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Kosuke Noro, [Motoya Shinozaki](https://orcid.org/0000-0001-9460-9156), [Yusuke Kozuka](https://orcid.org/0000-0001-7674-600X), Koichi Baba, Kazuma Matsumura, Yoshihiro Fujiwara, Takeshi Kumasaka, [Atsushi Tsukazaki](https://orcid.org/0000-0003-0251-063X), Masashi Kawasaki, [Tomohiro Otsuka](https://orcid.org/0000-0003-2532-643X)

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[Charge sensing of few-electron ZnO double quantum dots probed by radio-frequency reflectometry](https://mdr.nims.go.jp/datasets/915723b0-490a-42ab-83b2-987e03e12ba6)

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Charge sensing of few-electron ZnO double quantum dots probed by radio-frequency reflectometry1Kosuke Noro,1, 2, 3 Motoya Shinozaki,4, 3 Yusuke Kozuka,3, 4 Koichi Baba,1, 2 Kazuma Matsumura,1, 2 Yoshihiro2Fujiwara,1, 2 Takeshi Kumasaka,4 Atsushi Tsukazaki,5 Masashi Kawasaki,5, 6 and Tomohiro Otsuka4, 1, 2, 3, 7, 6, ∗31Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan42Department of Electronic Engineering, Graduate School of Engineering,5Tohoku University, 6-6 Aramaki Aza Aoba, Aoba-ku, Sendai 980-0845, Japan63Research Center for Materials Nanoarchitechtonics (MANA),7National Institute for Material Science (NIMS), 1-2-1 Sengen, Tsukuba 305-0047, Japan84WPI Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan95Department of Applied Physics and Quantum-Phase Electronics Center (QPEC),10University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan116Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan127Center for Science and Innovation in Spintronics, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan13(Dated: May 15, 2026)14Zinc oxide (ZnO) has garnered much attention as a promising material for quantum devices due to its uniquecharacteristics. To utilize the potential of ZnO for quantum devices, the development of fundamental techno-logical elements such as high-speed readout and charge sensing capabilities has become essential. In this study,we address these challenges by demonstrating radio-frequency (rf) reflectometry and charge sensing in ZnOquantum dots, thus advancing the potential for qubit applications. A device is fabricated on a high-quality ZnOheterostructure, featuring gate-defined target and sensor quantum dots. The sensor dot, integrated into an rfresonator circuit, enables the detection of single-electron charges in the target dots. Using this setup, we ob-serve the rf-detected charge stability diagram indicating the formation of few-electron double quantum dots andprovide the first benchmark of the bandwidth, sensitivity, and readout fidelity of rf reflectometry.I. INTRODUCTION15Gate-defined semiconductor quantum dots, called artificial16atoms, are representative systems that allow the control of17quantum states [1–3]. Few-electron quantum dots are used18as quantum bits (qubits), which are the fundamental building19blocks of quantum computing [4, 5]. Many efforts have been20underway to develop qubits with deeper understanding of ma-21terials. In the early stages, gallium arsenide (GaAs) systems22were widely used [6, 7] because the technology for forming23high-quality two-dimensional electron gases (2DEGs) had al-24ready been well established. Despite these advantages, the25strong hyperfine interaction with nuclear spins in GaAs lim-26ited spin coherence times, which motivated the exploration27of isotopically controlled silicon (Si) quantum-dot qubits [8–2811], where the absence of nuclear spins improves spin coher-29ence. Furthermore, two-dimensional materials [12–16] have30also been proposed as hosts for Kramers qubits [17], exploit-31ing additional degrees of freedom such as valley states. These32materials are expected to offer excellent qubit performance,33particularly with respect to the coherence time of quantum34states [18].35Zinc oxide (ZnO) is also considered a promising candidate36for qubits that could achieve high performance regarding both37long coherence times and efficient coupling to photons, ad-38vancing beyond current limitations in quantum device plat-39forms. These advantages are supported by ZnO’s unique ma-40terial properties. One is its low density of nuclear spins (only414% of naturally occurring Zn isotopes and 0.04% of O iso-42topes possess nuclear spin), which contributes to the potential43for long coherence times [18–20]. Moreover, ZnO is a direct44bandgap semiconductor [21], which is beneficial for efficient45coupling with photons [22].46In addition to these properties, 2DEG formed in ZnO47heterostructures exhibits a mobility comparable to that of48conventional high-quality semiconductor materials [23, 24]49which enables to form fine structures showing quantum trans-50port characteristics. Quantum transport phenomena such as51the quantum Hall effect [25–27], quantum point contacts [28],52and notably quantum dots [29] have been experimentally re-53ported in ZnO devices, leading to increasing research on quan-54tum devices. However, qubit operation in ZnO remains chal-55lenging, as it requires the formation of few-electron states in56quantum dots [1–3] and the development of high-speed qubit57readout techniques.58Charge sensing using radio-frequency (rf) reflectometry ad-59dresses these challenges, as it is capable of detecting a sin-60gle electron charge in few-electron states with a broad band-61width [30–32]. Devices should satisfy some criteria to per-62form rf reflectometry, one of which is possessing minimal63stray capacitance in the device structure [13, 33]. If device64design, typically QPC width and/or gate electrode pitch, is65not optimized, gate electric fields create depletion regions not66only directly below gate electrodes but also in channel re-67gions. Under such conditions, quantum dots tend to form be-68fore complete depletion occurs below the gate electrodes, re-69sulting in unexpected capacitive coupling between the 2DEG70and the gate electrodes. As a result, rf signals leak through71this parasitic capacitance, bypassing the quantum dots.72In this perspective, the device design is a particular concern73in the case of ZnO heterostructures due to their unique mate-74rial parameters such as the relative permittivity εZnO = 8.375and the effective mass mZnO = 0.3m0, where m0 is the bare76Kosuke_Noroハイライト表示2electron mass. [34, 35] These values are different from those77of conventional materials such as εGaAs = 12.9, εSi = 11.7,78mGaAs = 0.067m0, and mSi/SiGe = 0.22m0 [26]. These79parameters may affect the pinch-off characteristics and the80orbital level spacing. In fact, a previous experimental study81reported abrupt changes in the tunnel coupling between quan-82tum dots and leads as a function of gate voltage [29], which83complicates device design for rf reflectometry. Thus, several84open questions remain as to whether ZnO heterostructures can85utilize device designs similar to those proven effective for86GaAs and Si, or whether entirely new architectures are re-87quired for rf reflectometry of highly integrated qubit systems88in the future.89In this paper, we fabricate a device structure using a ZnO90heterostructure to form target and sensor quantum dots. The91sensor dot is integrated into the resonator circuit to demon-92strate rf reflectometry and provides a charge stability diagram93of few-electron double quantum dots. We also present the first94benchmark of the bandwidth, sensitivity, and readout fidelity95of rf reflectometry in ZnO-based quantum dots.96II. RESULTS AND DISCUSSION97A. Charge detection98The layer structure of the device is illustrated in Figure 1(a).99The numbers in parentheses represent the layer thicknesses in100nanometers. The 2DEG forms at the interface between the101(Mg,Zn)O and ZnO heterostructure. We prepare two types of102AlOx gate insulator stack structures: one with a 20-nm AlOx103layer and another with a 30-nm layer. The latter structure is104used for spin-state readout measurements.105Figure 1(b) shows a scanning electron microscope image of106the device and the schematic resonator. The upper dots cor-107respond to the charge sensor, while the bottom to the target108quantum dots. This device design is suitable for qubits inte-109gration, which is employed in other material systems[36, 37].110As part of our design process, we optimize the QPC width to111form quantum dots that avoid formation of the stray capaci-112tance. The sensor quantum dot is embedded in an rf resonator113circuit constructed with a 1.2 µH chip inductor and stray ca-114pacitance Cp. All experimental measurements are performed115within a dilution refrigerator maintained at 60 mK.116To demonstrate the charge sensor operation, we measure117two types of source-drain current: one through the sensor118dot Isensor and another through the target dot Itarget. Fig-119ure 1(c) shows Isensor and Itarget as a function of the gate120voltage VP1, where the sensor’s operating gate voltage VS1P121is set to the slope of the Coulomb peak as shown in the inset122of Fig. 1c. Itarget exhibits a typical Coulomb peak behavior,123indicating the formation of a quantum dot. At the peak posi-124tion of Itarget around VP1 = −5.0 V, the step-like variation125of Isensor reflects the increase or decrease of electrons in the126target dot because the electron acts as an effective gate voltage127on the sensor dot through the electrostatic coupling between128(a)(c)(b)Cprf in out1.2 H500 nmItargetIsensorP1 P2S1PS1L S1RZnO SubstrateZnO (200 nm)2DEG layer(Mg, Zn)O (100 nm)Al2O3 (20/30 nm)Ti/AuI sensorVS1POperation pointTargetSensorIsensorItargetFIG. 1. (a) Schematic of the device structure. (b) Scanning electronmicroscope image of the fabricated device and the resonance circuit.(c) Gate voltage VP1 dependence of the sensor current Isensor andtarget current Itarget. The inset shows an operation point of the sen-sor dot.the target and sensor dots. Note that VS1P is compensated129to maintain the operation point, as VP1 affects the sensor dot130conductance. Another noticeable change in Isensor is observed131at VP1 ≈ −5.25 V (indicated by the arrow) while Itarget re-132mains nearly constant at zero. This is because, in this region,133the tunnel couplings between the target dot and the lead elec-134trodes are extremely weak, resulting in nearly zero current,135even when an electron is added to the target dot. This behav-136ior is also observed in the previous study in GaAs by using137a quantum point contact sensor [31]. This condition corre-138sponds to an upper limit on the tunneling rate of 1.1 MHz by139considering our measurement resolution while Coulomb peak140observed at VP1 = −5.0 V corresponds to a tunneling rate141of approximately 5 GHz by assuming sequential tunneling in142the transport current measurement. These results demonstrate143that the charge sensor enables accurate counting of the num-144ber of electrons in the target dot, even when the direct current145through the target dot is too small to be detected.1463B. Radio-frequency reflectometry147Next, we investigate the resonator properties to perform the148rf reflectometry. The reflected signal from the resonator is149measured using a network analyzer connected through a di-150rectional coupler as shown in Fig. 2(a). Figure 2(b) shows151the transmission coefficients S21 as functions of frequency152and VS1P, while maintaining the gate voltages VS1R and VS1L153at fixed values of −3.84 V and −4.42 V, respectively. Note154that S21 is determined by measuring the input signal and the155reflected signal from the resonator using a directional cou-156pler, effectively representing the reflection coefficients. The157resonance frequency is approximately 174 MHz, correspond-158ing to Cp of 0.69 pF. We calculate the resonator Q factor159to be approximately 15 by using the full width at half max-160imum of the resonant dip. The dip depth is modulated by161VS1P, reflecting the changes in conductance of the sensor dot,162while the resonance frequency remains nearly constant sug-163gesting that unexpected capacitance leading to rf signal leak-164age is suppressed. Figure 2(c) shows typical traces of S21.165At VS1P = −4.32 V, a pronounced dip is observed where166the impedance matching condition is satisfied. In contrast, at167VS1P = −4.35 V, a trace without impedance matching shows168a small dip depth. This large variation in dip depth enables169high-sensitivity charge sensing under matching conditions.170C. Few-electron quantum dots171Next, we switch the measurement setup to a demodulator172circuit which is commonly used in rf reflectometry[31, 38].173Figure 3(a) illustrates the demodulator circuit for performing174rf reflectometry. The resonator, which incorporates a charge175sensor, receives the rf signal at a frequency of 174 MHz via176a directional coupler. The amplitude of the rf signal is set to177−93 dBm at the sample end. After reflection, this rf signal un-178dergoes amplification and is then mixed with a local oscillator179signal for demodulation. We optimize the phase shifter be-180tween the signal generator and the mixer. The resulting down-181converted signal voltage, denoted as Vrf , is digitized. The182sampling rate is set to 100 MHz. To find the operation point,183we measure the frequency and VS1P dependence of a numer-184ical derivative dVrf/dVS1P, as illustrated in Figure 3(b). A185phase difference between the reflected signal and the local os-186cillator at the mixer modulates Vrf . A typical additional phase187is caused by a phase shift induced by the circuit line, whose188effects appear as periodic changes on Vrf along the frequency189axis. This color pattern, also observed in previous studies us-190ing GaAs and GaN quantum dots [38, 39], shows optimum191operation points where the maximum sensitivity is obtained.192Figure 3(c) shows Isensor and Vrf with sweeping VS1P,193where we perform an integration of 2 × 105 data points to194reduce the noise in Vrf . The changes in Vrf and Isensor are195synchronized, allowing us to detect the change in Isensor by196monitoring Vrf . The region where Vrf approaches zero sat-197isfies the impedance matching condition, enabling high sen-198VS1P =-4.35 VVS1P =-4.32 V(b) (c)(a)Network analyzerPort 1 Port 2ResonatorDirectional coupler60 mK300 K1.5 KAmp.FIG. 2. (a) Measurement setup to evaluate the resonator properties.(b) VS1P dependence of the resonator’s S21 parameter. The colorscale represents the magnitude of S21 in dB. (c) S21 characteristicsshowing typical traces with (VS1P = −4.32 V) and without (VS1P =−4.35 V) impedance matching.sitivity for rf charge sensing. After establishing the rf charge199sensing technique, we apply this technique to probe the forma-200tion of double quantum dots in the target region. The charge201stability diagram obtained by monitoring Vrf while sweeping202VP1 and VP2 is shown in Fig. 3(d). Two distinct slopes in the203charge transition lines indicate the formation of double quan-204tum dots. The absence of charge transition lines in the more205negative gate voltage region indicates the full depletion of the206double quantum dot. By counting the number of electrons us-207ing the charge transition lines, we can assign the number of208electrons in each region as shown in the figure. This result209clearly shows we achieve few-electron states in this double210quantum dot system.211In this section, we have demonstrated charge detection uti-212lizing the sensor quantum dot and rf reflectometry, and ob-213served few-electron double quantum dots in ZnO. The em-214ployed device design has the potential to integrate more quan-215tum dots, suggesting that the ZnO quantum dots platform216could also become a candidate for high-density qubit systems2174(a) (c)(d)DigitizerResonatorPhase shifterfMixerAmp.300 K60 mK(b)(0, 0)(1, 0)(0, 1)(1, 1)(0, 2)(1, 2)(2, 2)(2, 1)(2, 0)Directional couplerSignal generator1.5 KFIG. 3. (a) Schematic of the demodulator circuit. (b) Frequency and VS1P dependence of dVrf/dVS1P. (c) Isensor and Vrf as a function ofVS1P. (d) Charge stability diagram of a few electron double quantum dots probed by Vrf . ∆Vrf is the numerical difference in Vrf along theVP1 axis direction.as well as Si systems. These are important steps toward real-218izing spin qubits utilizing ZnO and single-shot readout of the219qubit states.220D. Charge sensitivity and error rate calculation221Here, we estimate the charge sensitivity of our measure-222ment system. The noise σ0, defined as the standard devia-223tion of real-time measurement, is evaluated to be 36.8 mV.224From the charge stability diagram shown in Fig. 3(d), we es-225timate effective gate-voltage shifts of the sensor dot for each226single-electron transition in the target dots of (0,0) ↔ (1,0),227(0,0) ↔ (0,1), and (1,0) ↔ (0,1). The shifts for the (0,0) ↔228(1,0) and (0,0) ↔ (0,1) transitions are extracted to be 3.20 mV229and 1.00 mV, respectively. This difference allows us to distin-230guish the charge states (1,0) and (0,1) which is important for231observing the interdot charge transition in the spin blockade232measurement. Note that the sensor dot is biased over a wide233dynamic range to obtain such a wide stability diagram. Using234these values together with the charge sensor slope extracted235from Fig. 3(c), which corresponds to the most sensitive sensor236condition, the detection voltages dV for each single-electron237transition in the target dots of (0,0) ↔ (1,0), (0,0) ↔ (0,1),238and (1,0) ↔ (0,1) are estimated to be 2.19 mV, 0.69 mV and2391.51 mV, respectively. By using σ0 and dV , we find that time240integration to reduce the noise determines measurement band-241widths fbw of 178 kHz, 17.4 kHz and 84.2 kHz. These values242are required to achieve SNR = 1 defined by following equa-243tion,2445FIG. 4. Error rate for each single-electron transition in the target dotsof (0,0) ↔ (1,0), (0,0) ↔ (0,1), and (1,0) ↔ (0,1) as a function ofthe integration time tint.SNR =dVσ0√fbw/f0. (1)Here, f0 is the measurement bandwidth to evaluate σ0.245The charge sensitivities for three electron transitions are cal-246culated to be 2.37 × 10−3 eHz−1/2, 7.58 × 10−3 eHz−1/2,247and 3.45× 10−3 eHz−1/2 by considering found value of each248fbw. These values are consistent with the previous report us-249ing GaAs system [31].250We also estimate the potential error rate of single charge de-251tection in the presented system by using the following equa-252tions [13]253Error Rate = 0.5erfc(SNR2√2). (2)Figure 4 shows the calculated error rate as a function of an254integration time tint = 1fbw. The orange points indicate that255tint ≈ 60 µs, 128 µs, and 622 µs satisfy the reading accuracy256of 99% for each single-electron transition. These times are257shorter than the longitudinal relaxation time T1 reported for258shallow donor qubits in ZnO [19]. Note that our gate-defined259quantum dots differ from those donor systems in geometry260and mechanisms. Experimentally establishing T1 in these de-261vices will thus be important for future work.262Furthermore, we examine the noise on Vrf using other ZnO263devices and resonators while keeping the same rf-circuit com-264ponents and transmission lines, as described in Appendix sec-265tion. These measurements show similar noise levels, indicat-266ing that the dominant contribution to the noise on Vrf origi-267nates from the preamplifier, as previously discussed for GaAs268systems [38].269III. CONCLUSION270In this study, we demonstrate the charge sensing and rf re-271flectometry of ZnO quantum dots. The sensor dot detects272the charge state of the target dots, which has been difficult273to determine when measuring the source-drain current of the274target directly. Owing to the charge sensor with the integra-275tion suitable design, we observe the few-electron regime of a276double quantum dot system probed by rf reflectometry, which277is essential for utilizing these systems as future high-density278qubits. The presented device and measurement setup enable279charge sensing with a readout accuracy of 99% within an inte-280gration time ranging from 60 µs to 622 µs, which is compara-281ble to values reported for GaAs and Si systems. We have ad-282dressed the challenges associated with realizing few-electron283states and rf reflectometry in ZnO quantum dots, which are284essential for their application as qubits. These results indicate285that ZnO quantum devices can progress together with GaAs286and Si devices by leveraging the technology developed for287these material systems, paving the way for quantum informa-288tion processing applications using ZnO quantum devices.289ACKNOWLEDGEMENTS290The authors thank K. Dezaki, M. Takeuchi, A. Kurita,291and the RIEC Fundamental Technology Center and the Lab-292oratory for Nanoelectronics and Spintronics for fruitful dis-293cussions and technical support. Part of this work was sup-294ported by MEXT Leading Initiative for Excellent Young Re-295searchers, Grants-in-Aid for Scientific Research (21K18592,29622H04958, 23H01789, 23H04490), Tanigawa Foundation Re-297search Grant, Maekawa Foundation Research Grant, The298Foundation for Technology Promotion of Electronic Cir-299cuit Board, Iketani Science and Technology Foundation Re-300search Grant, The Ebara Hatakeyama Memorial Foundation301Research Grant, FRiD Tohoku University, and "Advanced302Research Infrastructure for Materials and Nanotechnology303in Japan (ARIM)" of the Ministry of Education, Culture,304Sports, Science and Technology (MEXT) (Proposal Number305JPMXP1224NM5072). AIMR and MANA are supported by306World Premier International Research Center Initiative (WPI),307MEXT, Japan.308COMPETING INTERESTS309The authors declare no competing interests.310APPENDIX A:NOISE EVALUATION WITH A DIFFERENT311DEVICE AND RESONATOR CIRCUIT312We evaluate the charge sensitivity for a ZnO quantum313dot device different from the device referred to in the main314Kosuke_Noroハイライト表示Kosuke_Noroハイライト表示6text. From the stability diagram shown in Fig. 5(a), we ex-315tract the effective gate-voltage shifts for each electron transi-316tions (0,1) ↔ (0,2), (0,1) ↔ (1,1), and (1,1) ↔ (0,2) to be3175.15 mV, 3.61 mV, and 4.34 mV, respectively. The noise stan-318dard deviation with a 48 MHz low-pass filter is measured to319be σ0 = 57.2 mV. Using these parameters, the bandwidths320for each electron transition are calculated to be 390 kHz,321191 kHz, and 277 kHz, corresponding to the charge sensi-322tivities of 1.60 × 10−3 eHz−1/2, 2.29 × 10−3 eHz−1/2, and3231.90×10−3 eHz−1/2, respectively. Furthermore, we also eval-324uate the noise for a different resonator circuit by using the de-325vice discussed in the main text. In this device, the resonator326circuit including an inductor of 1.2 µH is connected to the327sensor quantum dot side as shown in Fig. 1(b) while the target328side uses an inductor of 1.0 µH. The noise standard deviation329of each side is calculated to be 34.3 mV and 36.8 mV.330APPENDIX B:PERSPECTIVE FOR SPIN-BLOCKADE331MEASUREMENTS332After the formation of few-electron double quantum dots,333spin-state readout measurements are expected as the next step.334In this appendix section, we provide a perspective on spin335blockage measurements. For the spin blockade measure-336ment [40, 41], we measure the stability diagram with a gate337voltage pulse sequence under an in-plane magnetic field of33850 mT [32, 33, 42]. Here, the sampling rate is set to 125339MHz. We perform this measurement near the (0,2) to (1,1)340charge transition, where (nP1, nP2) indicates the number of341electrons in the quantum dots defined by VP1 and VP2. At the342reset pulse step R, the two-electron state is initialized to either343a singlet or one of the three triplet states. If initialized to the344singlet state, the state is transferred to the (0,2) charge state345during the next measure pulse step M. Conversely, if initial-346ized to one of the triplet states, it remains in the (1,1) charge347state during this pulse M. After the measurement, one of the348electrons is evacuated during the pulse step E to prepare the349next reset phase. As a result, the signal from the (1,1) state350is expected to appear in the region near the boundary between351the (0,2) and (1,1) states, approximately within the dashed re-352gion in Fig. 5(a) [32, 33, 42]. However, the absence of signals353in these regions indicates that spin blockade does not occur354and/or the spin state might be relaxed by not fully optimized355tunneling rates. Note that this measurement is performed in a356different device with similar structures.357Because there are many possible reasons for the absence358of spin blockade such as tuning of tunneling rates, it is dif-359ficult to determine the origin of the absence. Here, we360discuss the effect of electron correlation in ZnO as one of361the possible mechanisms. For a two-electron state, con-362sidering both orbital and spin degrees of freedom, the spin363states almost degenerate in the low magnetic field. These364spin states are represented as |T+⟩ = |↑⟩1 |↑⟩2, |T 0⟩ =3651√2(|↑⟩1 |↓⟩2 + |↓⟩1 |↑⟩2), |T−⟩ = |↓⟩1 |↓⟩2, and |S⟩ =3661√2(|↑⟩1 |↓⟩2 − |↓⟩1 |↑⟩2). As a result, the energy of the elec-367(a)(b)|e>|g>(c)ۧ|𝑆 ۧ|𝜓𝑆 Eۧ|𝑆 ۧ|𝜓𝑆 G ۧ|𝑇− ۧ|𝜓𝑇ۧ|𝑇0 ۧ|𝜓𝑇ۧ|𝑇+ ۧ|𝜓𝑇ۧ|𝑆 ۧ|𝜓𝑆 Gweak correlationEMR(0, 1)(0, 2)(1, 1)timeGate volt.E R MVP1VP2FIG. 5. (a) Charge stability diagram with a gate pulse sequence underan in-plane magnetic field of 50 mT. The inset indicates a three-stepgate pulse sequence to observe the spin blockade. The dwell timesof E, R, and M are 1000 ns, 600 ns, and 10000 ns, respectively. (b)Energy levels of the ground and excited orbital states. With strongelectron correlation, the formation of the ground singlet is forbiddenand the higher orbital is occupied by the second electron. (c) Energylevels of two-electron states considering both orbital and spin con-figurations with strong electron correlation. The dotted line indicatesthe ground state in the case of weak electron correlation.tronic state is determined by the orbital energy. Regarding the368(0, 2) state, the orbital states for the ground (excited) spin-369singlet |ψS⟩G (|ψS⟩E) and triplet |ψT ⟩ configurations can be370expressed as371|ψS⟩G = |g⟩1 |g⟩2 ,|ψS⟩E =1√2(|g⟩1 |e⟩2 + |e⟩1 |g⟩2) ,(3)372|ψT ⟩ =1√2(|g⟩1 |e⟩2 − |e⟩1 |g⟩2) . (4)Here, |g⟩ and |e⟩ are the ground and excited orbital states,373as shown in Fig. 5(b). If the Coulomb interaction energy is374larger than the difference between the ground and excited or-375bital levels, a second electron added to the quantum dot occu-376pies the excited level. Under this condition, |ψS⟩E becomes3777the ground state, whereas in devices with weak electron corre-378lation, such as GaAs, |ψS⟩G typically assumes this role. Con-379sequently, even in the (0, 2) state, two-electron states with380different spin configurations are nearly degenerate in energy,381as shown in Fig. 5(c). This is in contrast to the usual scenario382where only the singlet state forms the ground state |S⟩ |ψS⟩G,383enabling readout operations by spin-blockade. Indeed, the384Kondo effect has been observed even in even-electron states in385the ZnO quantum dot as a signature of strong electron correla-386tion [29, 43]. Such behavior based on strong correlation sup-387ports the presented physical pictures, and our results suggest388that improvements to the current situation or the establishment389of new principles for readout methods are necessary. One pos-390sible approach to the first solution is fabricating devices with391smaller designs, increasing the orbital energy spacing than the392electron interaction.393DATA AVAILABILITY394The data that support the findings of this study are available395in the article. Additional data related to this paper may be396requested from the authors.397∗ tomohiro.otsuka@tohoku.ac.jp398[1] S. Tarucha, D. Austing, T. Honda, R. Van der Hage, and L. 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