Superconducting Gatemon Qubit based on aProximitized Two-Dimensional Electron Gas

L. Casparis,1, ∗ M. R. Connolly,1, ∗ M. Kjaergaard,1, † N. J. Pearson,1, 2 A. Kringhøj,1 T. W. Larsen,1 F. Kuemmeth,1

T. Wang,3, 4 C. Thomas,3, 4 S. Gronin,4 G. C. Gardner,4 M. J. Manfra,3, 4, 5, 6 C. M. Marcus,1 and K. D. Petersson1, ‡

1Center for Quantum Devices, Station Q Copenhagen,Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

2Theoretische Physik, ETH Zurich, Zurich, Switzerland3Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA

4Station Q Purdue, and Birck Nanotechnology Center,Purdue University, West Lafayette, Indiana 47907, USA

5School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA6School of Electrical and Computer Engineering,

Purdue University, West Lafayette, Indiana 47907, USA

The coherent tunnelling of Cooper pairs acrossJosephson junctions (JJs) generates a nonlinearinductance that is used extensively in quantuminformation processors based on superconduct-ing circuits, from setting qubit transition fre-quencies [1] and interqubit coupling strengths[2], to the gain of parametric amplifiers [3] forquantum-limited readout. The inductance is ei-ther set by tailoring the metal-oxide dimensionsof single JJs, or magnetically tuned by paralleliz-ing multiple JJs in superconducting quantum in-terference devices (SQUIDs) with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizingall-electric alternative. The gatemon is a re-cently developed transmon variant which employslocally gated nanowire (NW) superconductor-semiconductor JJs for qubit control [4, 5]. Here,we go beyond proof-of-concept and demonstratethat semiconducting channels etched from awafer-scale two-dimensional electron gas (2DEG)are a suitable platform for building a scalablegatemon-based quantum computer. We show2DEG gatemons meet the requirements [6] byperforming voltage-controlled single qubit rota-tions and two-qubit swap operations. We mea-sure qubit coherence times up to ∼ 2 µs, limitedby dielectric loss in the 2DEG host substrate.

Figure 1(a) shows an optical micrograph of a typicaldevice hosting six 2DEG gatemon qubits. Each gate-mon comprises an Al island shunted to the ground planevia a 2DEG JJ and capacitively-coupled to a serpentine-shaped coplanar waveguide cavity. The self capacitanceC of the island together with the nonlinear inductanceof the JJ creates an anharmonic potential for plasmonoscillations across the JJ. The ground |0〉 and excited|1〉 states of the qubit correspond to the lowest twoharmonic oscillator states, which in the transmon limit(EJ � EC) are separated in energy by a transition fre-quency fQ ≈

√8ECEJ/h, where EC = e2/2C is the

charging energy, and EJ is the Josephson energy [1, 7].

Fixed frequency transmons, employing single metal-oxide JJs, benefit from longer coherence times, but atthe cost of slow (∼ 150 ns) two-qubit gate operationtimes [8] and frequency crowding [9]. Frequency tun-able qubits allow faster two-qubit gates, but flux noiseof ∼ 1 µΦ0/

√Hz in SQUIDs limits phase coherence to

T ∗2 ∼ 5 µs [10]. Moreover, the milliampere currents usedto control the flux in the SQUIDs place additional de-mands on cooling power and complicate the integrationwith 3D architectures. Qubit-qubit and qubit-couplercrosstalk can also exceed 4% and requires calibrationprotocols that scale with the number of qubits [11]. Insuperconductor-semiconductor JJs, EJ can be controlled

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FIG. 1. 2DEG gatemon. a, Optical micrograph of a sixqubit device. The 2DEG JJ is shunted by the T-shaped is-land to the surrounding ground plane and coupled to individ-ual readout cavities. The gate voltage V j changes the qubitfrequency of Qj. b, Schematic of the wafer stack. c, Falsecoloured scanning electron micrograph of the gate controlled2DEG JJ of width w.

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by local, capacitively-coupled gates [4, 5, 12], opening upthe possibility to tune and modulate fQ without crosstalkor sensitivity to flux noise.

In this work we realize scalable superconductor-semiconductor JJs using the 2DEG heterostructureshown schematically in Fig. 1(b). The 2DEG is formedin an InAs quantum well encapsulated between In-GaAs barriers. We leverage recent breakthroughs inin-situ epitaxy of Al on III-V semiconductors [13]to obtain a pristine high-transparency superconductor-semiconductor interface between a 50 nm-thick layerof superconducting aluminium and the 2DEG. Semi-insulating (Fe-doped) InP is used as a host substrate for

the 2DEG buffer layer, which is etched away before pat-terning the qubit island and microwave control circuitry.Figure 1(c) shows a false coloured scanning electron mi-crograph of the JJ.

First, we demonstrate that 2DEG gatemons can befabricated deterministically with reproducible properties.We fabricated three devices (S1, S2, S3) each hosting sixqubits with junction width w increasing from 0.3-2.6 µm(labelled Q1-Q6). To extract EJ of the as-fabricatedqubits the corresponding cavity frequency is measuredbefore any voltage is applied to the gate. Due to vacuumfluctuations in the electric field between the cavity andqubit, the cavity is Lamb-shifted from its bare resonance

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frequency by χ = g2cav/∆Q, where ∆Q/2π = fc − fQ

is the qubit-cavity detuning and gcav is the couplingstrength. This expression and the directly measuredgcav/2π ∼ 100 MHz, together with numerical simula-tions for C (EC ∼ 230 MHz), allows us to estimateEJ . Figure 2(a) plots the extracted EJ as a functionw for all measured qubits. The data show that EJ in-creases for wider junctions as expected for an increas-ing number of modes participating in Cooper pair trans-port [14]. Such precise control of EJ on a design param-eter w represents an important step towards engineer-ing scalable superconductor-semiconductor quantum in-formation processors, improving on previous realizationswhere w was limited by the 1D character of NWs.

Next, we show all-electric control by tuning the qubittransition frequency in Fig. 2(b). We operate in thetransmon regime, EJ/EC ∼ 70-130, and read out thequbit dispersively (gcav � |∆Q|) [15]. Using two-tonespectroscopy, we drive a single qubit (Q3) and iden-tify its frequency as a function of gate voltage fromthe state-dependent push on the cavity. The frequencyfQ3(V3) is monotonic over a wider voltage range than forNWs [4, 16] and can be tuned by ∆f ∼ 1 GHz for 1 V ap-plied to the gate (V j corresponds to the voltage appliedto j-th qubit Qj). The dependence of qubit frequency ongate voltage can be optimized by changing the thicknessof the dielectric layer and using 2DEGs with differentfield-effect mobility.

We next demonstrate basic operations of individualqubits using time domain manipulation and readout.Phase-controlled microwave pulses with frequency fd areapplied either via the cavity readout feedline or sepa-rately through the JJ top-gate. The rotation about theX-axis of the Bloch sphere is performed by applying thepulse for a time τRabi and reading out the state via thecavity [pulse sequence, Fig. 2(c)]. Plotting the probabil-ity to be in |1〉, P|1〉, as a function of τRabi and fd, revealsRabi oscillations [Fig. 2(c)], characteristic of the qubit ro-tation. These data are used to calibrate the pulse timesand amplitudes to rotate by π and π/2 around the X-axis(X and X/2 pulses respectively). We next show coherentaccumulation of dynamical phase by controlled rotationof the qubit around the Z-axis. Fig. 2(d) shows the pulsesequence comprising a resonant (fd = fQ) X/2 pulse,a gate pulse with amplitude ∆V3 and duration τRamsey,and a second X/2 pulse. When ∆V3 = 0 the qubit anddrive are phase locked, so the two X/2 pulses rotate thequbit to the |1〉 state. With increasing ∆V3 the qubitrotates around the Z-axis relative to the drive. Whilefurther experiments are required to establish fidelities,these data establish the high degree of control affordedby electrostatically-coupled gates.

To measure the relaxation time, T1, an X pulse ex-cites the qubit [blue pulse sequence, Fig. 3(a)] and P|1〉is plotted as a function of τ , the time delay before read-out. The probability decreases exponentially due to re-

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FIG. 3. Coherence times. a, Lifetime measurement for S1Q2 (blue) with qubit resonance frequency fQ2 ∼ 5 GHz. Inred, we perform a Hahn echo experiment to determine T2,echo.The black lines are exponential fits. Inset: pulse sequence fordephasing (T2,echo) [red] and relaxation (T1) [blue] measure-ments. The inset shows a Ramsey experiment which is per-formed to determine T2 for Q2 with the pulse sequence shownnext to the inset (black). The solid line is a fit to an exponen-tially damped sinusoid. b, Relaxation time measurements asa function of qubit frequency. The dashed line indicates thelimit on the qubit lifetime for a quality factor Q ∼ 6.4× 104.The inset shows the spectrum for Q2.

laxation. Fitting the decay (blue) yields T1 = 1.1 µs.To extract the dephasing time T ∗2 , two slightly detunedX/2 pulses are applied, black pulse sequence Fig. 3(a)inset, separated by delay time τ . A fit to the decayof the resulting Ramsey fringes [inset Fig. 3(a)] givesa dephasing time T ∗2 = 400 ns. In order to reduce in-homogeneous dephasing due to low-frequency noise, weperform a Hahn echo sequence comprising a refocusingX pulse between two X/2 pulses [Fig. 3(a), red]. Theextracted T2,echo = 2.2 µs ∼ 2T1 indicates that 2DEGgatemon dephasing is dominated by low frequency noise[17]. Figure 3(b) shows T1 as a function of qubit fre-quency. Relaxation times vary between 0.2 - 2 µs andfluctuate strongly with fQ [the spectrum is plotted in theinset Fig. 3(b)]. Owing to their periodicity, we attributethese fluctuations to on-chip modes, which is consistentwith previous results from devices lacking crossover wirebonds.

An estimate for the dielectric loss of the qubit capac-itor can be made using a test resonator coupled to thesame feedline (fres = 5.35 GHz) which shows an inter-nal quality factor Q ∼ 6.4 × 104 at low photon number.Using the expression T1 = Q/(2πfQ) we expect the re-laxation time due to dielectric loss to follow the blackdashed line [18]. The agreement between the measuredT1 times and this upper bound suggests the qubit life-time is indeed limited by dielectric loss. Similar Q’s areobtained on pure semi-insulating InP substrates, suggest-ing the presence of the 2DEG does not introduce addi-tional loss. Potential solutions for reducing microwaveloss in InP include deep-etching [19] and using flip-chiptechniques to host the qubit island on a low-loss sub-strate such as Si [20]. Using the measured lever arm of

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FIG. 4. Coherent two-qubit interaction. a, Measurement of the avoided level crossing between Q2 and Q3. The sum ofthe normalized heterodyne readout amplitude VΣ for both qubits is shown as a function qubit drive and V2. b, Pulse sequenceto probe the coherent coupling between the qubits. With Q2 and Q3 detuned, Q3 is prepared in the ground state and a Xpulse prepares Q2 in |1〉. A gate pulse with amplitude ∆V2 brings Q2 close to or in resonance with Q3 for time τswap. c, The|1〉 state probability, P|1〉, for Q3 as a function of ∆V2 and τswap. Lower panel: P|1〉 for both Q2 and Q3 at ∆V2 ∼ 72 mV, thatbrings the two qubits into resonance.

1 GHz/V and gate voltage fluctuations of ∼ 8 µV mea-sured in III-V semiconductors [21], we expect an upperlimit of T ∗2 ∼ 20 µs, suggesting the prospects are goodfor obtaining coherence times comparable with state-of-the-art flux-tuneable transmons, where T1 ∼ 30 µs andT ∗2 ∼ 5 µs [10].

Finally, we coherently swap excitations using the ca-pacitive coupling between neighbouring qubits. Themonotonicity and reproducibility of the qubit spectra es-tablished in Fig. 2 are critical for tuning adjacent qubitsinto resonance with each other. The signature of qubit-qubit coupling is a mutual push on the bare qubit fre-quencies due to hybridization. To detect this push, thequbits Q2 and Q3 are driven and read out through thefeedline and their respective cavities. For clarity thesignals detected from both cavities are added to yieldthe sum VΣ. Figure 4(a) shows VΣ as a function of thequbit drive and V2. As expected, due to the absenceof cross-talk, there are two peaks in VΣ as a functionof fd, only one of which (Q2) is tuned by V2. Whentuned onto resonance, the qubits anticross and a split-ting of 2g/2π ∼ 12 MHz between the two hybridizedstates is observed, where g is the qubit-qubit couplingstrength. Figure 4(b) shows the pulse sequence thatexploits the anticrossing to coherently transfer an excita-

tion between Q2 and Q3, the starting point for preparingarbitrary two-qubit states. With the two qubits detunedby ∼ 140 MHz and Q3 idling, Q2 is prepared in |1〉.A gate pulse is then applied for time τswap and bringsQ2 into resonance with Q3 [22]. Note that here the mi-crowave pulses are applied through the gate line, demon-strating qubit manipulation using a single control lineper qubit. We emphasize that single-gate control of ro-tations around the X, Y and Z-axis is an important ad-vantage of voltage-controlled qubits. The rate at whichexcitations swap between qubits depends on τswap andthe pulse amplitude ∆V2. Figure 4(c) shows the typicalchevron pattern of swap oscillations [23]. The lower in-set in Fig. 4(c) shows P|1〉 for each qubit separately. Theanticorrelation confirms that the excitation is transfer-ring between Q2 and Q3 and demonstrates the possibil-ity of generating entangled states using 2DEG gatemonqubits. From sinusoidal fits (solid lines) an interactionrate 2g/2π = 14 MHz is extracted, in good agreementwith electrostatic simulations yielding 2g/2π ∼ 15 MHzfor fQ = 5 GHz.

In summary, we have demonstrated that planar semi-conductor materials and superconducting microwave cir-cuits are compatible technologies that can be readily in-tegrated while maintaining quantum coherence. This

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opens new possibilities for highly integrated quantumprocessors with on-chip components. Through a com-bination of geometry and applied voltages, EJ can betailored to simultaneously suit qubits as well as periph-eral control circuits requiring higher EJ , such as tune-able couplers [2, 24] and on-chip microwave sources [25],and develop naturally into 3D architectures requiredto implement fault-tolerant processing [20, 26]. More-over since 2DEG gatemons represent a perfect quantumcounterpart to semiconductor-based cryogenic classicalcontrol logic [27–29], they take the first step towardsrealizing a scalable all-electric hybrid superconductor-semiconductor quantum processor.

METHODS

The sample

Separate transport characterization shows that the2DEGs exhibit a Hall mobility of approximately2000 cm2V-1s-1 and an induced gap of 200 µeV. Thequbits were fabricated by first wet etching a mesa forthe qubit JJ. The width w of the JJ was defined by themesa etch. The JJ was then formed by selectively wetetching a ∼ 100 nm long segment of the ∼ 50 nm thickAl. A 20 nm thick AlOx layer (yellow in Fig. 1(b)-(c))was deposited as a gate dielectric, followed by the evap-oration of an Al top gate (red). The heterostructure andthe buffer were removed almost everywhere on the chip,leaving only a few micron large mesa region to form theactive region of the qubit. The qubit islands, gate linesand readout cavities were defined in a lift-off process witha 100 nm Al layer. Finally, the epitaxial Al layer on topof the mesa and the microwave circuit were connectedin a contact step. For each qubit, EC/h is determinedby the capacitance of the T-shaped Al island to the sur-rounding ground plane and designed to be ∼ 230 MHz.All qubits are coupled to individual λ/4 superconductingcavities with resonant frequencies separated by 50 MHzand centred around 7.25 GHz. All six cavities are coupledto a common feed line [18].

Qubit manipulation and readout

All measurements presented in the paper are per-formed in a cryogen-free dilution refrigerator with a basetemperature below 50 mK. The sample is mounted insidean Al box to suppress magnetic fluctuations. This boxis placed inside a Cu box used to mount the sample atthe mixing chamber plate of the refrigerator. Both boxesare closed but not light tight and are further surroundedby a cylindrical cryoperm shield, which is also thermallyanchored to the mixing chamber.

The qubit is initialized in the |0〉 state by waiting formuch longer than the relaxation time T1. To manipulatea single qubit, one coaxial line and a DC line are used: thecoax line is filtered by a Minicircuits VLF-320 low passfilter and an ECCOSORB filter to reduce noise while al-lowing for gate pulses. At high frequencies (>2 GHz),the filter attenuates by roughly 20 dB allowing to drivethe qubit directly. The DC line is filtered with an RCfilter and added with a bias T at low temperature. ForX microwave control as well as readout, the pulses areshaped through IQ modulation of the microwave sourceand using an AWG channel for I and Q respectively. Forreadout, the signal line is heavily attenuated (60 dB) toreduce both the thermal occupation of the resonator andnoise to the sample. After passing through a magneti-cally shielded isolator, a travelling wave parametric am-plifier [30], another magnetically shielded isolator, a cryo-genic low noise factory HEMT amplifier and another am-plification stage at room temperature the qubit readoutsignals are mixed down to intermediate frequencies witha local oscillator, before sampling and performing digi-tal homodyne detection to extract the cavity magnituderesponse. Qubit state measurements are obtained by av-eraging over ∼ 1000 experimental runs. We use the rawRabi oscillation data for qubit state assignments. Thedata in Fig. 2(a) were acquired with a vector networkanalyzer. The data in all other figures were acquired us-ing heterodyne detection in the dispersive regime. ForFig. 4 we combine two drives with frequencies close tothe resonance frequencies of the cavities of Q2 and Q3on the signal line.

ACKNOWLEDGMENTS

We acknowledge helpful discussions withA. C. C. Drachmann, H. J. Suominen, E. O’Farrell,A. Fornieri, A. Whiticar and F. Nichele. This workwas supported by Microsoft Project Q, the U.S. ArmyResearch Office, the Innovation Fund Denmark, andthe Danish National Research Foundation. C.M.M.acknowledges support from the Villum Foundation.MRC was supported by a Marie Curie Fellowship andEPSRC (EP/L020963/1). MK gratefully acknowledgessupport from the Carlsberg Foundation. The travellingwave parametric amplifier used in this experiment wasprovided by MIT Lincoln Laboratory and Irfan SiddiqiQuantum Consulting (ISQC), LLC via sponsorship fromthe US Government.

AUTHOR CONTRIBUTIONS

T.W., C.T., S.G., G.C.G. and M.J.M. grew the prox-imitized 2DEG. M.K., L.C., C.M.M. and K.D.P designedthe experiment. L.C., M.R.C., A.K., N.J.P., T.W.L.,

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and K.D.P. prepared the experimental setup. L.C. andM.R.C. fabricated the devices and performed the ex-periment. L.C., M.R.C., M.K., A.K., T.W.L., F.K.,C.M.M., and K.D.P. analyzed the data and prepared themanuscript.

COMPETING FINANCIAL INTEREST

The authors declare no competing financial interests.

∗ Contributed equally to this work† Present address: Research Laboratory of Electronics,

Massachusetts Institute of Technology, Cambridge, MA02139, USA

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