Superconducting quantum circuits are typically housed in conducting enclosures in order to control their electromagnetic environment. As devices grow in physical size, the electromagnetic modes of the enclosure come down in frequency and can introduce unwanted long-range cross-talk between distant elements of the enclosed circuit. Incorporating arrays of inductive shunts such as through-substrate vias or machined pillars can suppress these effects by raising these mode frequencies. Here, we derive simple, accurate models for the modes of enclosures that incorporate such inductive-shunt arrays. We use these models to predict that cavity-mediated inter-qubit couplings and drive-line cross-talk are exponentially suppressed with distance for arbitrarily large quantum circuits housed in such enclosures, indicating the promise of this approach for quantum computing. We find good agreement with a finite-element simulation of an example device containing more than 400 qubits.Superconducting quantum circuits are typically housed in conducting enclosures in order to control their electromagnetic environment. As devices grow in physical size, the electromagnetic modes of the enclosure come down in frequency and can introduce unwanted long-range cross-talk between distant elements of the enclosed circuit. Incorporating arrays of inductive shunts such as through-substrate vias or machined pillars can suppress these effects by raising these mode frequencies. Here, we derive simple, accurate models for the modes of enclosures that incorporate such inductive-shunt arrays. We use these models to predict that cavity-mediated inter-qubit couplings and drive-line cross-talk are exponentially suppressed with distance for arbitrarily large quantum circuits housed in such enclosures, indicating the promise of this approach for quantum computing. We find good agreement with a finite-element simulation of an example device containing more than 400 qubits.

Sep 4, 20191 citation

Crosstalk Dispersion and Spatial Scaling in Superconducting Qubit Arrays

Mohammed Alghadeer, Simon Pettersson Fors, Shuxiang Cao +5 more

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 $4 \times 4$ 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.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 $4 \times 4$ 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.

quant-pharXiv:2512.18148Physical Review ResearchDec 23, 20250 citations

Extracting Electromagnetic Bare Mode Couplings in Large Superconducting Quantum Processors

Reza Molavi, Ebrahim Forati, Yaxing Zhang +9 more

High-fidelity control of superconducting quantum processors requires accurate characterization of electromagnetic coupling strengths among the device's constituent elements. Accurately extracting these couplings across large-scale architectures, presently featuring hundreds of qubits, poses a challenging multi-scale modeling problem. This requires resolving scales from the nanometer-scale geometry of Josephson junctions and their leads to the centimeter-scale size of the enclosing metallic packages. We present four numerical coupling extraction methods based on the avoided level crossing, the energy participation ratio, the induced electromotive force, and the impedance matrix. These methods are tailored to work with commercially available 3D electromagnetic solvers. We benchmark these techniques on a $10\times10$ array of transmon qubits, extracting their couplings to standing package modes. Our results show that these methods yield consistent coupling strengths with a maximum relative difference of less than 5%.High-fidelity control of superconducting quantum processors requires accurate characterization of electromagnetic coupling strengths among the device's constituent elements. Accurately extracting these couplings across large-scale architectures, presently featuring hundreds of qubits, poses a challenging multi-scale modeling problem. This requires resolving scales from the nanometer-scale geometry of Josephson junctions and their leads to the centimeter-scale size of the enclosing metallic packages. We present four numerical coupling extraction methods based on the avoided level crossing, the energy participation ratio, the induced electromotive force, and the impedance matrix. These methods are tailored to work with commercially available 3D electromagnetic solvers. We benchmark these techniques on a $10\times10$ array of transmon qubits, extracting their couplings to standing package modes. Our results show that these methods yield consistent coupling strengths with a maximum relative difference of less than 5%.

quant-pharXiv:2609.22442Sep 22, 20260 citations

S-Parameter-Based Simulation Technique and Crosstalk Suppression for Large-Scale Superconducting Quantum-Computing Chip Design

Shoichi Shiba, Shuhei Tamate, Peter Spring +5 more

The increasing size of superconducting quantumcomputer chips requires a shift in evaluation methods for chip design. Three-dimensional (3D) electromagnetic (EM) simulations become computationally intractable as model size increases owing to the exponential growth in computation time. To address this challenge, we develop a technique that analyzes the circuit parameters of large-scale superconducting qubit chips by combining S-parameters simulated in smaller-scale 3D EM models. Herein, we design a four-qubit unit cell for large-scale qubit devices and evaluate both residual qubit-qubit coupling and control-line-to-qubit crosstalk for distant qubit pairs. In addition, we propose guard structures around qubits to mitigate nearestneighbor crosstalk. Although previous methods are limited to chips with at most ten qubits, our approach enables the analysis of systems with over a hundred qubits.The increasing size of superconducting quantumcomputer chips requires a shift in evaluation methods for chip design. Three-dimensional (3D) electromagnetic (EM) simulations become computationally intractable as model size increases owing to the exponential growth in computation time. To address this challenge, we develop a technique that analyzes the circuit parameters of large-scale superconducting qubit chips by combining S-parameters simulated in smaller-scale 3D EM models. Herein, we design a four-qubit unit cell for large-scale qubit devices and evaluate both residual qubit-qubit coupling and control-line-to-qubit crosstalk for distant qubit pairs. In addition, we propose guard structures around qubits to mitigate nearestneighbor crosstalk. Although previous methods are limited to chips with at most ten qubits, our approach enables the analysis of systems with over a hundred qubits.

IEEE MTT-S International Microwave Symposium digestJun 15, 20250 citations

Developing a tileable superconducting circuit for quantum computation

Peter Spring

Superconducting circuits have been demonstrated at the ~50 qubit scale, with gate fidelities approaching the thresholds required for error correction using surface codes. It is generally considered that maintaining and improving this performance while scaling to >100 qubits will require 3D integration of control wiring, and techniques to prevent or mitigate the effects of unwanted electromagnetic modes which emerge in the circuit environment at larger scales. At the present time, no single design has emerged as the clear scaling "winner'', and many different modalities are being explored. In this thesis, we describe one potential scaling architecture for superconducting circuits, which is based on a unit cell containing a set of controllable, measurable qubits. In analogy to the unit cell of a crystal, this unit cell can be tiled, in this case to form 2D arrays of individually controllable and measurable qubits. This is enabled by three key technologies: 3D integrated off-chip control wiring, reverse-side readout resonators, and inductive shunting of the device enclosure with micromachined pillars. To validate this approach, we design and build a demonstration device featuring four transmon qubits and containing within it a single unit cell of the architecture. The device construction involves the fabrication of reverse-side circuits and the use of novel CNC drilling of the circuit substrate. We measure coherence times and single-qubit gate fidelities comparable with the state-of-the-art for transmon qubits (avg. T1 = 149 µs, avg. echoed pure dephasing T2 = 189 µs, avg. F > 99.98%), establishing that the design is compatible with high coherence. An important feature of the design is that the infinite construct formed by tiling the plane with the unit cell possesses a cutoff frequency, below which the circuit environment cannot sustain any electromagnetic modes. We develop models to predict this cutoff frequency, and predict that environment mediated crosstalk between qubits inside this structure decays exponentially with spatial separation. This crosstalk can be viewed as being mediated by evanescent waveguide modes, or by bound states formed by the interaction of qubits with the environmental modes around the cutoff. Both models provide quantitative predictions for the rate of crosstalk decay, which are shown to be in good agreement. We propose this architecture as a promising candidate for building 2D arrays of hundreds or thousands of nearest neighbour coupled superconducting qubits, which could provide a testbed of quantum error correction schemes such as the surface code.Superconducting circuits have been demonstrated at the ~50 qubit scale, with gate fidelities approaching the thresholds required for error correction using surface codes. It is generally considered that maintaining and improving this performance while scaling to >100 qubits will require 3D integration of control wiring, and techniques to prevent or mitigate the effects of unwanted electromagnetic modes which emerge in the circuit environment at larger scales. At the present time, no single design has emerged as the clear scaling "winner'', and many different modalities are being explored. In this thesis, we describe one potential scaling architecture for superconducting circuits, which is based on a unit cell containing a set of controllable, measurable qubits. In analogy to the unit cell of a crystal, this unit cell can be tiled, in this case to form 2D arrays of individually controllable and measurable qubits. This is enabled by three key technologies: 3D integrated off-chip control wiring, reverse-side readout resonators, and inductive shunting of the device enclosure with micromachined pillars. To validate this approach, we design and build a demonstration device featuring four transmon qubits and containing within it a single unit cell of the architecture. The device construction involves the fabrication of reverse-side circuits and the use of novel CNC drilling of the circuit substrate. We measure coherence times and single-qubit gate fidelities comparable with the state-of-the-art for transmon qubits (avg. T1 = 149 µs, avg. echoed pure dephasing T2 = 189 µs, avg. F > 99.98%), establishing that the design is compatible with high coherence. An important feature of the design is that the infinite construct formed by tiling the plane with the unit cell possesses a cutoff frequency, below which the circuit environment cannot sustain any electromagnetic modes. We develop models to predict this cutoff frequency, and predict that environment mediated crosstalk between qubits inside this structure decays exponentially with spatial separation. This crosstalk can be viewed as being mediated by evanescent waveguide modes, or by bound states formed by the interaction of qubits with the environmental modes around the cutoff. Both models provide quantitative predictions for the rate of crosstalk decay, which are shown to be in good agreement. We propose this architecture as a promising candidate for building 2D arrays of hundreds or thousands of nearest neighbour coupled superconducting qubits, which could provide a testbed of quantum error correction schemes such as the surface code.

Jan 1, 20210 citations

Simple, accurate lumped-element models of distributed resonators for superconducting quantum circuits

Elizabeth H. Kunz, Eli M. Levenson-Falk

Superconducting quantum circuit design is reliant on accurately mapping design parameters to a quantum Hamiltonian. Designers typically rely on computationally intensive finite-element electromagnetic simulations. However, effective circuit-level models can in principle capture much of the relevant physics for these systems, reducing the need for finite-element simulations. A barrier to implementing these simpler models has been the prevalence of distributed elements such as coplanar waveguides resonators in device designs. Techniques for modeling these distributed elements have been developed, but may be difficult to scale, reduce intuition, and give inaccurate results under strong coupling. In this work we describe a simple effective circuit-level model that faithfully reproduces the scattering parameters, and subsequently can predict certain Hamiltonian parameters, for a coupled, distributed element within a broader two-port network even up to strong coupling. Our approach does not explicitly require an electromagnetic simulation. Our model, along with other common lumped models used in black box quantization, is publicly available to researchers via an open-source code package, $\texttt{simpleLOMs}$ .Superconducting quantum circuit design is reliant on accurately mapping design parameters to a quantum Hamiltonian. Designers typically rely on computationally intensive finite-element electromagnetic simulations. However, effective circuit-level models can in principle capture much of the relevant physics for these systems, reducing the need for finite-element simulations. A barrier to implementing these simpler models has been the prevalence of distributed elements such as coplanar waveguides resonators in device designs. Techniques for modeling these distributed elements have been developed, but may be difficult to scale, reduce intuition, and give inaccurate results under strong coupling. In this work we describe a simple effective circuit-level model that faithfully reproduces the scattering parameters, and subsequently can predict certain Hamiltonian parameters, for a coupled, distributed element within a broader two-port network even up to strong coupling. Our approach does not explicitly require an electromagnetic simulation. Our model, along with other common lumped models used in black box quantization, is publicly available to researchers via an open-source code package, $\texttt{simpleLOMs}$.

quant-pharXiv:2607.19543Jul 23, 20260 citations

4 \times 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.

10\times10

array of transmon qubits, extracting their couplings to standing package modes. Our results show that these methods yield consistent coupling strengths with a maximum relative difference of less than 5%.

\texttt{simpleLOMs}