Characterizing and Mitigating Flux Crosstalk in Superconducting Qubits-Couplers System

Abstract

Superconducting qubits have achieved exceptional gate fidelities, exceeding the error-correction threshold in recent years. One key ingredient of such improvement is the introduction of tunable couplers to control the qubit-to-qubit coupling through frequency tuning. Moving toward fault-tolerant quantum computation, increasing the number of physical qubits is another step toward effective error correction codes. Under a multiqubit architecture, flux control (Z) lines are crucial in tuning the frequency of the qubits and couplers. However, dense flux lines result in magnetic flux crosstalk, wherein magnetic flux applied to one element inadvertently affects neighboring qubits or couplers. This crosstalk obscures the idle frequency of the qubit when flux bias is applied, which degrades gate performance and calibration accuracy. In this study, we characterize flux crosstalk and suppress it in a multiqubit-coupler chip with multi-Z lines without adding additional readout for couplers. By quantifying the mutual flux-induced frequency shifts of qubits and couplers, we construct a cancellation matrix that enables precise compensation of non-local flux, demonstrating a substantial reduction in Z-line crosstalk from 56.5$\,$permille$\,$to 0.13$\,$permille$\,$ which is close to statistical error. Flux compensation corrects the CZ SWAP measurement, leading to a symmetric map with respect to flux bias. Compared with a crosstalk-free calculated CZ SWAP map, the measured map indicates that our approach provides a near-zero crosstalk for the coupler-transmon system. These results highlight the effectiveness of our approach in enhancing flux crosstalk-free control and supporting its potential for scaling superconducting quantum processors.

Figures (5)

• Figure 1: Subsystem used to characterize magnetic flux crosstalk. (a) Illustration of flux crosstalk. Magnetic flux from the Z-lines causes unwanted frequency shifts of nearby tunable elements. (b) Optical micrograph of the chip, which has five flux-tunable transmon qubits with readout resonators and four flux-tunable couplers. (c) Optical micrograph of the subsystem consisting of two qubits (Q1, Q2) in blue and two couplers (C1, C2) in orange. The inset shows a zoomed-in picture of the device with visual termination of the flux lines adjacent to the SQUID. Color labels are assigned based on the corresponding components in the subsystem's lumped circuit model shown in (d).
• Figure 2: Qubit and coupler spectrum as a function of flux bias. (a) represents pulse sequences in (c) and (e) to probe qubit's f$_{\text{01}}$, using each qubit's flux bias (green), microwave drive $f_{\text{XY}}$ (red) and readout pulse (gold) as noted in the gray box. (b) represents the pulse sequences in (d) and (f) used for the coupler where the flux bias came from the coupler while the microwave and readout drives came from an adjacent qubit and resonator. Readout pulses in (a) and (c) have a 20n s delay to minimize overlap between flux pulse transients and readout pulse which degrades the contrast. We probe the qubit and coupler spectrum as a function of the flux shown in (c,e) and (d,f) for qubits and couplers, respectively. Green dashed lines refer to the fit of the f$_{\text{01}}$ transition frequencies with the flux-tunable transmon model. The top and bottom horizontal axes refer to the normalized flux bias and applied voltage, respectively.
• Figure 3: Characterization of flux crosstalk. (a) Pulse sequence used to extract crosstalk of MZLC: a probing element is driven at a fixed frequency, while both probe voltage and source voltage are applied simultaneously. The XY, Z, and readout pulses have 20n s delays to avoid timing mismatch artifacts. Spectra with crosstalk are illustrated in intensity plots with C1 as source and Q1 as probe (b) and vice versa (d). The horizontal, vertical, and intensity axes are the source flux (S-Flux), probe flux (P-Flux), and readout signal voltage, respectively. Applying flux-compensated pulses to (b) ($-0.39\times\text{P-Flux}_\text{Q1}$) and (d) ($-0.34\times\text{P-Flux}_\text{C1}$) after characterizing the flux crosstalk results in spectra immune to S-Flux as shown in (c) ($-0.39\times\text{P-Flux}_\text{C1}$) and (e) ($-0.33\times\text{P-Flux}_\text{Q1}$), respectively. In (f) ($-0.40\times\text{P-Flux}_\text{C1}$) and (g) ( $-0.24\times\text{P-Flux}_\text{C1}$), as the frequency detuning of probe C1 from its sweet spot frequency of $f_\text{C1,max}(\Phi_{p}=0)=8046.6\,\pm\,0.2\,$MHz decreases, the spectral linewidth of C1 increases. All measurement conditions in this figure have an identical readout pulse buffer and initialization time.
• Figure 4: Flux crosstalk matrices between tunable elements. Rows correspond to detector elements, and columns to source Z-lines. (a) Displaying results obtained from two-tone spectroscopy averaged over 100 repetitions to estimate statistical uncertainty. (b) shows corresponding results from Ramsey, which agrees with statistical error to (a). (c) show the crosstalk matrix after compensation, demonstrating suppression of all off-diagonal elements to below $0.5\,$‰. Values smaller than their uncertainties are kept to show the nominal measurement mean, which otherwise rounds to zero.
• Figure 5: Time-domain measurements of the coherent oscillations between $|11\rangle$ (red) and $|02\rangle$ (blue) states, named CZ SWAP, under varying coupler flux and different flux pulse durations. The pulse schedule in (a), with the XY drive being the $\pi_{01}$ pulse, and the results before flux compensation (b) and after flux compensation (c) are displayed. The flux-compensated time-domain measurements agree with simulations in (d). (e) 2D Fast Fourier transform (FFT) of the time-domain oscillations in (b), (c), and (d), which quantifies the conditional phase-mediated coupling strength $|g_{\mathrm{eff}}|$ as a function of coupler flux. Inset shows the residuals (dotted lines) expressed in MHz. Panels from (b) to (e) share the same x-axis, representing the applied flux on the coupler.