Gate-tunable spectrum and charge dispersion mitigation in a graphene superconducting qubit

TL;DR

This paper demonstrates gate-tunable graphene-based superconducting qubits where the qubit spectrum, anharmonicity, and charge dispersion can be controlled in situ by a gate voltage. By modeling the graphene junction as a superconducting quantum point contact with Andreev bound states across multiple transmission channels, the authors show that high channel transmission suppresses charge dispersion while maintaining sizable anharmonicity. The experiments on two devices reveal GHz-scale frequency tunability and reveal how geometry and contact-induced doping influence performance, with a theoretical framework that quantitatively describes the spectra via an effective $E_J(V_g)$ and $\tau(V_g)$. The results highlight graphene-based qubits as versatile building blocks for advanced superconducting circuits, offering fast gate control and reduced charge-noise sensitivity, with avenues for further improving coherence through enhanced channel control and resonant-level modeling near the Dirac point.

Abstract

Controlling the energy spectrum of quantum-coherent superconducting circuits, i.e. the energies of excited states, the circuit anharmonicity and the states' charge dispersion, is essential for designing performant qubits. This control is usually achieved by adjusting the circuit's geometry. In-situ control is traditionally obtained via an external magnetic field, in the case of tunnel Josephson junctions. More recently, semiconductor-weak-links-based Josephson junctions have emerged as an alternative building block with the advantage of tunability via the electric-field effect. Gate-tunable Josephson junctions have been succesfully integrated in superconducting circuits using for instance semiconducting nanowires or two-dimensional electron gases. In this work we demonstrate, in a graphene superconducting circuit, a large gate-tunability of qubit properties: frequency, anharmonicity and charge dispersion. We rationalize these features using a model considering the transmission of Cooper pairs through Andreev bound states. Noticeably, we show that the high transmission of Cooper pairs in such weak link strongly suppresses the charge dispersion. Our work illustrates the potential for graphene-based qubits as versatile building-blocks in advanced quantum circuits.

Figures (13)

• Figure 1: Devices description. (a) Electrical circuit diagram of a charge qubit made of a graphene Josephson junction (gJJ) shunted to ground by a $C_\mathrm{S}$ capacitance, and coupled to a readout resonator by a $C_\mathrm{qr}$ capacitance, a drive line by a $C_\mathrm{d}$ capacitance, and a gate line by a $C_\mathrm{g}$ capacitance to control conduction through graphene. The qubit superconducting island is defined by the superconducting leads (red) between the junction and the $C_\mathrm{S}$ capacitance. The qubit is read out by probing the transmission scattering parameter, $S_\mathrm{21}$, of a transmission line (TL) coupled to a microwave resonator by a $C_\mathrm{c}$ capacitance. (b) Optical micrograph of the h-BN/graphene/h-BN heterostructure of device Q$_\mathrm{1}$. (c,d) Schematics of the top-gated gJJs side-contacted to the Ti/Al superconducting electrodes. In device Q$_\mathrm{1}$ (c), a third h-BN layer is deposited on top of the electrodes as a gate dielectric to build an Al topgate. In device Q$_\mathrm{2}$ (d), the top h-BN of the heterostructure is directly used as a gate dielectric and a narrow (100 nm-wide) Al electrode is deposited in between the superconducting electrodes.
• Figure 2: Superconducting quantum point contact (S-QPC) model for a qubit based on a gate-tunable weak link between two superconducting electrodes. (a) Energy potential of the quantum harmonic oscillator (black) and the transmon qubit (red). In the latter, the Josephson junction's nonlinearity turns the energy spectrum anharmonic, such that energy levels are not evenly spaced. (b) Josephson potential of a S-QPC. When the transmission $\tau$ is below unity (black dotted line), $2 \pi$-quantum phase slips ($2 \pi$-QPSs) can occur, which is directly responsible for charge dispersion. For $\tau=1$ (solid orange line), the two ABS branches cross and $2 \pi$-QPS is forbidden, leading to a vanishing charge dispersion. Inset: effective model describing our devices as a gate-tunable S-QPC shunted by a capacitor.
• Figure 3: Gate-tunability of the qubit frequency. (a) Qubit frequency, $f_{\mathrm{01}}$, as a function of the gate voltage, $V_{\mathrm{g}}$ for device Q$_\mathrm{1}$. A pronounced asymmetry is observed about the charge neutrality point (CNP) of graphene ($V_{\mathrm{CNP}} \sim -1.81$ V). Reproducible oscillations are observed in the $p$-doped regime of graphene, which are attributed to a Fabry-Pérot effect. (b) Same kind of data for device Q$_\mathrm{2}$. The inset shows a typical two-tone measurement of the qubit dispersively coupled to a readout resonator. When the drive tone frequency, $f_{\mathrm{d}}$, matches the qubit frequency, the qubit is excited from state $\ket{0}$ to state $\ket{1}$. The resonant frequency of the resonator is shifted accordingly and probed by a change in the amplitude, $|S_{\mathrm{21}}|$, of the readout tone.
• Figure 4: Qubit spectrum and charge dispersion in device Q$_\mathrm{2}$. (a) Two-tone measurement of the first two qubit transitions as a function of the charge offset, $n_{\mathrm{g}}$, at $V_{\mathrm{g}} = 0.41$ V. Solid and dashed lines represent the fitted frequency of the two charge parities (odd and even, labeled 'o' and 'e') of the $\ket{0}$-$\ket{1}$ and $\ket{0}$-$\ket{2}$ transitions. (b) Reconstruction of the qubit spectrum at $V_\mathrm{g}=0.41$ V using only the set of $\left (\delta f_{\mathrm{01}}, f_{\mathrm{01}} \right )$ values derived from the experimental data. The model (dashed lines) accounts for the $\ket{0}$-$\ket{1}$ transition, and correctly reproduces the $\ket{0}$-$\ket{2}$ transition too, without free parameters. (c) Charge dispersion, $\delta f_{\mathrm{01}}$, as a function of $E_\mathrm{J} \left ( V_\mathrm{g} \right ) / E_\mathrm{C}$, extracted from data such as in (a) (as shown in the inset), varying $V_{\mathrm{g}}$ from 400 mV to 486 mV. The coloured solid lines represent the charge dispersion predicted by Hamiltonian \ref{['ITLZ H']} for different values of transmission.
• Figure 5: Gate-dependent anharmonicity in device Q$_\mathrm{1}$. (a) Anharmonicity, $-\alpha$, as a function of $E_\mathrm{J} \left ( V_\mathrm{g} \right ) / E_\mathrm{C}$, where $E_{\mathrm{J}}$ is tuned by the gate voltage, in the $p$-doped conduction regime of graphene. The solid lines are the model predictions for a set of transmissions. (b) Similar data in the $n$-doped regime of graphene.