Characterization and Optimization of Tunable Couplers via Adiabatic Control in Superconducting Circuits

Abstract

In the pursuit of scalable superconducting quantum computing, tunable couplers have emerged as a pivotal component, offering the flexibility required for complex quantum operations of high performance. In most current architectures of superconducting quantum chips, such couplers are not equipped with dedicated readout circuits to reduce complexity in both design and operation. However, this strategy poses challenges in precise characterization, calibration, and control of the couplers. In this work, we develop a hardware-efficient and robust technique based on adiabatic control to address the above issue. The critical ingredient of this technique is adiabatic swap (aSWAP) operation between a tunable coupler and nearby qubits. Using this technique, we have characterized and calibrated tunable couplers in our chips and achieved straightforward and precise control over these couplers. For example, we have demonstrated the calibration and correction of the flux distortion of couplers. In addition, we have also expanded this technique to tune the dispersive shift between a frequency-fixed qubit and its readout resonator over a wide range.

Figures (4)

• Figure 1: (a) Partial schematic of a superconducting quantum circuit with tunable coupling. $Q_1$ and $Q_2$ are two qubits with fixed frequencies and $C_{12}$ is a tunable coupler (in this work, $f_{Q_1}$ = 4.636 GHz, $f_{Q_2}$ = 4.127 GHz). All three components are capacitively coupled to each other. Each qubit has its own readout resonator. (b)&(c) Illustration of two types of aSWAP operations used in this work. The dashed lines indicate bare energy levels of the coupler (red) and the qubit (blue). Near the two crossing points of the dashed lines, strong coupling between the coupler and the qubit hybridizes their states and lifts the degeneracy, resulting in the spectra of dressed states (solid lines). The color gradient in the solid lines indicates the relative weight of the bare states in the dressed states. The filled and hollow circles represent first-excited and ground states, respectively. (d) Transmission coefficient of the readout pulse as the flux bias of the coupler is varied. The two peaks correspond to two anticrossing points where the coupler comes close to resonance with the two qubits.
• Figure 2: Characterization of the coupler $C_{12}$. (a) Spectroscopy of the coupler's frequency as a function of its flux bias. The inset shows the measurement sequence of pulses applied to the $Z$-line, $XY$-line, and the readout resonator, respectively (see Fig. \ref{['circuit']}(a)). The $Z$ pulse sets the magnetic flux $\Phi$ and thus the frequency of the coupler. The $XY$ pulse is felt by both the coupler and the qubit $Q_1$ (see Fig. \ref{['circuit']}(a)). To achieve a complete aSWAP operation, one needs to make sure that the frequency of the coupler be tuned in a range wide enough covering an anticrossing point. With the knowledge of approximate positions of the anticrossing points obtained in Fig. \ref{['circuit']}(d), the above requirement can always be fulfilled. (b) Histogram of measuring the state of $C_{12}$ using the readout resonator of $Q_1$ via an aSWAP operation. (c) Rabi oscillation on $C_{12}$ at its highest frequency. (d) Relaxation process of $C_{12}$ at its highest frequency. (e) Ramsey interference on $C_{12}$ at its highest frequency.
• Figure 3: Calibration the flux distortion of a coupler. (a) Phase accumulation as a function of the delay time measured by a modified Ramsey interference. The uncorrected results exhibit a significant extra phase due to the flux distortion in the coupler up to several microseconds. The corrected results almost coincide with those obtained in a reference measurement in which no $Z$-pulse is applied and switched to zero at $\tau_0$ (thus no distortion at all), indicating high precise correction of the distortion. Inset: pulse sequence for the Ramsey interference. (b) A comparison of using adiabatic flattop (a duration of 50 ns for the rising and falling edges, respectively), nonadiabatic flattop (5 ns for the rising and falling edges, respectively), and stepwise (also nonadiabatic) pulses for the detection signal between the two $\pi/2$ pulses. The result shows that adiabaticity of the detection signal is critical for an accurate measurement of the accumulated phase. In these measurements, the frequency of the coupler is adjusted to its linear range during the flattop phase so that it is sensitive to the flux change.
• Figure 4: Dispersive shift of a readout resonator and its influence on the resonator's transmission coefficient. The dispersive shift of the $Q_1$ readout resonator varies with the frequency of $C_{12}$(see Fig. \ref{['circuit']}). The gray dashed line is numerical simulation result and the green circles are experimental results. Insets: Changes in the readout resonator's transmission coefficient with the qubit at $|0\rangle$ (blue squares) and $|1\rangle$ (red hexagons) states as the dispersive shift varies as a function of the flux bias of the coupler.