Absence of Charge Offset Drift in a Transmon Qubit

Abstract

Superconducting quantum circuits are sensitive to their electrostatic environment: uncontrolled charges accumulating on the electrodes of a Josephson junction shift the energy levels of a qubit, perturbing its operation and restricting their design. This effect is captured by a single parameter - the charge offset - whose slow, unpredictable drift has proven difficult to eliminate in practice. Here, we report a tantalum-based transmon qubit in which the charge offset remains pinned at zero over nearly three months of measurements, including two thermal cycles, with no observable compromise to the qubit lifetime. This exceptional stability disappears in later cooldowns, indicating a fragile mechanism at play. We attribute it to the inductance of a thin superconducting layer inadvertently formed in parallel with the Josephson junction during fabrication. X-ray surface spectroscopy suggests this layer arises from an incomplete wet-etch of tantalum on sapphire. Deliberately engineering such a layer offers a route to eliminating charge-offset drift in superconducting circuits more broadly.

Figures (20)

• Figure 1: Device and charge dispersion.a, Optical image of the device. The circuit is made of tantalum on sapphire except the Al/AlOx/Al Josepshon junction. Inset: inductive coupling between the readout resonator and its Purcell filter. b, False-colored electron-beam image of the device which includes a transmon island (pink), the junction (dark pink), a readout resonator (yellow) and a charge line (blue). c, Circuit schematic where an inductive or resistive element (orange) stabilizes the charge offset $n_g$. d, Charge dispersion of the first four energy transitions Chitta2022Groszkowski2021 of the transmon qubit ($E_J=16.5GHz$, $E_C=199MHz$). Blue solid line: transition frequencies $f_{i i+1}$ for even number of quasiparticles $n_\mathrm{qp}$ on the island. Orange dashed line: odd $n_\mathrm{qp}$.
• Figure 2: Probing the transition frequency $f_{34}$. a, Pulse sequence applied on the charge line to map Ramsey oscillations between states $\ket{3}$ and $\ket{4}$ onto the $\{\ket{0}, \ket{4}\}$ basis. The $3-4$ pulse is applied at a detuned frequency $\overline{f_{34}}+\delta f=4.2084GHz$. b, Blue dots: In-phase quadrature as a function of the delay $\tau$ in the Ramsey experiment, averaged over one thousand repetitions. Black line: fit combining two cosine functions ($f_1=4.0MHz$ and $f_2=6.0MHz$) with a decay time $T_2^{(34)}=1.4µ s$. c, Blue dots: Fourier transform $\lvert\tilde{I}(f)\rvert$ of the same signal. Black line: Fit with a combination of two Lorentzian peaks centered at $f_1$ and $f_2$. Pink vertical line: mean frequency $\delta f=5.0MHz$ indicating $\overline{f_{34}}=4.2034GHz$.
• Figure 3: Absence of charge offset drift. Continuous record of the measurement presented in \ref{['fig:2']}c. The left plot was measured on March 5th, 2024 during run 17 every $17s$, the middle plot was measured from May 3rd to May 10th, 2024 during run 17 every $58s$, and the right plot was measured on May 29th, 2024 during run 18 every $65s$. The frequency splitting is constant, indicating a constant value of the charge offset. In the middle panel, the lines are split into two doublets, which we attribute to a two-level system dispersively coupled to the qubit.
• Figure 4: Evolution of the charge offset in later runs.a, Record of $f_{34}$ using the protocol presented in \ref{['fig:2']}c over more than five days during run 21, every $231s$. Color: Fourier transform of Ramsey oscillations of the $3-4$ transition. b, Record of $f_{34}$ obtained during run 25, every $16s$. c, $3-4$ transition frequencies as a function of applied voltage $V_{\rm DC}$ on the charge line (referred to the source) and corresponding value of charge offset $n_g$ during run 22. The whole measurement takes $38s$, shorter than the charge drift timescale. White dots: fitted transition frequencies. Black dashed line: sinusoidal fit of the white dots $f_{34}^\pm=\overline{f_{34}}\pm \frac{\Delta f_{34}}{2}\cos(2\pi n_g)$. Here $\Delta f_{34} = 2MHz$ and $n_g = n_g^0+\frac{V_{\rm DC}}{12~{\rm V}}$.
• Figure 5: Parity switching. a, Signal $I_{\tau_0}$ for $2,000$ realizations in the absence of charge drift (situation of \ref{['fig:3']}, run 17). The signal alternates between two values, corresponding to the even and odd parities of the charge offset. The measurement is repeated every $12µ s$ on average. b, Autocorrelation function $\langle I_{\tau_0}(0)I_{\tau_0}(t)\rangle$ extracted from more than $10^6$ realizations of $I_{\tau_0}$ during run 17. The black dotted and dashed correspond respectively to an exponential and a stretched exponential fit. c, Signal $I_{\tau_0}$ for $2,000$ realizations in the presence of charge drift (run 24). The measurement is repeated every $3µ s$ on average. d, Autocorrelation function $\langle I_{\tau_0}(0)I_{\tau_0}(t)\rangle$ for run 24. Black: fits as in b.