Offset Charge Dependence of Measurement-Induced Transitions in Transmons

Abstract

A key challenge in achieving scalable fault tolerance in superconducting quantum processors is readout fidelity, which lags behind one- and two-qubit gate fidelity. A major limitation in improving qubit readout is measurement-induced transitions, also referred to as qubit ionization, caused by multiphoton qubit-resonator excitation occurring at specific photon numbers. Since ionization can involve highly excited states, it has been predicted that in transmons -- the most widely used superconducting qubit -- the photon number at which measurement-induced transitions occur is gate charge dependent. This dependence is expected to persist deep in the transmon regime where the qubit frequency is gate charge insensitive. We experimentally confirm this prediction by characterizing measurement-induced transitions with increasing resonator photon population while actively stabilizing the transmon's gate charge. Furthermore, because highly excited states are involved, achieving quantitative agreement between theory and experiment requires accounting for higher-order harmonics in the transmon Hamiltonian.

Figures (12)

• Figure 1: Dispersive readout. (a) Schematics of a qubit-resonator setup with charge control. The magnetic flux ($\phi_{\mathrm{ext}}$) tunable transmon (orange) is capacitively coupled to a readout resonator (green) which is measured in reflection through a line with a DJJAA amplifier DJJA_ref; see \ref{['A_SetUp']} for full experimental setup. The qubit is capacitively coupled to a line that allows changing the charge offset $n_g$. (b) Example of a 2D scatter plot of the dispersive measurement outcomes of transmon A, distributed in the $IQ$ quadratures in units of measured photons $\sqrt{\bar{n}_m}$ . We continuously pump the readout resonator at $\omega_d/2\pi = 6.11972GHz$ and integrate the output every 2 $\mathrm{\mu s}$. We show the resulting histograms for two different experiments using two different resonator photon numbers, $\sqrt{\bar{n}_r }= 8$ and $\sqrt{\bar{n}_r }= 31$.
• Figure 2: Flux and Charge Dependence.(a,b) Flux dependence of the 0-1 and 0-2 transmon transitions for device A ($E_J/E_C = 18.5$) and device B ($E_J/E_C = 40.2$) at zero gate charge $n_g=0$. Energy levels are shown for both even parity states (full lines) and odd parity states (dashed lines) assuming symmetric junctions . (c) Charge stabilized dependence of the Fourier transform of a Ramsey interference experiment performed at 3.9965 GHz on device A. $\mathrm{\Delta f}$ giving the frequency difference to the ramsey pulse. The average $\bar{f}_{01}$ at 3.9992 GHz is indicated with a dashed line. (d) Left panel: IQ clouds corresponding to state $|2,\mathrm{o}\rangle$ and $|2,\mathrm{e}\rangle$ in units of $\sqrt{\bar{n}_m}$ after a 4 $\mathrm{\mu s}$ pulse for device B. We observe direct dispersive readout of the parity serniak_direct_2019. Right panel: Imaginary part for each distribution corresponding to the even and odd second transmon excited state over one charge period.
• Figure 3: Probability $\boldsymbol{1-P(0)}$ to find the transmon in an excited state vs. flux and charge offset.(a) For device A, we continuously populate the resonator with $\bar{n}_r \approx 6$ photons at frequency $\omega_d/2\pi=6.11972GHz$ and integrate over 25 $\mu s$. In the central part of the plot we lower the photon number to $\bar{n}_r \approx 1.5$ to reduce the width of the features. (b) For device B, we stroboscopically pump the resonator with $\bar{n}_r \approx 2$ photons at $\omega_d/2\pi=7.0535GHz$ with a 2 $\mathrm{\mu s}$ pulse every 3 $\mathrm{\mu s}$. In both panels, the qubit frequency corresponding to $\phi_{\mathrm{ext}}$ and $n_{g} =0$ is indicated by the right axis. We show as side panels selected $IQ$ clouds for specific values of flux and gate charge to highlight the contrast between negligible (circle) and significant (square) leakage. The photon number $\bar{n}_{r}$ is calibrated with an ac-Stark shift experiment performed at low power. The multiphoton resonance conditions $\omega_{0j}=n\omega_d$, labeled as $0\to j$, are plotted on top of the experimental results (orange-red lines). The remaining discrepancies $\lesssim 100MHz$ are consistent with frequency shifts expected from sources that are presently not accounted for in our model, such as junction asymmetry. The dashed lines indicate the theory for inelastic scattering with a spurious mode of frequency $0.78GHz$.
• Figure 4: Probability of leaving the initial state for device B.(a) Experimental pulse sequence. We apply a high-power 200 ns readout pulse with variable amplitude ($\bar{n}_{r,\mathrm{max}} \in [10,125]$), straddled by two low-power 1 $\mathrm{\mu}s$ readout pulses ($\bar{n}_{r,\mathrm{max}} = 7$) for high-fidelity preparation and readout. An optional $\pi$-pulse enables preparation of the excited state. All pulses have frequency $\omega_d/2\pi=7.0535GHz$. The insets show the IQ data for the preparation and final measurements for $\bar{n}_{r,\mathrm{max}} = 50$ and $n_{g} = 0$. (b) Measurement-induced transition probability as a function of gate charge and maximum average photon number in the resonator when initializing the qubit in the ground state (left) or excited state (right). The photon number at higher powers is calibrated by extrapolating a nonlinear semiclassical model of resonator dynamics; see \ref{['A_Photon_calib']}. Red circles indicate the positions of avoided crossings in the Floquet quasienergy spectrum. The dot area is proportional to the gap size $\Delta_{ac}$. (c) Numerical simulation of the experiment from the semiclassical time dynamics. The color bars are the same for theory and experiment.
• Figure 5: Experimental setup