Coherence-limited digital control of a superconducting qubit using a Josephson pulse generator at 3 K

TL;DR

This work tackles the scalability of superconducting qubit control by relocating a Josephson pulse generator (JPG) to the 3 K stage and benchmarking it against traditional room-temperature semiconductor electronics. By optimizing a 2D transmon with a dedicated drive line, the authors demonstrate nearly coherence-limited single-qubit control with JPG pulses, achieving a randomized benchmarking gate fidelity of about 99.54% (per-gate error ~0.46%), and showing good agreement with the qubit's T1 and T2* lifetimes and with coherence-limited expectations. Simulations of leakage to higher excited states under subharmonic JPG drive support the observed fidelity and guide design choices such as pulse width and anharmonicity. Overall, the results indicate that a 3 K JPG-based cryogenic control scheme is a viable, scalable path for high-fidelity qubit control with reduced dissipation and improved integration prospects for large-scale quantum processors.

Abstract

Compared to traditional semiconductor control electronics (TSCE) located at room temperature, cryogenic single flux quantum (SFQ) electronics can provide qubit measurement and control alternatives that address critical issues related to scalability of cryogenic quantum processors. Single-qubit control and readout have been demonstrated recently using SFQ circuits coupled to superconducting qubits. Experiments where the SFQ electronics are co-located with the qubit have suffered from excess decoherence and loss due to quasiparticle poisoning of the qubit. A previous experiment by our group showed that moving the control electronics to the 3 K stage of the dilution refrigerator avoided this source of decoherence in a high-coherence 3D transmon geometry. In this paper, we also generate the pulses at the 3 K stage but have optimized the qubit design and control lines for scalable 2D transmon devices. We directly compare the qubit lifetime $T_1$, coherence time $T_2^*$ and gate fidelity when the qubit is controlled by the Josephson pulse generator (JPG) circuit versus the TSCE setup. We find agreement to within the daily fluctuations for $T_1$ and $T_2^*$, and agreement to within 10% for randomized benchmarking. We also performed interleaved randomized benchmarking on individual JPG gates demonstrating an average error per gate of $0.46$% showing good agreement with what is expected based on the qubit coherence and higher-state leakage. These results are an order of magnitude improvement in gate fidelity over our previous work and demonstrate that a Josephson microwave source operated at 3 K is a promising component for scalable qubit control.

Figures (8)

• Figure 1: (Color) Digital qubit control using a JPG. (a) Photo of the packaged JPG chip mounted at the 3 K stage of the DR. The drive input (JPG output) is the left (right) coplanar waveguide microwave launch. (b) Layout of the qubit chip mounted on the base temperature stage. The input/output line for the readout cavity is shown in black (top pad) and the direct drive line connected to the JPG to drive the transmon qubit (red) is shown in blue (bottom pad). Inset shows the transmon qubit with the capacitor plates (red) and junction (green). (c) Simplified schematic of the experiment. JPG pulses (along with the larger subharmonic ($\omega_d = \omega_{10} / 2$) sinusoidal drive signal) are routed directly to the qubit drive port. A commercial TSCE 65 GSa/s arbitrary waveform generator serves as the JPG clock to drive the JPG. The TSCE qubit control/readout synthesizers, and cold readout components are attached to the $\lambda/2$ cavity input port. A detailed description of the setup, including the placement of the attenuation in both lines is shown in the Supplementary Materials.
• Figure 2: JPG calibration procedure: (a) JPG $I$-$V$ curve, shown here with $\omega_d / 2 \pi = 3.0349$ GHz, are first used to establish rough bounds on the range of $I_b$ giving a constant Rabi oscillation period with respect to the number of drive periods $\nu$. From this dc measurement we extract a locking range of 1.8--2.8 mA, which is indicated in all plots with dashed lines. (b) Rabi oscillation scan using the JPG as the drive while scanning current bias $I_b$ and number of drive periods, $\nu$. (c) Extracted number of JPG drive periods required for a $\pi$ rotation of the qubit $\nu_{\pi}$ versus bias. The inset shows a zoomed-in area where the Rabi-oscillation period of the qubit is insensitive to variations in $I_b$, with red dashed lines bounding $\nu_\pi$ by $\pm$ 1 pulse. For a bias of $I_b = 2.6$ mA we extract $\nu_\pi$ of 187 pulses ($\pi$-gate time of $62$ ns).
• Figure 3: (a) Typical Rabi oscillation driven by the JPG for drive times equal to the longest randomized benchmarking sequences used in this experiment. From this we extract an approximate decay time of 13.5 $\mu$s, close to the expected decay based on the observed $T_1$ and $T_2^*$.Andreasdynamic(b) Time window analysis of the rabi oscillations shown in (a). The window used is approximately two oscillations. The x-axis in (b) is the same length as in (a) but it has been transformed to time rather than number of drive periods. We do not observe significant deviation in the number of pulses for a $\pi$ rotation $\nu_\pi$ across the entire experiment. (c) Comparison of the measured qubit lifetime $T_1$ and (d) Ramsey coherence time $T_2^*$ using a TSCE setup and a JPG at 3 K. Histograms and Gaussian fits of both the $T_1$ and $T_2^*$ distributions show excellent agreement in the mean ($\mu$) and standard deviation ($\sigma$). The black dashed line represents the $2T_1$ limit for $T_2$.
• Figure 4: (Color) (a) Depolarizing curve for single qubit RB using the full Clifford set. Both TSCE and 3 K JPG qubit control setups have very similar performance. Solid lines are a fit to Eq. \ref{['eq:rb_fidelity']}. We extract an average error per gate of $r_{TSCE} = (3.9 \pm 0.2) \times 10^{-3}$ and $r_{JPG} = (4.6 \pm 0.3) \times 10^{-3}$, showing an improvement of almost an order of magnitude compared to previous JPG implementations. Uncertainties in $r=1-\altmathcal{F}$ are determined as the standard error of the fits to Eq. \ref{['eq:rb_fidelity']}. (b) Depolarizing curves for the six interleaved RB gate sequences and for the shorter reference sequence (without $\altmathcal{C}_i$) in black using the JPG for the drive. Inset list shows the measured fidelities.
• Figure 5: (Color) Leakage to the second excited state as a function of $\sigma_n$ for different anharmonicities. For $\pi$ rotations of transmons with typical anharmonicities of 3--7%, a minimum pure-state leakage of approximately 0.07--0.3% is observed in the $\delta$-function pulse-width limit and driving at the $k=2$ subharmonic. For our case, with $\alpha = 3.3$% (dashed curve) and $\sigma_n=0.1-0.2$ (vertical gray band), leakage of $\rho_{ff}=0.07-0.2$ % can be expected and would explain the small disagreement between the observed gate fidelity and the calculated coherence-limit.