Pari, P. Forget, andM. de Combarieu. We acknowledge support from
European project Solid, ANR projects Masquelspec and
QINVC, C’Nano, Capes, and Fondation Nanosciences deGrenoble.
Note added.—After redaction of this work, a related
work reporting the coupling of a flux qubit to an ensembleof NV centers was published [30].

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