Charge noise is an important factor limiting qubit coherence and relaxation in solid-state devices. In bilayer graphene (BLG) quantum dots, recently established as a promising platform for spin- and valley-based qubits, both the origin and magnitude of charge noise remain largely unexplored. Here, we investigate high-frequency charge noise using Landau-Zener-Stückelberg-Majorana (LZSM) interference spectroscopy. We study a single-particle charge qubit formed in a BLG double quantum dot at frequencies between 5 and 10 GHz and extract a noise spectral density S_ε on the order of 0.5-0.9 neV/√(Hz). This is comparable to values reported for III-V semiconductor platforms and silicon. From the temperature and frequency dependence of the charge qubit decoherence, we conclude that thermal (Johnson) noise or electron-phonon coupling dominates over two-level fluctuators.

We report on an experimental study of spin and valley blockade in two-electron bilayer graphene (BLG) double quantum dots (DQDs) and explore the limits set by asymmetric orbitals and electronelectron interactions. The results obtained from magnetotransport measurements on two-electron BLG DQDs, where the resonant tunneling transport involves both orbital symmetric and antisymmetric two-particle states, show a rich level spectrum. We observe a magnetic field tunable spin and valley blockade, which is limited by the orbital splitting, the strength of the electron-electron interaction and the difference in the valley g-factors between the symmetric and antisymmetric twoparticle orbital states. Our conclusions are supported by simulations based on rate equations, which allow the identification of prominent interdot transitions associated with the transition from single to two-particle states observed in the experiment.

The valley degree of freedom in two-dimensional (2D) semiconductors, such as gapped bilayer graphene (BLG) and transition metal dichalcogenides, is a promising carrier of quantum information in the emerging field of valleytronics. While valley dynamics have been extensively studied for moderate band gap 2D semiconductors using optical spectroscopy techniques, very little is known about valley lifetimes in narrow band gap BLG, which is difficult to study using optical techniques. Here, we report single-particle valley relaxation times T1 exceeding several microseconds in electrostatically defined BLG quantum dots using a pulse-gating technique. The observed dependence of T1 on perpendicular magnetic field can be understood qualitatively and quantitatively by a model in which T1 is limited by electron-phonon coupling. We identify the coupling to acoustic phonons via the bond length change and via the deformation potential as the limiting mechanisms.

We report on the investigation of proximity-induced spin-orbit coupling (SOC) in a heterostructure of bilayer graphene (BLG) and tungsten diselenide (WSe2). A BLG quantum dot (QD) in the few-particle regime acts as a sensitive probe for induced SOC. Finite bias and magnetotransport spectroscopy measurements reveal a significantly enhanced SOC that decreases with the applied displacement field, distinguishing it from pristine BLG. Furthermore, our measurements demonstrate a reduced valley g factor at larger displacement fields, consistent with weaker lateral confinement of the QD. Our findings show evidence of the influence of WSe2 across BLG layers, driven by reduced real-space confinement and increased layer localization of the QD states on the BLG layer distant to the WSe2 at higher displacement fields. This study demonstrates the electrostatic tunability of the spin-orbit gap in BLG/WSe2 heterostructures, which is especially relevant for the field of spintronics and future spin qubit control in BLG QDs.

High-fidelity detection of charge transitions in quantum dots (QDs) is a key ingredient in solid-state quantum computation. We demonstrate high-bandwidth radio-frequency charge detection in bilayer graphene quantum dots (QDs) using a capacitively coupled quantum point contact (QPC). The device design suppresses screening effects and enables a sensitive QPC-based charge readout. The QPC is arranged to maximize the readout contrast between two neighboring coupled electron and hole QDs. We apply the readout scheme to a single-particle electron-hole double QD and demonstrate time-resolved detection of charge states as well as magnetic field dependent tunneling rates. This promises a high-fidelity readout scheme for individual spin and valley states, which is important for the operation of spin, valley, or spin-valley qubits in bilayer graphene.

Zusammenfassung Nachdem erstmals ein Einzelelektronen‐Quantenpunkt in zweilagigem Graphen gezeigt wurde, folgten in kurzer Zeit wegweisende Experimente. Dazu zählen die Untersuchung des Ein‐ und Zweiteilchenspektrums, der Elektronen‐Loch‐Übergang, die kontrollierbare Kopplung von Quantenpunkten, Ladungsdetektion, Pauli‐Blockade und die hier gezeigten Messungen der Spin‐Relaxationszeit. Diese Experimente tragen wesentlich zum Verständnis der elektronischen Zustände in Graphen‐Quantenpunkten bei. Sie sind wichtige Meilensteine auf dem Weg zur Realisierung eines graphenbasierten Qubits. Die gemessenen Spin‐Relaxationszeiten sind bereits hinreichend lang und Mechanismen zur Spin‐Detektion sind vorhanden. Damit lassen sich Spin‐Qubits angehen.

The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-Stückelberg-Majorana (LZSM) interference. LZSM interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and T_2^* charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZSM interference and photon assisted tunneling. Both techniques yield T_2^* average values in the range of 400 to 500 ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments.

Particle-hole symmetry plays an important role for the characterization of topological phases in solid-state systems. It is found, for example, in free-fermion systems at half filling, and it is closely related to the notion of antiparticles in relativistic field theories. In the low energy limit, graphene is a prime example of a gapless particle-hole symmetric system described by an effective Dirac equation, where topological phases can be understood by studying ways to open a gap by preserving (or breaking) symmetries. An important example is the intrinsic Kane-Mele spin-orbit gap of graphene, which leads to a lifting of the spin-valley degeneracy and renders graphene a topological insulator in a quantum spin Hall phase, while preserving particle-hole symmetry. Here, we show that bilayer graphene allows realizing electron-hole double quantum-dots that exhibit nearly perfect particle-hole symmetry, where transport occurs via the creation and annihilation of single electron-hole pairs with opposite quantum numbers. Moreover, we show that this particle-hole symmetry results in a protected single-particle spin-valley blockade. The latter will allow robust spin-to-charge conversion and valley-to-charge conversion, which is essential for the operation of spin and valley qubits.

Data Repository for the Publication: Impact of competing energy scales on the shell-filling sequence in elliptic bilayer graphene quantum dots Abstract: We report on a detailed investigation of the shell-filling sequence in electrostatically defined elliptic bilayer graphene quantum dots (QDs) in the regime of low charge carrier occupation, N < 12, by means of magnetotransport spectroscopy and numerical calculations. We show the necessity of including both short-range electron-electron interaction and wavefunction-dependent valley g-factors for understanding the overall fourfold shell-filling sequence. These factors lead to an additional energy splitting at half-filling of each orbital state and different energy shifts in out-of-plane magnetic fields. Analysis of 31 different BLG QDs reveals that both valley g-factor and electron-electron interaction induced energy splitting increase with decreasing QD size, validating theory. However, we find that the electrostatic charging energy of such gate-defined QDs does not correlate consistently with their size, indicating complex electrostatics. These findings offer significant insights for future BLG QD devices and circuit designs.

The importance of controlling both the charge carrier density and the band gap of a semiconductor cannot be overstated, as it opens the doors to a wide range of applications, including, e.g., highly-tunable transistors, photodetectors, and lasers. Bernal-stacked bilayer graphene is a unique van-der-Waals material that allows tuning the band gap by an out-of-plane electric field. Although the first evidence of the tunable gap was already found ten years ago, it took until recent to fabricate sufficiently clean heterostructures where the electrically induced gap could be used to fully suppress transport or confine charge carriers. Here, we present a detailed study of the tunable band gap in gated bilayer graphene characterized by temperature-activated transport and finite-bias spectroscopy measurements. The latter method allows comparing different gate materials and device technologies, which directly affects the disorder potential in bilayer graphene. We show that graphite-gated bilayer graphene exhibits extremely low disorder and as good as no subgap states resulting in ultraclean tunable band gaps up to 120 meV. The size of the band gaps are in good agreement with theory and allow complete current suppression making a wide range of semiconductor applications possible.

The relaxation time of a single-electron spin is an important parameter for solid-state spin qubits, as it directly limits the lifetime of the encoded information. Thanks to the low spin-orbit interaction and low hyperfine coupling, graphene and bilayer graphene (BLG) have long been considered promising platforms for spin qubits. Only recently, it has become possible to control single-electrons in BLG quantum dots (QDs) and to understand their spin-valley texture, while the relaxation dynamics have remained mostly unexplored. Here, we report spin relaxation times ( T 1 ) of single-electron states in BLG QDs. Using pulsed-gate spectroscopy, we extract relaxation times exceeding 200 μ s at a magnetic field of 1.9 T. The T 1 values show a strong dependence on the spin splitting, promising even longer T 1 at lower magnetic fields, where our measurements are limited by the signal-to-noise ratio. The relaxation times are more than two orders of magnitude larger than those previously reported for carbon-based QDs, suggesting that graphene is a potentially promising host material for scalable spin qubits.

Future quantum computers capable of solving relevant problems will require a large number of qubits that can be operated reliably. However, the requirements of having a large qubit count and operating with high-fidelity are typically conflicting. Spins in semiconductor quantum dots show long-term promise but demonstrations so far use between one and four qubits and typically optimize the fidelity of either single- or two-qubit operations, or initialization and readout. Here we increase the number of qubits and simultaneously achieve respectable fidelities for universal operation, state preparation and measurement. We design, fabricate and operate a six-qubit processor with a focus on careful Hamiltonian engineering, on a high level of abstraction to program the quantum circuits and on efficient background calibration, all of which are essential to achieve high fidelities on this extended system. State preparation combines initialization by measurement and real-time feedback with quantum-non-demolition measurements. These advances will allow for testing of increasingly meaningful quantum protocols and constitute a major stepping stone towards large-scale quantum computers.

We report on finite bias spectroscopy measurements of the two-electron spectrum in a gate defined bilayer graphene (BLG) quantum dot for varying magnetic fields. The spin and valley degree of freedom in BLG give rise to multiplets of six orbital symmetric and ten orbital antisymmetric states. We find that orbital symmetric states are lower in energy and separated by ≈ 0.4-0.8  meV from orbital antisymmetric states. The symmetric multiplet exhibits an additional energy splitting of its six states of ≈ 0.15-0.5  meV due to lattice scale interactions. The experimental observations are supported by theoretical calculations, which allow to determine that intervalley scattering and "current-current" interaction constants are of the same magnitude in BLG.

Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μ eV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the K and K^' states below 20 μ eV.

We present a highly controllable double quantum dot device based on bilayer graphene. Using a device architecture of interdigitated gate fingers, we can control the interdot tunnel coupling between 1 and 4GHz and the mutual capacitive coupling between 0.2 and 0.6meV, independent of the charge occupation of the quantum dots. The charging energy and, hence, the dot size remain nearly unchanged. The tuning range of the tunnel coupling covers the operating regime of typical silicon and GaAs spin qubit devices.

We demonstrate dispersive readout of individual charge states in a gate-defined few-electron quantum dot in bilayer graphene. We employ a radio frequency reflectometry circuit, where an LC resonator with a resonance frequency close to 280 MHz is directly coupled to an ohmic contact of the quantum dot device. The detection scheme based on changes in the quantum capacitance operates over a wide gate-voltage range and allows to probe excited states down to the single-electron regime. Crucially, the presented sensing technique avoids the use of an additional, capacitively coupled quantum device such as a quantum point contact or single electron transistor, making dispersive sensing particularly interesting for gate-defined graphene quantum dots.

We present transport measurements through an electrostatically defined bilayer graphene double quantum dot in the single electron regime. With the help of a back gate, two split gates and two finger gates we are able to control the number of charge carriers on two gate-defined quantum dot independently between zero and five. The high tunability of the device meets requirements to make such a device a suitable building block for spin-qubits. In the single electron regime, we determine interdot tunnel rates on the order of 2 GHz. Both, the interdot tunnel coupling, as well as the capacitive interdot coupling increase with dot occupation, leading to the transition to a single quantum dot. Finite bias magneto-spectroscopy measurements allow to resolve the excited state spectra of the first electrons in the double quantum dot; being in agreement with spin and valley conserving interdot tunneling processes.

A gate‐defined quantum dot in bilayer graphene is utilized as a sensitive probe for the charge density of its environment. Under the influence of a perpendicular magnetic field, the charge carrier density of the channel region next to the quantum dot oscillates due to the formation of Landau levels. This is experimentally observed as oscillations in the gate‐voltage positions of the Coulomb resonances of the nearby quantum dot. From the frequency of the oscillations, the charge carrier density in the channel is extracted, and from the amplitude the shift of the quantum dot potential. These experimental results are compared with an electrostatic simulation of the device and good agreement is found.

Electron and hole Bloch states in bilayer graphene exhibit topological orbital magnetic moments with opposite signs, which allows for tunable valley-polarization in an out-of-plane magnetic field. This property makes electron and hole quantum dots (QDs) in bilayer graphene interesting for valley and spin-valley qubits. Here, we show measurements of the electron–hole crossover in a bilayer graphene QD, demonstrating opposite signs of the magnetic moments associated with the Berry curvature. Using three layers of top gates, we independently control the tunneling barriers while tuning the occupation from the few-hole regime to the few-electron regime, crossing the displacement-field-controlled band gap. The band gap is around 25 meV, while the charging energies of the electron and hole dots are between 3 and 5 meV. The extracted valley g-factor is around 17 and leads to opposite valley polarization for electrons and holes at moderate B-fields. Our measurements agree well with tight-binding calculations for our device.