Rapid Driven Reset of a Qubit Readout Resonator

Using a circuit QED device, we demonstrate a simple qubit-measurement pulse shape that yields fast ring-up and ring-down of the readout resonator regardless of the qubit state. The pulse differs from a square pulse only by the inclusion of additional constant-amplitude segments designed to effect a rapid transition from one steady-state population to another. Using a Ramsey experiment performed shortly after the measurement pulse to quantify the residual population, we find that compared to a square pulse followed by a delay, this pulse shape reduces the time scale for cavity ring-down by more than twice the cavity time constant. At low drive powers, this performance is achieved using pulse parameters calculated from a linear cavity model; at higher powers, empirical optimization of the pulse parameters leads to similar performance.

Figure 1

(a) Schematic shape of the piecewise-constant CLEAR pulse (solid red line) with a square pulse (dashed black line) for reference. The CLEAR pulse consists of two ring-up segments of length $t_{\mathrm{kick}}$ followed by one segment of length $t_{\text{steady}}$ and then two ring-down segments of length $t_{\mathrm{kick}}$. (b) Pulse sequence used to extract the residual cavity population after a measurement pulse. The qubit is prepared in either the ground or excited state and then a measurement pulse (either a square pulse or a CLEAR pulse) of length $t_{M1}$ is applied. After the measurement pulse, an adjustable delay $t_{\text{relax}}$ precedes a pair of $X_{90}$ pulses separated by $t_R$ comprising a Ramsey experiment. The Ramsey experiment is followed by a delay $t_{\text{buffer}}$ and finally a square measurement pulse of length $t_{M2}=10\mu \mathrm{s}$.

Figure 2

(a) Sample Ramsey experiment and fit. The black curve is a fit of Eq. (1) to the data (red circles), yielding an initial cavity population of $n_0\approx 0.9$. (b) The markers indicate $n_0$ versus wait time $t_{\text{relax}}$ after a square measurement pulse with drive power $P_{\mathrm{norm}}=2$. Here and throughout, blue and red denote experiments in which the qubit was prepared in the ground and excited states, respectively. Solid blue and red curves are exponential fits to the respective data sets. (c) $n_0$ versus drive power measured at $t_{\text{relax}}=40\mathrm{ns}$ after a square measurement pulse. The dashed line indicates the prediction for a linear cavity, accounting for $t_{\text{relax}}$. The solid curves account for the cavity’s self-Kerr nonlinearity calculated from the measured qubit and cavity parameters.

Figure 3

(a),(b) $IQ$-plane cavity trajectories in response to a square pulse and CLEAR pulse, respectively. In each plot, the experimental results (markers) are superimposed on the theoretical calculations (solid curves), the dashed circle indicates the target population $n=3.6$, the black cross indicates the origin, and the black arrows indicate the directions of the trajectories. (c) Residual cavity population versus pulse power for both square and CLEAR pulse shapes. For the CLEAR pulse, the Ramsey experiment begins immediately at the end of the pulse, while for the square pulse, a delay of approximately 300 ns is inserted to match the total length of the CLEAR pulse’s two ring-down segments.

Figure 4

(a) $n_0$ versus drive power for the shortened CLEAR pulse (120-ns ring-down segments), for $t_{\text{relax}}=0$. (b) Evolution of $n_0$ at each step of an empirical optimization algorithm for the shortened CLEAR pulse with $P_{\mathrm{norm}}=10$. Inset: shortened CLEAR pulse shape before optimization (magenta) and after (green). (c) Ramsey traces immediately after initial shortened CLEAR pulse, yielding $n_0\approx 2.2$ for the ground state and $n_0\approx 0.91$ for the excited state. (d) Ramsey traces immediately after final shortened CLEAR pulse, yielding $n_0<0.1$ for both qubit states.