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arXiv:2511.05031 · Physical Review Applied

Frequency collisions in parametrically modulated superconducting circuits

Zhuang Ma, Peng Zhao, Xinsheng Tan, Yang Yu

quant-phSubmitted Nov 7, 2025• Announced Nov 10, 2025• 0 citations• Revised Sep 19, 2026 (v2)
v1 · Nov 7, 2025v2 · Sep 19, 2026
arXivHTMLPDF

Abstract

Superconducting circuits are a leading platform for scalable quantum computing, where parametric modulation is a widely used technique for implementing high-fidelity multi-qubit operations. A critical challenge, however, is that this modulation can induce a dense landscape of parasitic couplings, leading to detrimental frequency collisions that constrain processor performance. In this work, we develop a comprehensive numerical framework, grounded in Floquet theory, to systematically analyze and mitigate these collisions. Our approach integrates this numerical analysis with newly derived analytical models for both qubit-modulated and coupler-modulated schemes, allowing us to characterize the complete map of parasitic sideband interactions and their distinct error budgets. This analysis forms the basis of a constraint-based optimization methodology designed to identify parameter configurations that satisfy the derived physical constraints, thereby avoiding detrimental parasitic interactions. We illustrate the utility of this framework with applications to analog quantum simulation and gate design. Our work provides a predictive tool for co-engineering device parameters and control protocols, enabling the systematic suppression of crosstalk and paving the way for large-scale, high-performance quantum processors.

Journal reference
Phys. Rev. Applied 26, 034042 (2026)
DOI
10.1103/ptj2-kcpc
Comments
30 pages,11 figures

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Superconducting circuits are a leading platform for scalable quantum computing, where parametric modulation is a widely used technique for implementing high-fidelity multi-qubit operations. A critical challenge, however, is that this modulation can induce a dense landscape of parasitic couplings, leading to detrimental frequency collisions that constrain processor performance. In this work, we develop a comprehensive numerical framework, grounded in Floquet theory, to systematically analyze and mitigate these collisions. Our approach integrates this numerical analysis with newly derived analytical models for both qubit-modulated and coupler-modulated schemes, allowing us to characterize the complete map of parasitic sideband interactions and their distinct error budgets. This analysis forms the basis of a constraint-based optimization methodology designed to identify parameter configurations that satisfy the derived physical constraints, thereby avoiding detrimental parasitic interactions. We illustrate the utility of this framework with applications to analog quantum simulation and gate design. Our work provides a predictive tool for co-engineering device parameters and control protocols, enabling the systematic suppression of crosstalk and paving the way for large-scale, high-performance quantum processors.
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As superconducting quantum processors continue to scale, high-performance quantum control becomes increasingly critical. In densely integrated architectures, unwanted interactions between nearby qubits give rise to crosstalk errors that limit operational performance. In particular, direct exchange-type (XY) interactions are typically minimized by designing large frequency detunings between neighboring qubits at the hardware level. However, frequency crowding in large-scale systems ultimately restricts the achievable frequency separation. While such XY coupling facilitates entangling gate operations, its residual presence poses a key challenge during single-qubit controls. Here, we propose a scalable pulse-level control framework, incorporating frequency modulation (FM) and dynamical decoupling (DD), to suppress XY crosstalk errors. This framework operates independently of coupling strengths, reducing calibration overhead and naturally supporting multi-qubit connectivity. Numerical simulations show orders-of-magnitude reductions in infidelity for both idle and single-qubit gates in a two-qubit system. We further validate scalability in a five-qubit layout, where crosstalk between a central qubit and four neighbors is simultaneously suppressed. Our crosstalk suppression framework provides a practical route toward high-fidelity operation in dense superconducting architectures.
Single-qubit gates on superconducting quantum processors are typically implemented using microwave pulses applied through dedicated control lines. However, these microwave pulses may also drive other qubits due to crosstalk arising from capacitive coupling and wavefunction overlap in systems with closely spaced transition frequencies. Crosstalk and frequency crowding increase errors during simultaneous single-qubit operations relative to isolated gates, thus forming a major bottleneck for scaling superconducting quantum processors. In this work, we combine model-based qubit frequency optimization with pulse shaping to demonstrate crosstalk error mitigation in single-qubit gates on a 49-qubit superconducting quantum processor. We introduce and experimentally verify an analytical model of simultaneous single-qubit gate error caused by microwave crosstalk that depends on a given pulse shape. By employing a model-based optimization strategy of qubit frequencies, we minimize the crosstalk-induced error across the processor and achieve a mean simultaneous single-qubit gate fidelity of 99.96% for a 16-ns gate duration, approaching the mean individual gate fidelity. To further reduce the simultaneous error and required qubit frequency bandwidth on high-crosstalk qubit pairs, we introduce a crosstalk transition suppression (CTS) pulse shaping technique that minimizes the spectral energy around transitions inducing leakage and crosstalk errors. Finally, we combine CTS with model-based frequency optimization across the device and experimentally show a systematic reduction in the required qubit frequency bandwidth for high-fidelity simultaneous gates, supported by simulations of systems with up to 1000 qubits. By alleviating constraints on qubit frequency bandwidth for parallel single-qubit operations, this work represents an important step for scaling towards larger quantum processors.
Maintaining or even improving gate performance with growing numbers of parallel controlled qubits is a vital requirement for fault-tolerant quantum computing.For superconducting quantum processors, though isolated one-or two-qubit gates have been demonstrated with high fidelity, implementing these gates in parallel commonly shows worse performance.Generally, this degradation is attributed to various crosstalks between qubits, such as quantum crosstalk due to residual inter-qubit coupling.An understanding of the exact nature of these crosstalks is critical to figuring out respective mitigation schemes and improved qubit architecture designs with low crosstalk.Here we give a theoretical analysis of quantum crosstalk impact on simultaneous gate operations in a qubit architecture, where fixed-frequency transmon qubits are coupled via a tunable bus, and sub-100-ns controlled-Z (CZ) gates can be realized by applying a baseband flux pulse on the bus.Our analysis shows that for microwave-driven single-qubit gates, the dressing from the qubit-qubit coupling can cause non-negligible cross-driving errors when qubits operate near frequency collision regions.During CZ gate operations, although unwanted nearest-neighbor interactions are nominally turned off, sub-MHz parasitic next-nearest-neighbor interactions involving spectator qubits can still exist, causing considerable leakage or control error when one operates qubit systems around these parasitic resonance points.To ensure high-fidelity simultaneous operations, a request could be raised to figure out a better way to balance the gate error from target qubit systems themselves and the error from nonparticipating spectator qubits.Overall, our analysis suggests that towards useful quantum processors, the qubit architecture should be examined carefully in the context of high-fidelity simultaneous gate operations in a scalable qubit lattice.
Crosstalk between qubits fundamentally limits the scalability of quantum processors, necessitating physics-based models that can handle the complexity of large qubit arrays. Here, we develop a comprehensive theoretical and experimental framework that captures residual interactions between both adjacent and non-adjacent qubits in fixed-frequency transmon lattices. The model integrates the combined effects of exponential localization in banded capacitance matrices, suppression of virtual couplings through detuning products across intermediate modes, and evanescent decay of below-cutoff electromagnetic fields, yielding predictive scaling relations for coupling strength as a function of spatial separation and spectral detuning. Experimental characterization of a 4×44 \times 44×4 superconducting-qubit lattice with inductive shunt pillars reveals exponential spatial decay and frequency-dependent suppression consistent with theoretical predictions, achieving quantitative agreement for all nearest-neighbor couplings across the \qtyrange[range-phrase = --, range-units = single]{4}{6}{\giga\hertz} operating range. Our results show that standard dispersive Hamiltonian approximations systematically overestimate long-range coupling when spatial and spectral dependencies are neglected; these errors propagate into circuit simulation and design strategies. Our framework provides design guidance for crosstalk mitigation in larger-scale quantum processors under realistic fabrication constraints, addressing a bottleneck in scalability.
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.