Characterizing charge-parity detection based on an offset-charge-tunable transmon qubit via randomized benchmarking

Abstract

Superconducting qubits are compelling platforms for charge-parity detection and, due to their theoretical sensitivity on the meV energy scale, hold promise for rare event searches. In this work, we realize high-fidelity mapping of charge-parity states onto qubit states using an offset-charge-tunable transmon qubit and efficiently characterize the fidelity of the charge-parity detection via randomized benchmarking. Specifically, a gate control line is applied to control offset charge, allowing us to achieve the single-qubit gate fidelity up to 99.96%. We combine a net-zero-based pulse on the gate line with a spin-echo-based sequence to realize charge-parity mapping, achieving a fidelity of 99.37%. Then, we demonstrate continuous monitoring of the charge-parity state with over 93.4% fidelity at a 4-μs sampling interval. Finally, an error analysis of charge-parity detection is performed, and it is found that qubit readout is currently the largest source of error. We believe this work lays the foundation for future exploration of ultra-low energy particles.

Figures (9)

• Figure 1: (a) False-colored optical image of a single-qubit unit in the device. The bottom chip comprises a microwave (MW) or flux control line (blue), a gate control line (magenta), and a $\lambda/4$ readout resonator (orange). The top chip contains only a transmon qubit (green). (b) The circuit diagram of the device shown in (a). (c) The two lowest energy levels ($E_0$ and $E_1$) of the qubit as a function of the offset charge $n_g(2e)$ for even (solid line) or odd (dashed line) charge-parity states. The parity-dependent qubit frequencies ($f_e$ and $f_o$) are degenerate at $n_g = 0.5n+0.25, n=0,\pm1,\pm2,...$ (degeneracy points). The $n_g$ can be tuned away and back to the degeneracy point with a gate pulse (magenta) to accumulate parity-dependent phases of the qubit. (d) Spin-echo-based sequence with an inserted net-zero-based gate pulse for charge-parity mapping, named EchoCPM, where several Bloch sphere diagrams show corresponding qubit states. Charge-parity detection can be realized by first resetting the qubit, performing the EchoCPM, and then following the qubit measurement.
• Figure 2: (a) Qubit spectrum as a function of flux $\Phi/\Phi_0$, where $\Phi_0$ is the single flux quantum. The flux point with the lowest qubit frequency is chosen as the idle point, featuring the best coherence. The blue dashed line is a fit based on the transmon Hamiltonian. (b) Qubit spectrum as a function of the offset charge $n_g(2e)$. Two traces for two charge-parity states are fitted to give the charge dispersion energy difference. Their cross points (white dots) are identified as the degeneracy points. (c) The Ramsey-based sequence with a duration of 800 ns to rapidly and precisely identify the degeneracy point. (d) The qubit population as a function of the gate voltage, with the qubit drive frequency set at the degeneracy point. The maximum points (blue dots) are identified as the degeneracy points.
• Figure 3: (a) Single-qubit randomized benchmarking (RB) at $n_g = 0.25$ (circles) and $n_g = 0.5$ (squares). After power-law fitting, we achieve average single-qubit-gate fidelities of 99.96$\%$ and 99.8$\%$ for $n_g = 0.25$ and $n_g = 0.5$, respectively. Error bars denote the standard deviation. The inset depicts the reference RB sequence. (b) Duration calibration of the net-zero-based gate pulse. The pulse sequence is the same as Fig. \ref{['fig:Figure_1']}(d) except that the Y/2 gate is replaced by the X/2 (circles) and -X/2 (triangles) gates. The cross point (star) with a duration of 217 ns is selected as the working point. (c) A pulse sequence consisting of two opposite-sign, echo-based phase accumulation (echoPA and echoPA$^\prime$) is used as the Z gate, and is called a pseudo-Z gate. (d) Interleaved RB for three gates—X/2 (diamonds), Y/2 (stars), and pseudo-Z (triangles). Power-law fittings using the RB in (a) as reference yield gate fidelities of 99.95$\%$ (X/2), 99.97$\%$ (Y/2), and 98.91$\%$ (pseudo-Z). Error bars denote the standard deviation. The inset shows the interleaved RB sequence. The single echoPA fidelity is $\sqrt{98.91\%} = 99.45\%$ and the fidelity of the charge-parity mapping is 99.45$\%\times$99.95$\%\times$99.97$\%$=99.37$\%$.
• Figure 4: (a) A 1.6-ms time slice of the charge-parity detection trace shows a charge-parity switching event. The event is zoomed in the inset, which shows that the time interval between adjacent data points is $\Delta t = 4~\mu$s. (b) Power spectral density of the detection trace. The red curve represents the Lorentzian fit. Inset: histograms of the qubit readout distribution for ground and excited states.
• Figure 5: Schematic of the measurement setup.