Suppressing microwave crosstalk in superconducting quantum processors by designing parasitic drive capacitances

AI summary

Overview

Research area: Superconducting quantum computing hardware — specifically microwave control engineering, device design, and coherent-error mitigation in transmon-based processors.

Technical level: Intermediate to Advanced. The experimental narrative and design conclusions are accessible to a graduate-level reader, while Sections II.1–II.3 involve circuit Lagrangian quantization, high-frequency (Floquet-type) expansions, and Bogoliubov diagonalization.

Scope (one sentence): The paper builds and experimentally validates a detailed circuit model showing that parasitic drive capacitances — normally treated as fabrication imperfections — set the frequency dependence of microwave drive crosstalk and can be deliberately chosen to null it in a two-transmon-plus-coupler processor.

Note on completeness: the supplied text ends mid-Section IV.1 (at "In Fig. 5 (c), we see t"), so the later parts of the Discussion, the Conclusions (Sec. V), and Appendices A–L are not available here. Findings from those parts, including the off-resonant crosstalk analysis announced in Sec. IV, are therefore not reported below.

What This Paper Is About

As superconducting processors grow to hundreds of qubits, a microwave pulse intended for one qubit (the target) inevitably perturbs others (the victims), producing coherent errors either by direct near-resonant driving or by off-resonant AC Stark shifts. The authors ask where this crosstalk physically comes from on-chip, and show that the answer involves not only the direct drive-to-victim coupling and the qubit–qubit coupling, but also the parasitic capacitance between each drive line and the tunable coupler. By measuring and modeling crosstalk versus coupler frequency in a two-qubit device, they demonstrate that these parasitic paths interfere, and that a crosstalk null can be engineered rather than merely minimized.

Key Contributions

1. A comprehensive circuit model including parasitic drive paths. The authors write the Lagrangian for two floating fixed-frequency transmon qubits, a grounded flux-tunable coupler, direct qubit–qubit coupling, and five drive capacitances per line (two to the target qubit's pads, one to the coupler, two to the victim qubit's pads). Earlier treatments typically keep only drive-to-target coupling.

2. An analytical, dressed-basis expression for crosstalk. Starting from the driven Hamiltonian, they apply a high-frequency expansion to first order in 1/Ω (retaining corrections from the 2Ω counter-rotating terms), then diagonalize the residual linear coupling with a Bogoliubov transformation. The result is a closed-form dressed drive amplitude Θ_m (Eq. 17) that is a coherent sum of three contributions — target, victim, and coupler — so that interference and nulls can be read off directly.

3. Experimental demonstration that the crosstalk minimum is not the J_eff = 0 point. They measure self- and cross-Rabi frequencies versus coupler frequency and locate the crosstalk dip roughly 0.3 GHz away from the coupler frequency where the effective qubit–qubit coupling vanishes (3.665 GHz), ruling out coupling cancellation as the sole explanation.

4. Design guidance contrasting floating and grounded qubit architectures. Using the fitted and simulated capacitances, they map how the crosstalk-null frequency depends on drive-to-coupler and drive-to-victim capacitance, and show that floating qubits offer more convenient co-alignment of the two drive lines' nulls than grounded qubits.

Main Findings

• A clear crosstalk dip exists as a function of coupler frequency. Both measured cross-Rabi frequencies (Q2 driven via XY1, and Q1 driven via XY2) show a pronounced minimum at a specific coupler bias, indicating strong reduction of the effective drive amplitude at the victim qubit.

• Coupling cancellation alone cannot explain the dip. The condition J_eff = 0 is estimated to occur at 3.665 GHz, approximately 0.3 GHz below the observed minima in the cross-Rabi data.

• Interference among drive pathways explains the null. Equation (17) shows the dressed drive amplitude is a sum of terms weighted by the renormalized relative drive strengths λ̃₁₁, λ̃₂₁, and λ̃_c1, multiplied by combinations of g̃₁₂, g̃₁c, g̃₂c, and detunings. As the coupler is tuned, these weights and couplings vary together, and destructive interference produces Θ_m = 0 for the victim mode.

• Including parasitic capacitances is necessary for quantitative agreement. Fitting self- and cross-Rabi data simultaneously with the full model — target, coupler, and victim drive capacitances — reproduces the measured frequency dependence, including the suppression; the paper states that excluding the additional drive pathways does not reproduce it (Appendix F).

• Extracted capacitances differ from design values. From Table 1 (in aF): XY1 target 80, 157 designed versus 96.6, 145.4 fitted; XY1 coupler 19 versus 18.4; XY1 victim 6, 5 versus 2.3, 7.7. XY2 target 152, 68 versus 122.1, 105.6; XY2 coupler 30 versus 29.5; XY2 victim 11, 7 versus 2.5, 10.3. The authors attribute deviations partly to fabrication and possibly to electromagnetic modes in the sample holder.

• Separate amplitude scaling factors are needed per line. Fitted values k = 1.911 for XY1 and k = 0.420 for XY2 account for different attenuation in the cryostat wiring; the cross-Rabi definition is modified to R^cross_{i,j} ≡ k R_{i,j}(ω_eff,j).

• The model overpredicts suppression for one direction. In the crosstalk data of Fig. 4 (Λ₂,₁ and Λ₁,₂ versus coupler frequency), the model predicts a stronger suppression of Λ₁,₂ that is not observed experimentally; the authors suggest additional microwave-crosstalk mechanisms outside the present circuit model. Specific dB values of the measured crosstalk are not reported in the available text.

• Floating versus grounded architectures behave differently. For floating qubits, the two crosstalk-null frequencies shift with slopes of the same sign as the drive-to-coupler capacitance changes, so a single horizontal line can intersect both curves — the two lines' nulls can be brought to coincide. For grounded qubits the slopes have opposite sign and the nulls are more widely separated, requiring a larger adjustment of drive-to-coupler capacitance.

• Crosstalk nulls depend strongly on drive-to-victim capacitance for floating qubits. In the floating case the differential victim capacitance ΔC_victim is defined as the difference between the drive line's capacitances to the victim's two pads; Fig. 5(c) shows the null frequency versus this quantity. For grounded qubits (Fig. 5(d)), a horizontal dashed line marks the maximum coupler frequency.

Methodology in Plain English

The team fabricated a small processor: two fixed-frequency floating transmon qubits, each with its own XY drive line and readout resonator, connected to each other directly and through a flux-tunable grounded coupler acting as a tunable transformer (Fig. 1, Fig. 2). They wrote down the full electrical Lagrangian of this network, including every relevant capacitance — the strong intended ones and the weak parasitic ones from each drive line to the coupler and to the other qubit.

Because solving the driven, time-dependent circuit directly is unwieldy, they moved into a frame rotating at the drive frequency Ω. In that frame the bare qubit frequencies become small detunings, so a high-frequency expansion in 1/Ω becomes valid (it requires the detunings, couplings, anharmonicities, and drive strengths ε_k to be small compared with Ω; the authors emphasize it does not require a large qubit–coupler detuning, so it works both far-detuned and near-resonant). Truncating at first order leaves a time-independent Hamiltonian with renormalized frequencies, couplings, and drive amplitudes (Eqs. 13–15). A final rotation into the true normal modes gives the drive amplitude felt by each dressed mode, Θ_m.

Experimentally, they calibrated each drive line so the target qubit had a self-Rabi frequency of 20 MHz with the coupler far detuned, then held the power fixed and measured cross-Rabi frequencies while sweeping the coupler frequency (via its flux). They probed on-resonance crosstalk — driving at the victim's own resonance — as the worst case for gate operations. They fitted the self- and cross-Rabi data simultaneously with the model, starting from the designed capacitance values, and compared the resulting crosstalk in decibels, Λ_{i,j} = 20 log₁₀(R^cross/R^self), against measurement.

Why This Matters

The work reframes a nuisance as a design knob: parasitic couplings are not simply defects to be minimized but can be chosen to cancel coherent crosstalk at a desired operating point. Because crosstalk is device-specific — mediated by control lines, the PCB, sample-holder box modes, and wirebonds — a predictive, capacitance-level model gives hardware designers a quantitative target rather than a purely empirical tuning problem.

Real-world applications:

• Layout and electromagnetic design of multi-qubit superconducting chips, where drive-line routing and pad geometry determine the parasitic capacitances that this model relates to crosstalk.
• Coupler-bias operating-point selection in processors with tunable couplers, so that idling or gate frequencies coincide with a crosstalk null.
• Calibration and benchmarking tooling: predicting self- and cross-Rabi rates from layout parameters reduces the number of time-consuming on-hardware crosstalk measurements.
• Packaging and microwave-engineering decisions (PCB design, wirebonding, sample-holder mode suppression), which the introduction identifies as additional crosstalk channels that must be co-designed with the chip.

Industry relevance: the results bear directly on the fidelity budget of gate operations in scaled superconducting processors, and on the workflow of foundry-style fabrication, where process variation in capacitance (visible in Table 1) must be anticipated rather than treated as a surprise.

Future Directions

• Extend the model beyond the on-chip circuit. The unexplained discrepancy in Λ₁,₂ points to crosstalk channels not in the circuit model, such as PCB-mediated coupling, box modes, and wirebonds, which the introduction lists as known contributors.
• Analyze off-resonant crosstalk. Section IV announces a treatment of off-resonant crosstalk, more common in practice than the worst-case resonant case measured here, and its relation to the resonant results; that analysis lies beyond the available text.
• Deliberately engineer parasitic capacitances in fabricated devices. The authors' stated broader strategy is to design coupling paths rather than minimize them, which requires validating null engineering on hardware built to a target capacitance set.
• Scale the approach to larger arrays. The demonstration uses two qubits and one coupler; whether nulls for many drive lines can be co-aligned simultaneously across a lattice, and how fabrication spread affects them, remains open.

Target Audience

Quantum-hardware experimentalists and device designers working on superconducting processors; microwave and cryogenic engineers responsible for control-line layout and packaging; theorists interested in driven circuit-QED modeling and effective-Hamiltonian techniques; and graduate students or industry R&D teams who need a concrete, quantitatively validated example of how parasitic couplings govern crosstalk and how to turn them into a design resource.

Authors’ abstract

As superconducting quantum processors scale to large qubit counts, unwanted microwave drive crosstalk becomes an important source of coherent errors. Here, we investigate the role of parasitic coupling paths in the suppression of drive crosstalk in a processor with two fixed-frequency transmon qubits and a tunable coupler. To account for the many different coupling paths, we develop a detailed circuit model to capture the dependence of crosstalk on the coupler frequency. We experimentally demonstrate suppression of crosstalk, finding that the suppression does not originate solely from cancellation of the effective qubit-qubit coupling, but also is a result of interference between other coupling paths. Building on these insights, we show that drive crosstalk can be suppressed with the right choice of parasitic capacitances, which otherwise often are treated as unwanted design imperfections. Our results provide practical guidance for low-crosstalk device design of superconducting quantum processors and point toward a broader strategy in which parasitic coupling paths are engineered rather than simply minimized.