Single-Step Phase-Engineered Pulse for Active Readout Cavity Reset in Superconducting Circuits

TL;DR

In circuit QED, residual photons after dispersive readout hinder mid-circuit operations, and passive decay is too slow for scalable quantum computing. The authors introduce a Single-Step Phase-Engineered (SSPE) pulse that appends a reset segment with amplitude $\varepsilon_r$ and phase $\phi_r$ to a square readout pulse, with linear-regime scaling $\varepsilon_r' = \beta_r \varepsilon_r$ ($\beta_r=\beta_n$) and invariant $\phi_r$, aiming to drive $|\alpha_j(\Delta\tau)|^2=0$ for $j=0,1$. The SSPE protocol achieves cavity depletion about six times faster than passive decay, with measured rates $\kappa_{|0|}^{SSPE}/2\pi \approx 10.97$ MHz and $\kappa_{|1|}^{SSPE}/2\pi \approx 11.62$ MHz, while also minimizing measurement backaction (excitation $\gamma_o$ as low as $0.05\%$ and relaxation $\gamma_b$ around $7.22\%$). The method is hardware-efficient, calibration-friendly, and compatible with mid-circuit measurement and fast feedback, outperforming Square and CLEAR in backaction suppression and offering a scalable tool for fast, low-backaction cavity reset in superconducting circuits.

Abstract

In a circuit QED architecture, we experimentally demonstrate a simple and hardware-efficient Single-Step Phase-Engineered (SSPE) pulse scheme for actively depopulating the readout cavity. The method appends a reset segment with tailored amplitude and phase to a normal square readout pulse. Within the linear-response regime, the optimal reset amplitude scales proportionally with the readout amplitude, while the optimal reset phase remains nearly invariant, significantly simplifying the calibration process. By characterizing the cavity photons dynamics, we show that the SSPE pulse accelerates photon depletion by up to a factor of six compared to passive free decay. We further quantify the qubit backaction induced by the readout pulse and find that the SSPE pulse yields the lowest excitation and relaxation rates compared to a Square and CLEAR pulses. Our results establish the SSPE scheme as a practical and scalable approach for achieving fast, smooth, low-backaction cavity reset in superconducting quantum circuits.

Figures (7)

• Figure 1: Structure and Performance of the SSPE Pulse.(a) Schematic of the SSPE pulse, which consists of two segments: a normal readout segment with drive amplitude $\varepsilon_n$ and phase $\phi_n$, followed by a reset segment with drive amplitude $\varepsilon_r$ and phase $\phi_r$. (b) Equivalent lumped-element circuit model. (c), (d) Residual photon number at the end of the SSPE pulse as a function of the reset amplitude and phase for the qubit prepared in $\ket{0}$ and $\ket{1}$, respectively. A residual photon number of zero indicates that the cavity field has returned to vacuum, corresponding to complete photon dissipation. Light cyan contours denote the photon number level of 0.1.
• Figure 2: Residual Photon Population and Parameter Scaling of the SSPE Pulse.(a) Residual photon population as a function of the drive amplitude, measured either at a delay of $\Delta \tau = 50$ ns following the end of a Square pulse or immediately after the SSPE pulse. The drive amplitude is parameterized by the scale factor $\beta_n$ defined in the main text, where $\beta_n=1$ corresponds to the calibrated readout amplitude that yields high readout fidelity. (b) Scaling behavior of the optimal reset parameters. The rescaling factors for the optimal reset amplitude and reset phase, extracted for each value of the rescaled readout amplitude $\beta_n$, are plotted as a function of $\beta_n$. Gray dashed lines denote the reference lines $y=1$ and $y=x$.
• Figure 3: Cavity Reset Dynamics.(a-c) IQ-plane trajectories of the cavity field during the reset interval for the SSPE pulse, CLEAR pulse, and free decay, respectively. In each panel, the blue cross marks the origin, and the green stars denotes the initial point of the trajectory. The colorbars represent the time index, with the "copper" colormap (top) and "cool" colormap (bottom) corresponding to the qubit in $\ket{0}$ and $\ket{1}$, respectively. (d), (e) Photon reset dynamics for the three different reset schemes. The full time-resolved dynamics are provided in Appendix \ref{['sec: appendixB']}. The green and red curves correspond to exponential fits for the free-decay and SSPE pulse reset processes, respectively.
• Figure 4: Qubit Backaction Characterization.(a) Experimental pulse sequence employed to characterize measurement-induced backaction on the qubit. A SSPE pulse is first applied as a pre-measurement to ensure the qubit is initialized in $\ket{0}$. The qubit is then prepared in either $\ket{0}$ or $\ket{1}$, followed by repeated measurements using one of three reset schemes: SSPE (red), CLEAR (blue), and Square (free decay, unfilled). (b) Probability $P_m(1|0)$ for the qubit prepared in $\ket{0}$. (c) Probability $P_m(1|1)$ for the qubit prepared in $\ket{1}$. The black dashed line denotes the intrinsic relaxation expected from $T_1=26.51\ \mu s$ at the photon-induced ac-Stark-shifted qubit frequency under the steady-state readout photon number. The experimental data points in panels (b) and (c) are plotted by sampling every two measurement cycles.
• Figure 5: Time-Resolved Characterization of Cavity Photon Dynamics.(a) Experimental pulse sequence used to characterize photon dynamics. The qubit is prepared in either $\ket{0}$ or $\ket{1}$, followed by a frequency-swept calibrated qubit $\pi$-pusle to measure the photon-induced ac-Stark shift. A final square readout pulse is then used to perform high-fidelity qubit state discrimination. The delay between the two readout pulses is set to 300 ns (500 ns) for SSPE and CLEAR pulse (Square pulse), ensuring that residual photons have fully depleted prior to the second measurement. (b), (c) Time-resolved measurements of the intracavity photon number for the qubit prepared in $\ket{0}$ and $\ket{1}$, respectively. Light gray curves correspond to fits obtained from the nonlinear cavity dynamics model described by Eq. \ref{['eq-B1']}.