Coherent long-distance spin-qubit-transmon coupling
A. J. Landig, J. V. Koski, P. Scarlino, C. Müller, J. C. Abadillo-Uriel, B. Kratochwil, C. Reichl, W. Wegscheider, S. N. Coppersmith, Mark Friesen, A. Wallraff, T. Ihn, K. Ensslin
CCoherent long-distance spin-qubit–transmon coupling
A. J. Landig, J. V. Koski, P. Scarlino, C. M¨uller, J. C. Abadillo-Uriel, B. Kratochwil, C.Reichl, W. Wegscheider, S. N. Coppersmith, ∗ Mark Friesen, A. Wallraff, T. Ihn, and K. Ensslin Department of Physics, ETH Z¨urich, CH-8093 Z¨urich, Switzerland IBM Research Zurich, CH-8803 R¨uschlikon, Switzerland Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, United States
Spin qubits and superconducting qubits are among the promising candidates for a solid statequantum computer. For the implementation of a hybrid architecture which can profit from theadvantages of either world, a coherent long-distance link is necessary that integrates and couplesboth qubit types on the same chip. We realize such a link with a frequency-tunable high impedanceSQUID array resonator. The spin qubit is a resonant exchange qubit hosted in a GaAs triplequantum dot. It can be operated at zero magnetic field, allowing it to coexist with superconductingqubits on the same chip. We find a working point for the spin qubit, where the ratio between itscoupling strength and decoherence rate is optimized. We observe coherent interaction between theresonant exchange qubit and a transmon qubit in both resonant and dispersive regimes, where theinteraction is mediated either by real or virtual resonator photons.
INTRODUCTION
A future quantum processor will benefit from the ad-vantages of different qubit implementations [1]. Twoprominent workhorses of solid state qubit implementa-tions are spin- and superconducting qubits. While spinqubits have a high anharmonicity, a small footprint [2]and promise long coherence times [3–5], superconductingqubits allow fast and high fidelity read-out and control[6, 7]. To integrate both qubit systems on one scalablequantum device, a coherent long-distance link betweenthe two is required. A technology to implement sucha link is circuit quantum electrodynamics (cQED) [8],where microwave photons confined in a superconductingresonator couple coherently to the qubits. cQED wasinitially developed for superconducting qubits [9], wherelong-distance coupling [10, 11] enables two-qubit gate op-erations [12]. Recently, coherent qubit-photon couplingwas demonstrated for spin qubits [13–15] in few electronquantum dots. However, coupling a spin qubit to anotherdistant qubit has not yet been shown. One major chal-lenge for an interface between spin and superconductingqubits is that spin qubits typically require large magneticfields [16, 17], to which superconductors are not resilient[18].We overcome this challenge by using a spin qubit thatrelies on exchange interaction [19]. This resonant ex-change (RX) qubit [20–24] is formed by three electronsin a GaAs triple quantum dot (TQD). We implement thequbit at zero magnetic field without reducing its coher-ence compared to earlier measurements at finite magneticfield [15]. The quantum link is realized with a frequency-tunable high impedance SQUID array resonator [25],that couples the RX and the superconducting qubit co-herently over a distance of a few hundred micrometers.The RX qubit coupling strength to the resonator and itsdecoherence rate are tunable electrically. We find thattheir ratio is comparable to previously reported values for spin qubits in Si [13, 14]. We demonstrate coherentcoupling between the two qubits first by resonant andthen by virtual photons in the quantum link. Thereby weelectrostatically tune the RX qubit to different regimes,where the qubit states have either a dominant spin orcharge character. We also report that the SQUID ar-ray resonator can affect the qubit performance, which wesuspect to be caused by charge noise introduced throughthe resonator.
SAMPLE AND QUBIT CHARACTERIZATION
The design of our sample is illustrated schematicallyin Fig. 1(a). It is similar to Ref. 26, where the focus wason charge qubits. We use a superconducting qubit inthe standard transmon configuration [28, 29]. It consistsof an Al SQUID grounded on one side and connected inparallel to a large shunt capacitor. We tune the transitionfrequency ν T between the transmon ground | T (cid:105) and firstexcited state | T (cid:105) by changing the flux Φ T through theSQUID loop with an on-chip flux line.The transmon and the RX qubit are capacitively cou-pled to the same end of a SQUID array resonator, whichwe denote as coupling resonator in the following, withelectric dipole coupling strengths g T and g RX . The otherend of the coupling resonator is connected to DC ground.It is fabricated as an array of Al SQUID loops [25], whichenables us to tune its resonance frequency ν C within arange of a few GHz with a magnetic flux Φ C produced bya coil mounted close to the sample. In addition, the res-onator has a high characteristic impedance that enhancesits coupling strength to both qubits. The transmon fluxΦ T has a negligible effect on ν C .The transmon is also capacitively coupled to a 50 Ω λ/ g R / π (cid:39)
141 MHz. Throughout this article, we refer tothis resonator as the read-out resonator, because it allows a r X i v : . [ c ond - m a t . m e s - h a ll ] M a r us to independently probe the transmon without popu-lating the coupling resonator with photons. The read-outresonator has a bare resonance frequency ν R = 5 .
62 GHzand a total photon decay rate κ R / π = 5 . ν p . In addition, we can applya drive tone at frequency ν d to both qubits via the res-onators. For the experiments presented in this work, theprobe tone power is kept sufficiently low to ensure thatthe average number of photons in both resonators is lessthan one.In Fig. 1(b) we characterize the transmon with two-tone spectroscopy. The first tone probes the read-outresonator on resonance ( ν p = ν R ), while the second toneis a drive at frequency ν d that is swept to probe thetransmon resonance. Once ν d = ν T , the transmon isdriven to a mixed state, which is observed as a change inthe resonance frequency of the dispersively coupled read-out resonator. This frequency shift is detected with astandard heterodyne detection scheme [30] as a changein the complex amplitude A = I + iQ of the signal re-flected by the resonator. In Fig. 1(b) we observe a peakin | A − A | centered at ν d = ν T . Here, A is the complexamplitude in the absence of the drive. From a fit of thetransmon dispersion to the multi-level Jaynes-Cummingsmodel and by including the position of higher excitedstates of the transmon probed by two photon transitions(not shown) [31, 32], we obtain the maximum Josephsonenergy E J , max = 18 .
09 GHz and the transmon chargingenergy E c = 0 .
22 GHz.At a distance of approximately 200 µ m from the trans-mon, we form a TQD by locally depleting a two-dimensional electron gas in a GaAs/AlGaAs heterostruc-ture with the Al top gate electrodes shown in Fig. 1(c).One of the electrodes directly extends to the coupling res-onator to enable electric dipole interaction between TQDstates and coupling resonator photons. Another elec-trode allows us to apply RF signals at frequency ν dRX .We use a QPC charge detector to help tune the TQDto the three electron regime. The symmetric (1 , , , ,
1) and (1 , ,
2) charge config-urations are relevant for the RX qubit as they are lowestin energy. We sweep combinations of voltages on theTQD gate electrodes to set the energy of the asymmetricconfigurations equal and control the energy detuning ∆of the symmetric configuration with respect to the asym-metric ones [see Fig. 1(d)]. There are two spin stateswithin (1 , ,
1) that have S = S z = 1 / S = 1 / S z = − / t l g RX Φ T Φ C ν p, ν d g T g R ν dRX ν R ... ν C ν T ν RX QPC
400 nm (a)
Δ/h [GHz]0 4 8-43.64.04.4 ν d R X [ G H z ] A - A | (arb. u.)-8 1.5(1,0,2)(1,1,1)(2,0,1)(d) Δ(<0) (b) 0(c) (e) 5.0 ν d [ G H z ] T /Φ spin chargeTransmon sampleS DS D Transmon t l t r
200 μmI+iQDC+ν dRX coupl. res. RX FIG. 1. Sample and qubit dispersions. (a) Schematic ofsample and measurement scheme. The signals at frequencies ν p (probe) and ν d (drive) are routed with circulators as indi-cated by arrows. The reflected signal I + iQ at ν p is measured.The sample (dashed line) contains four quantum systems withtransition frequencies ν i : a coupling resonator that consists ofan array of SQUID loops ( ν C , blue), an RX qubit ( ν RX , red),a transmon ( ν T , green) and a read-out resonator ( ν R , gray).Empty black double-squares indicate electron tunnel barriersseparating the three quantum dots (red circles) as well as thesource (S) and drain (D) electron reservoirs. A drive toneat frequency ν dRX can be applied to one of the dots. Filledblack squares denote the Josephson junctions of SQUIDs. Yel-low circles with arrows mark coupling between the quantumsystems with coupling strengths g i . Φ C and Φ T denote cou-pling resonator and transmon flux, respectively. (b) Two-tonespectroscopy of the transmon, with the RX qubit energeti-cally far detuned. We plot the complex amplitude change | A − A | (see main text) as a function of drive frequency ν d and Φ T / Φ . The dashed line indicates the calculated ν T .(c) Scanning electron micrograph of the TQD and quantumpoint contact (QPC) region of the sample. Unused gate linesare grayed out. The gate line extending to the coupling res-onator is highlighted in blue. (d) TQD energy level diagramindicating the tunnel couplings t l and t r and the electrochem-ical potentials, parametrized by ∆, of the relevant RX qubitstates ( N l , N m , N r ) with N l electrons in the left, N m electronsin the middle and N r electrons in the right quantum dot. (e)Two-tone spectroscopy of the RX qubit, with the transmonenergetically far detuned for ν p (cid:39) ν C = 4 .
84 GHz as a func-tion of ∆ and ν dRX . The dashed line shows the expected qubitenergy as obtained from theory. ( t r ) between the left (right) quantum dot and the middlequantum dot hybridizes these states, which leads to theformation of the two RX qubit states | RX (cid:105) and | RX (cid:105) .For ∆ < | RX (cid:105) and | RX (cid:105) have predominantly the(1 , ,
1) charge configuration but different spin arrange-ment. Consequently, quantum information is predomi-nantly encoded into the spin degree of freedom. With in-creasingly negative ∆, the spin character of the qubit in-creases, which reduces the qubit dephasing due to chargenoise. This comes at the cost of a reduced admixtureof asymmetric charge states and therefore a decrease inthe electric dipole coupling strength g RX . In contrast,for ∆ > , ,
1) and (1 , , g RX , with increasing positive ∆.Independent of ∆, the RX qubit states have the sametotal spin and spin z -component such that they can di-rectly be driven by electric fields [33] and be operated inthe absence of an applied external magnetic field. Thisis in contrast to other spin qubit implementations, whichrely on engineered or intrinsic spin-orbit interaction [34–39] for spin-charge coupling.Four similar RX qubit tunnel coupling configurationswere used in this work as listed in Table I. We use two-tone spectroscopy [31] to characterize the RX qubit dis-persion: we apply a probe tone on resonance with thecoupling resonator, drive the qubit via the gate line andtune its energy with ∆. The spectroscopic signal inFig. 1(e) agrees with the theoretically expected qubit dis-persion for qubit configuration 3 (see Table I). RESONANT INTERACTION
First, we investigate the resonant interaction betweenthe coupling resonator and the RX qubit. To startwith, both qubits are energetically detuned from thecoupling resonator. Then, we sweep ∆ to cross a res-onance between the RX qubit and the resonator, whilekeeping the transmon far detuned. We observe a wellresolved avoided crossing in the | S | reflectance spec-trum shown in Fig. 2(a) and extract a spin qubit-photon coupling strength of g RX / π = 52 MHz from afit to the vacuum Rabi mode splitting shown in black inFig. 2(c). The spin qubit and the coupling resonator pho-tons are strongly coupled since g RX > κ C , γ ,RX , where γ , RX / π = 11 MHz is the RX qubit decoherence rateand κ C / π = 4 . C from the RX qubit and extrapolate the width of thepeak observed in the two-one spectroscopy response [c.f.Fig. 1(e)] to zero drive power [31].Next, we characterize the interaction between thetransmon and the coupling resonator. We tune the trans-mon through the resonator resonance by sweeping Φ T .For this measurement the RX qubit is far detuned inenergy. We resolve the hybridized states of the trans-mon and the resonator photons in the measured | S | spectrum in Fig. 2(b). They are separated in energy bythe vacuum Rabi mode splitting 2 g T / π = 360 MHz il-lustrated in Fig. 2(c) in green. We perform power de-pendent two-tone spectroscopy to extract the transmonlinewidth by probing the read-out resonator. We obtain Δ/h [GHz] ν p [ G H z ] -9 -8 -7 -6(a) Φ T /Φ |S |00.250.50.751 ν p [ G H z ] Δ/h [GHz]-10 -8 -6 -4(d) 0.25 0.3 0.35RX Tmon | + | -RX ν RX ν C ν T ∆3.94.14.34.53.94.14.34.5 |S |0.60.81res. res. 10.5|S ||S |(b) (c)(f) | + | - | - , - ν RX ν C ν T Φ T ν RX ν C ν T ∆ 10.5 10.5Δ/h [GHz]-10 -8 -4-6(e)E EE | - , + | +,- | +,+ 0.2 FIG. 2. Resonant interaction. The schematics at the top ofthe graphs indicate the energy levels of the RX qubit ( ν RX ),coupling resonator ( ν C ) and transmon ( ν T ). Theory curves inthe absence (presence) of coupling are shown as dashed black(red) lines. (a) Reflected amplitude | S | as a function of RXdetuning ∆ and probe frequency ν p for RX qubit configura-tion 2. (b) Reflected amplitude | S | as a function of relativetransmon flux Φ T / Φ and ν p . The states |±(cid:105) are discussed inthe main text. (c) Cuts from panel (a) at ∆ /h (cid:39) − . T / Φ (cid:39) . | S | by 0.1. Theory fits are shown as red dashed lines. (d) | S | as a function of ∆ and ν p for RX qubit configuration2. The states |− , ±(cid:105) and | + , ±(cid:105) are explained in the maintext. (e) Theory result for parameters as in (d). Values for | S | are scaled to the experimental data range in (d). (f)Cuts from panel (d) and from panel (e) (without scaling) at∆ /h (cid:39) − . /h (cid:39) − . | S | by 0.2. γ , T / π = 0 . g T > κ C , γ ,T is also realized for transmon and cou-pling resonator photons.We now demonstrate that the two qubits interact co-herently via resonant interaction with the coupling res-onator. For this purpose, we first set the transmon andthe coupling resonator on resonance, where the hybridsystem forms the superposition states |±(cid:105) = ( | T , C (cid:105) ±| T , C (cid:105) ) / √ |−(cid:105) and the higher energy state | + (cid:105) . In the | S | spectrum inFig. 2(d), avoided crossings are visible at both resonancepoints. This indicates the coherent interaction of thethree quantum systems that form the states |− , ±(cid:105) and (cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:1)(cid:1)(cid:1)(cid:1) (cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:1)(cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:1)(cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2) (cid:2)(cid:2) (cid:1)(cid:1) (cid:2)(cid:2) (cid:1)(cid:1) (cid:2)(cid:2) (a) γ , R X / п [ M H z ] (cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:1)(cid:1)(cid:1)(cid:1) (cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:1)(cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:1)(cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2) (cid:2)(cid:2) (cid:1)(cid:1) (cid:2)(cid:2) (cid:1)(cid:1) (cid:2)(cid:2) Δ/h [GHz]0 10 20-20 -10 g R X / γ , R X ν d R X [ G H z ] A - A | (arb. u.)0 0.5 1 1.5 ν d R X [ G H z ] Δ/h [GHz]2 2.5 44.204.244.28 3 3.5 4.5 ν d R X [ G H z ] ν d R X [ G H z ] A - A | (arb. u.)0 0.5 1 1.5 2| A - A | (arb. u.)0 0.25 0.75(d) (g)RXTmon | A - A | (arb. u.)0 0.5 1 1.5(f) Δν dRX [MHz]0 20 40-40 -20-60 60(h) | A - A | ( a r b . u . ) | RX drive ν dRX probe ν p =ν R Δ C ≈3g T (c)2530 Δ/h [GHz]0 10 20-20 -10 (b)0.5 Tmon Tmon TmonΔ | - e | + e | - e | + e | - e | + e | - e | + e RX RX0.8 ν RX ν C ν T E 10.510 | RX | T | T | C | C FIG. 3. RX qubit working points and virtual photon-mediated interaction. (a) RX qubit decoherence rate γ , RX as a function ofdetuning ∆. The dotted vertical lines specify the four working points used in (d)-(g). The corresponding colored data points wereobtained for a coupling resonator-RX qubit detuning of ν C − ν RX (cid:39) (13 . , . , . , . g RX for ∆ /h (cid:39) ( − . , − . , . , .
2) GHzand the RX qubit configurations 3 (circle) and 4 (triangle). For the black data points, ν C − ν RX ≥ . g RX with qubitconfiguration 1 (circle) and 2 (triangle). The dashed red line is a fit of a theory model (see main text) to the black data points.Error bars indicate the standard error of fits and an estimated uncertainty of the RX qubit energy of 50 MHz. (b) Ratio of g RX , as obtained from theory, and γ , RX as shown in (a). The color and shape code of the data points is the same as in (a). (c)Ground ( | i (cid:105) ) and excited states ( | i (cid:105) ) level alignment used in (d)-(g). (d)-(g) Two-tone spectroscopy at ν p = ν R (cid:39) . ν dRX . Dashed black (red) lines indicate transmon and RX qubit energies in the absence(presence) of coupling. The frame color refers to the RX qubit working points as specified in (a). The inset in (e) shows theresult from theory with the same axes as the main graph. (h) Cuts from panels (d)-(g) at ∆ as specified with arrows in thecorresponding panels. The cuts are centered around zero by accounting for a frequency offset ν dRX , ≡ ν dRX − ∆ ν dRX . Thedashed lines show the corresponding theory results. | + , ±(cid:105) , where the second label indicates a symmetric orantisymmetric superposition of the RX qubit state withthe transmon-resonator |±(cid:105) states. The splitting 2 g ∓ be-tween |− , ±(cid:105) and | + , ±(cid:105) is extracted from the Rabi cutsin Fig. 2(f). We obtain 2 g + / π = 84 MHz at ∆ /h (cid:39)− . g − / π = 63 MHz at ∆ /h (cid:39) − . g − compared to g + is due the decrease of the RX qubit dipole momentwith more negative ∆. The experimental observation inFig. 2(d) is well reproduced by a quantum master equa-tion simulation shown in Fig. 2(e) and further discussedin Ref. 27. RX QUBIT OPTIMAL WORKING POINT
While γ , T is limited by Purcell decay and thereforedoes not depend on Φ T , γ , RX changes with ∆ [15].For obtaining the data shown in Fig. 3(a) we use powerdependent two-tone spectroscopy via the coupling res-onator to measure γ , RX as a function of ∆. We ob-serve an increase of γ , RX as the charge character of thequbit is increased with ∆. Compared to Ref. 15, the data in Fig. 3(a) covers a larger range in ∆, in partic-ular for | ∆ | (cid:29) t l , r . The data suggests a lower limit of γ , RX / π (cid:39) . (cid:28)
0. This is in agreementwith Refs. 42 and 15, where the RX qubit was operatedat a finite magnetic field of a few hundred mT. Hence, ourexperiment indicates that the RX qubit can be operatednear zero magnetic field without reducing its optimal co-herence. In our experiment, the maximum external mag-netic field determined by Φ C is of the order of 1 mT. Tomodel the RX qubit decoherence in Fig. 3(a), we consideran ohmic spectral density for the charge noise as well asthe hyperfine field of the qubit host material that actson the spin part of the qubit (see Ref. 27 for details).Theory and experiment in Fig. 3(a) match for a width σ B = 3 .
48 mT of the hyperfine fluctuations in agreementwith other work on spin in GaAs [43–45]. This suggeststhat γ , RX is limited by hyperfine interactions.The colored data points in Fig. 3(a) were measuredfor a smaller RX qubit-coupling resonator detuning com-pared to the black data points (numbers are given inFig. 3 caption). The smaller detuning is used for thevirtual interaction measurements explained below. Weobserve an increase of γ , RX for small qubit-resonatordetuning compared to large detuning. This increase isabout one order of magnitude larger than our estimateddifference of Purcell decay and measurement induced de-phasing for those different data sets. In contrast, for thetransmon that is insensitive to charge noise, we do notobserve this effect. This suggests that the effect is due tocharge noise induced by the coupling resonator.As γ , RX increases with ∆ in Fig. 3(a), the RX qubitcoupling strength g RX to the coupling resonator in-creases. This implies the possible existence of an opti-mal working point for the RX qubit, where g RX /γ , RX is maximal. While a distinct optimal point is not dis-cernible for the black points in Fig. 3(b), the averagedvalue of g RX /γ , RX (cid:39) − < ∆ /h < . /h (cid:39) − . g RX /γ , RX is reduced at small qubit-resonator detuning in Fig. 3(b)compared to the black data points at large detuning dueto the influence of the coupling resonator on γ , RX dis-cussed above. VIRTUAL PHOTON COUPLING
In the following we investigate the RX qubit-transmoninteraction mediated by virtual photons in the couplingresonator at the RX qubit working points marked incolor in Fig. 3(a). The two qubits are resonant whilethe coupling resonator is energetically detuned, such thatthe photon excitation plays only a minor role in the su-perposed two-qubit eigenstates. This coupling scheme,illustrated in Fig. 3(c), is typically used for supercon-ducting qubits to realize two-qubit operations [12]. Wemeasure the virtual coupling at the optimal workingpoint (∆ /h (cid:39) − . /h (cid:39) − . /h (cid:39) . γ , RX in Fig. 3(a) saturates, aswell as in the intermediate regime at ∆ /h (cid:39) . C ≡ ν C − ν T (cid:39) g T from the coupling resonator. Torealize this detuning for every working point, we adjustthe qubit and resonator energies with Φ T , t l , r and Φ C .We drive the RX qubit at frequency ν dRX [see Fig. 1(a)]and investigate its coupling to the transmon by prob-ing the dispersively coupled read-out resonator at itsresonance frequency ( ν p = ν R (cid:39) . /h (cid:39) − . /h (cid:28) −
10 GHz), the spectroscopic signal ofthe transmon is barely visible as the drive mainly ex-cites the bare RX qubit. The signal increases with ∆as the RX qubit approaches resonance with the trans-mon, such that driving the RX qubit also excites thetransmon due to their increasing mutual hybridization. On resonance, we weakly resolve the two entangled spinqubit-transmon states, which can be approximated as |±(cid:105) e (cid:39) ( | RX , T (cid:105)±| RX , T (cid:105) ) / √
2. These states are sepa-rated in energy by the virtual-photon-mediated exchangesplitting 2 J (cid:39) g RX g T / ∆ C . The splitting is enhanced atthe other working points in Figs. 3(e)-(g), for which theRX qubit control parameter ∆ and consequently g RX islarger. The theory inset in Fig. 3(e) agrees well withthe experimental observation. The influence of the RXqubit decoherence rate γ , RX on the virtual interactionmeasurement is quantified in Fig. 3(h), where we showaveraged cut measurements on resonance, as indicated byarrows in Figs. 3(d)-(g). The theory fits in Fig. 3(h) showexcellent quantitative agreement with the experimentalcurves. As discussed in detail in Ref. 27, fit parameterspreviously obtained from Fig. 2 had to be adjusted toaccount for significant power broadening in these mea-surements. The exchange splitting is best resolved at theoptimal working point, corresponding to the solid greencurve in Fig. 3(h), where we obtain 2 J/ π (cid:39)
32 MHzfrom the fit.
CONCLUSION
In conclusion, we have implemented a coherent long-distance link between an RX qubit and a transmon thateither utilizes real or virtual microwave photons for thequbit-qubit interaction. The RX qubit was operated inboth spin and charge dominated regimes. We found anoptimal working point at which the ratio between its res-onator coupling and its decoherence rate is maximal andcomparable to state of the art values achieved with spinqubits in Si. We also reported that the coupling res-onator introduces charge noise that can have significantimpact on the RX qubit coherence. The performance ofthe quantum link in this work is limited by the minimumdeoherence rate of the qubit, which is determined by hy-perfine interaction in the GaAs host material. Once thespin coherence is enhanced by using hyperfine free ma-terial systems such as graphene [46, 47] or isotopicallypurified silicon [48], the spin could be used as a mem-ory that can be coupled on-demand to the transmon bypulsing the qubit control parameter. As the coherenceof the RX qubit is not altered at zero magnetic field incontrast to other spin qubit implementations, relying onlarge external magnetic fields, the quantum device archi-tecture used in this work is promising for a high fidelitytransmon–spin-qubit and spin-qubit–spin-qubit interfacein a future quantum processor.We acknowledge discussions with Guido Burkard,Michele Collodo, Christian Kraglund Andersen and Max-imilian Russ. We also thank David van Woerkom for hiscontribution to the sample fabrication and for input tothe manuscript. This work was supported in part by theSwiss National Science Foundation through the NationalCenter of Competence in Research (NCCR) QuantumScience and Technology. S.N.C. and M.F. acknowledgesupport of the Vannevar Bush Faculty Fellowship pro-gram sponsored by the Basic Research Office of the As-sistant Secretary of Defense for Research and Engineeringand the funding by the Office of Naval Research throughGrant No. N00014-15-1-0029. M.F. and J.C.A.U. ac-knowledge the support by ARO (W911NF-17-1-0274).The views and conclusions contained in this work arethose of the authors and should not be interpreted asnecessarily representing the official policies or endorse-ments, either expressed or implied, of the Army ResearchOffice (ARO) or the U.S. Government. The U.S. Govern-ment is authorized to reproduce and distribute reprintsfor Governmental purposes, notwithstanding any copy-right notation thereon.A.J.L., J.V.K. and P.S. fabricated the sample. A.J.L.and J.V.K. performed the measurements with inputfrom B.K. A.J.L. analyzed the data. A.J.L., C.M. andJ.C.A.U. wrote the manuscript with input from all au-thors. C.R. grew the heterostructure under the supervi-sion of W.W. C.M. developed the cQED theory. J.C.A.U.derived the hyperfine noise model under the supervisionof S.N.C. and M.F. A.W., T.I. and K.E. supervised theexperiment.
RX QUBIT TUNNEL COUPLINGCONFIGURATIONS
Throughout this work, we use the four RX qubit tunnelcoupling configurations listed in Table I.
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