Graphene Superconducting Quantum Circuits

• Graphene-based superconducting quantum circuits are systems integrating graphene Josephson junctions into cQED setups for electrical tunability and multi-modality.
• They employ diverse device architectures—including transmons, SQUIDs, and parametric amplifiers—enabling gate-controlled qubit dynamics and improved coherence.
• Recent designs demonstrate enhanced tunability, noise suppression, and scalability, paving the way for topological and hybrid quantum computing applications.

Graphene-based superconducting quantum circuits integrate graphene Josephson junctions (JJs) or van der Waals heterostructures into superconducting circuit quantum electrodynamics (cQED) architectures, supporting functionalities from gate-tunable transmons and SQUIDs to parametric amplifiers and charge-spin qubit buses. The unique material properties of graphene and its heterostructures—high mobility, atomic thickness, ballistic Dirac transport, tunable critical current densities, and compatibility with high magnetic fields—enable quantum circuits with electrical tunability, multi-modality, and, in certain designs, topological non-triviality.

1. Device Architectures and Material Platforms

Graphene-based superconducting quantum circuits employ a range of device geometries and materials integration strategies:

• Josephson Junctions (gJJ): Junctions are formed by monolayer or bilayer graphene (typically hBN-encapsulated for mobility and noise suppression) contacted by superconducting leads (Al, Nb, NbTiN, MoRe) via edge or side contacts (Chiu et al., 24 Dec 2025, Aparicio et al., 5 Jun 2025). Junctions can be single, forming phase-slip, single-junction qubits, or paired in parallel as SQUIDs for flux-tunable Josephson energy (Chiu et al., 24 Dec 2025, Chiu et al., 2023).
• 3D and Planar cQED Integration: Devices are mounted at the center of 3D copper microwave cavities (TE₁₀₁ mode) for clean electromagnetic environments and flexible strong/dispersive coupling regimes (Chiu et al., 24 Dec 2025, Chiu et al., 2023); planar integration employs coplanar waveguide (CPW) or microstrip resonators (Aparicio et al., 5 Jun 2025, Schmidt et al., 2018).
• Gate Integration: Top or side gates (Al, Ti/Au) separated by dielectric layers (hBN, Al₂O₃) enable electrostatic control of carrier density and transmission in the graphene weak link, providing in situ tunability of $I_c$ and $E_J$ (Aparicio et al., 5 Jun 2025, Generalov et al., 10 Jan 2024).
• Hybrid Architectures: Tailored weak-links in bilayer graphene (BLG) (Kraft et al., 2017), compact double-layer graphene SQUIDs for topological applications (Indolese et al., 2020), and integration with atomically thin superconductors such as 2D-Ga on epitaxial graphene (Bersch et al., 2019).

Fabrication involves van der Waals assembly (polymer-free dry transfer for high-mobility stacks), precise electron-beam lithography for mesa and gate patterning, and optimized edge-contact formation to maximize transparency and uniformity (Chiu et al., 24 Dec 2025, Generalov et al., 10 Jan 2024). Large-scale integration is demonstrated with wafer-scale CMOS-compatible processing (Generalov et al., 10 Jan 2024).

2. Circuit Hamiltonians, Coupling Regimes, and Gate Control

• Single-Qubit Jaynes–Cummings Model: The fundamental Hamiltonian for a transmon-type circuit is:

$$\hat{H} = \hbar\omega_r \hat{a}^\dagger \hat{a} + \frac{\hbar\omega_q}{2}\hat{\sigma}_z + \hbar g(\hat{a}\hat{\sigma}_+ + \hat{a}^\dagger\hat{\sigma}_-)$$

where $\omega_r$ is the cavity frequency, $\omega_q \approx \sqrt{8E_JE_C}/\hbar$ the qubit frequency, $g$ the qubit-cavity coupling. Gate and flux tunability enter via $E_J$ (through $I_c$), allowing dynamic control of $\omega_q$ and system detuning (Chiu et al., 24 Dec 2025, Aparicio et al., 5 Jun 2025).

• Two-Qubit and Multi-Element Hamiltonians: For multi-qubit circuits, a sum over qubit–cavity and inter-qubit terms is included, with capacitive or direct inter-qubit coupling $J$ tunable via device capacitances and weak-link properties (Chiu et al., 24 Dec 2025). Bilayer graphene charge qubits dipole-coupled to high-impedance microwave resonators are modeled by Jaynes–Cummings and input–output theory, fully quantified in the dispersive and resonant regimes (Ruckriegel et al., 2023).
• Andreev Bound State (ABS) Description: High-transparency gJJs are accurately described as superconducting quantum point contacts (S-QPC) with N channels of transmission $\tau$, yielding ABSs at $$E_{\pm}(\varphi) = \pm\Delta\sqrt{1-\tau\sin^2(\varphi/2)}$$ and a Josephson potential with gate-dependent $E_J(V_g)$ (Aparicio et al., 5 Jun 2025).
• Electrical and Flux Tunability: Critical current $I_c$ and thus $E_J$ are tuned continuously with gate voltage, shifting qubit frequency and spectrum (3–9 GHz typical range over a <1 V gate span) (Aparicio et al., 5 Jun 2025, Chiu et al., 24 Dec 2025). SQUID geometries enable magnetic flux control of $E_J$ via interference (Chiu et al., 24 Dec 2025, Chiu et al., 2023). JoFETs fabricated at wafer scale show $I_C$ tunable over orders of magnitude by $V_{tg}$, on/off ratios > 20 (Generalov et al., 10 Jan 2024).

3. Coherence, Loss Mechanisms, and Figures of Merit

• Coherence Times: Coherence times in 3D cavity graphene transmons are currently $T_1\approx 48$ ns, $T_2^*\approx 18$ ns (Chiu et al., 24 Dec 2025); planar devices achieve $T_1=716$ ns, $T_2^*=62$ ns at optimal bias (Aparicio et al., 5 Jun 2025). Shorter coherence (e.g., $T_1\approx 12$–36 ns (Wang et al., 2018), $T_2^*\approx 2$–3 ns (Kroll et al., 2018)) is associated with charge noise, low-frequency flux noise, and dielectric losses, often away from the sweet spot or in earlier generations.
• Loss Mechanisms: Dissipation is traced to subgap Andreev bound states, charge-trap and dielectric loss (e.g., at the SiO₂ substrate or in high-κ gate oxides), and imperfect S–N interfaces. The measured subgap resistance $R_{sg}$ is in the $\sim1$ k$\Omega$ range, with $R_{sg}/R_n \sim 10$–40 (Schmidt et al., 2018). The use of hBN encapsulation, optimization of interface transparency, and improved filtering, as well as the implementation of high-Q 3D cavities, are effective in mitigating losses (Chiu et al., 24 Dec 2025, Aparicio et al., 5 Jun 2025).
• Charge Dispersion and Anharmonicity: High-transmission ($\tau\to1$) in short gJJs strongly suppresses charge dispersion compared to standard tunnel junctions, offering a strategy to approach both low charge noise sensitivity and large anharmonicity, suitable for advanced transmon and hybrid-transmon designs (Aparicio et al., 5 Jun 2025).

4. Quantum Circuit Modalities and Functionality

• Transmons and Gatemons: Gate-tunable transmons ("gatemons") are now robustly realized with graphene JJs as the nonlinear element; their transition frequencies, anharmonicities, and charge dispersion are all electrical-field-tunable (Chiu et al., 24 Dec 2025, Kroll et al., 2018, Aparicio et al., 5 Jun 2025).
• SQUIDs and Multi-Qubit Architectures: 3D cavity integration of devices with parallel JJs enables flux-tunable qubits (via symmetric and asymmetric SQUID designs), as well as two-qubit and scaling toward multi-qubit architectures with joint or individual readout (Chiu et al., 24 Dec 2025, Chiu et al., 2023, Indolese et al., 2020).
• Parametric Amplifiers: Fully gate-tunable Josephson parametric amplifiers (JPAs) based on graphene weak links achieve $>20$ dB gain, quantum-limited noise, and frequency tunability of over 1 GHz without the crosstalk or flux-hysteresis issues of SQUID-based JPAs (Butseraen et al., 2022).
• Charge-Spin Qubit Coupling: Dipole coupling of bilayer graphene double quantum dots to high-impedance microwave resonators reaches $g/2\pi\approx50$ MHz; dispersive charge sensing is achieved with state-of-the-art speed and SNR for graphene quantum-dot platforms (Ruckriegel et al., 2023).

5. Gate-Tunability and High Magnetic Field Operation

• Gate Control: Graphene-based circuits provide in-situ, all-electrical control over Josephson energy and transitions, enabling "fluxless" frequency tunability, fast real-time parameter modulation (timescales $\sim 100$ ns), and programmable coupling networks for advanced logic and coupling schemes (Aparicio et al., 5 Jun 2025, Chiu et al., 24 Dec 2025).
• Magnetic Field Resilience: Unlike conventional Al/AlOₓ JJs (limited to $<10$ mT), graphene JJs in NbTiN or MoRe circuits maintain functional qubit operation up to at least 1 T, a prerequisite for integration with topological systems (e.g., Majorana platforms) and for study of hybrid quantum Hall–superconductor physics (Kroll et al., 2018, Indolese et al., 2020).

6. Scalability, Integration Challenges, and Outlook

• CMOS and Wafer-Scale Integration: Fully lithographic, large-area transfer processes for CVD graphene, in combination with encapsulation and standard ALD dielectrics, have demonstrated >90% device yield at 150 mm wafer scale (Generalov et al., 10 Jan 2024), supporting practical routes to integration with established superconducting circuit foundry processes.
• Superconducting Atomic Layer Hybrids: 2D superconductors (e.g., 2D-Ga under graphene) offer air-stable, atomically-thin superconducting circuit elements with $T_c\sim4$ K, coherence length $\xi(0)\sim 36$ nm and critical fields $B_{c2}(0) \sim 260$ mT, with direct patternability for circuit definition (Bersch et al., 2019).
• Topological and Hybrid Functionality: Compact double-layer graphene SQUIDs with independent gating are a tunable platform for engineering topological superconductivity via coupling to helical edge states in the quantum Hall regime. Achieving interlayer spacing $d_{gg} < \xi_S$, good layer alignment, and phase-bias control are identified as essential for realizing Majorana zero modes and topological qubits (Indolese et al., 2020).

Advancements in device uniformity, interface transparency, noise suppression, and coherence engineering are prioritized for bringing graphene-based superconducting quantum circuits to parity with state-of-the-art Al/AlOₓ systems, opening new regimes of in situ control, multi-qubit scaling, and hybrid material platforms (Chiu et al., 24 Dec 2025, Aparicio et al., 5 Jun 2025).